explain experimental study of photoelectric effect

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Experimental physics i & ii "junior lab", photoelectric effect, description.

Photoelectric effect experiment equipment. (Image courtesy of MIT Junior Lab staff.)

The maximum kinetic energy of electrons ejected from a metal surface by monochromatic light is measured for several wavelengths. The value of Planck’s constant, h, is derived by an analysis of the data in the light of Einstein theory of the photoelectric effect.

Photoelectric Effect Lab Guide (PDF)

Planck, Max. Nobel Prize Lecture, “ The Genesis and Present State of Development of the Quantum Theory .” (1918).

Einstein, Albert. Nobel Prize Lecture, “ Fundamental Ideas and Problems of the Theory of Relativity .” (1921).

Millikan, R.A. “ A Direct Photoelectric Determination of Planck’s ‘h’ .”  Phys. Rev ., 7, 355 (1916).

Hughes, Arthur L., and Lee A. Du Bridge. Photoelectric Phenomena . Boston, MA: McGraw-Hill, (1932).

Discusses phenomena such as the velocity distribution of the electrons, effects of polarization and angle of incidence of the light, influence of the surface temperature, photoelectric behavior of thin films and composite materials, etc.

Harnwell, G. P., and Livingood, J. J. “Thermionic and Photoelectric Effects.” In Experimental Atomic Physics . Boston, MA: McGraw-Hill, 1933, pp. 214-223. ISBN: 9780070266605.

Melissinos, Adrian C. “Photoelectric Effect.” In Experiments in Modern Physics . New York, NY: Academic Press, (1968).

Selected Resources

Baumeister, P. and G. Pincus. “Optical Interference Coatings.”  Scientific American 223, 58-75 (December 1970).

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Photons and Matter Waves

Photoelectric Effect

Samuel J. Ling; Jeff Sanny; and William Moebs

Learning Objectives

By the end of this section you will be able to:

• Describe physical characteristics of the photoelectric effect
• Explain why the photoelectric effect cannot be explained by classical physics
• Describe how Einstein’s idea of a particle of radiation explains the photoelectric effect

When a metal surface is exposed to a monochromatic electromagnetic wave of sufficiently short wavelength (or equivalently, above a threshold frequency), the incident radiation is absorbed and the exposed surface emits electrons. This phenomenon is known as the photoelectric effect . Electrons that are emitted in this process are called photoelectrons .

The experimental setup to study the photoelectric effect is shown schematically in (Figure) . The target material serves as the anode, which becomes the emitter of photoelectrons when it is illuminated by monochromatic radiation. We call this electrode the photoelectrode . Photoelectrons are collected at the cathode, which is kept at a lower potential with respect to the anode. The potential difference between the electrodes can be increased or decreased, or its polarity can be reversed. The electrodes are enclosed in an evacuated glass tube so that photoelectrons do not lose their kinetic energy on collisions with air molecules in the space between electrodes.

When the target material is not exposed to radiation, no current is registered in this circuit because the circuit is broken (note, there is a gap between the electrodes). But when the target material is connected to the negative terminal of a battery and exposed to radiation, a current is registered in this circuit; this current is called the photocurrent . Suppose that we now reverse the potential difference between the electrodes so that the target material now connects with the positive terminal of a battery, and then we slowly increase the voltage. The photocurrent gradually dies out and eventually stops flowing completely at some value of this reversed voltage. The potential difference at which the photocurrent stops flowing is called the stopping potential .

Characteristics of the Photoelectric Effect

The photoelectric effect has three important characteristics that cannot be explained by classical physics: (1) the absence of a lag time, (2) the independence of the kinetic energy of photoelectrons on the intensity of incident radiation, and (3) the presence of a cut-off frequency. Let’s examine each of these characteristics.

The absence of lag time

When radiation strikes the target material in the electrode, electrons are emitted almost instantaneously, even at very low intensities of incident radiation. This absence of lag time contradicts our understanding based on classical physics. Classical physics predicts that for low-energy radiation, it would take significant time before irradiated electrons could gain sufficient energy to leave the electrode surface; however, such an energy buildup is not observed.

The intensity of incident radiation and the kinetic energy of photoelectrons

Typical experimental curves are shown in (Figure) , in which the photocurrent is plotted versus the applied potential difference between the electrodes. For the positive potential difference, the current steadily grows until it reaches a plateau. Furthering the potential increase beyond this point does not increase the photocurrent at all. A higher intensity of radiation produces a higher value of photocurrent. For the negative potential difference, as the absolute value of the potential difference increases, the value of the photocurrent decreases and becomes zero at the stopping potential. For any intensity of incident radiation, whether the intensity is high or low, the value of the stopping potential always stays at one value.

At this point we can see where the classical theory is at odds with the experimental results. In classical theory, the photoelectron absorbs electromagnetic energy in a continuous way; this means that when the incident radiation has a high intensity, the kinetic energy in (Figure) is expected to be high. Similarly, when the radiation has a low intensity, the kinetic energy is expected to be low. But the experiment shows that the maximum kinetic energy of photoelectrons is independent of the light intensity.

The presence of a cut-off frequency

For any metal surface, there is a minimum frequency of incident radiation below which photocurrent does not occur. The value of this cut-off frequency for the photoelectric effect is a physical property of the metal: Different materials have different values of cut-off frequency. Experimental data show a typical linear trend (see (Figure) ). The kinetic energy of photoelectrons at the surface grows linearly with the increasing frequency of incident radiation. Measurements for all metal surfaces give linear plots with one slope. None of these observed phenomena is in accord with the classical understanding of nature. According to the classical description, the kinetic energy of photoelectrons should not depend on the frequency of incident radiation at all, and there should be no cut-off frequency. Instead, in the classical picture, electrons receive energy from the incident electromagnetic wave in a continuous way, and the amount of energy they receive depends only on the intensity of the incident light and nothing else. So in the classical understanding, as long as the light is shining, the photoelectric effect is expected to continue.

The Work Function

The photoelectric effect was explained in 1905 by A. Einstein . Einstein reasoned that if Planck’s hypothesis about energy quanta was correct for describing the energy exchange between electromagnetic radiation and cavity walls, it should also work to describe energy absorption from electromagnetic radiation by the surface of a photoelectrode. He postulated that an electromagnetic wave carries its energy in discrete packets. Einstein’s postulate goes beyond Planck’s hypothesis because it states that the light itself consists of energy quanta. In other words, it states that electromagnetic waves are quantized.

This equation has a simple mathematical form but its physics is profound. We can now elaborate on the physical meaning behind (Figure) .

In Einstein’s interpretation, interactions take place between individual electrons and individual photons. The absence of a lag time means that these one-on-one interactions occur instantaneously. This interaction time cannot be increased by lowering the light intensity. The light intensity corresponds to the number of photons arriving at the metal surface per unit time. Even at very low light intensities, the photoelectric effect still occurs because the interaction is between one electron and one photon. As long as there is at least one photon with enough energy to transfer it to a bound electron, a photoelectron will appear on the surface of the photoelectrode.

Photoelectric Effect for Silver Radiation with wavelength 300 nm is incident on a silver surface. Will photoelectrons be observed?

Solution The threshold wavelength for observing the photoelectric effect in silver is

The incident radiation has wavelength 300 nm, which is longer than the cut-off wavelength; therefore, photoelectrons are not observed.

Significance If the photoelectrode were made of sodium instead of silver, the cut-off wavelength would be 504 nm and photoelectrons would be observed.

Einstein’s model also gives a straightforward explanation for the photocurrent values shown in (Figure) . For example, doubling the intensity of radiation translates to doubling the number of photons that strike the surface per unit time. The larger the number of photons, the larger is the number of photoelectrons, which leads to a larger photocurrent in the circuit. This is how radiation intensity affects the photocurrent. The photocurrent must reach a plateau at some value of potential difference because, in unit time, the number of photoelectrons is equal to the number of incident photons and the number of incident photons does not depend on the applied potential difference at all, but only on the intensity of incident radiation. The stopping potential does not change with the radiation intensity because the kinetic energy of photoelectrons (see (Figure) ) does not depend on the radiation intensity.

Work Function and Cut-Off Frequency When a 180-nm light is used in an experiment with an unknown metal, the measured photocurrent drops to zero at potential – 0.80 V. Determine the work function of the metal and its cut-off frequency for the photoelectric effect.

Solution We use (Figure) to find the kinetic energy of the photoelectrons:

Finally, we use (Figure) to find the cut-off frequency:

The Photon Energy and Kinetic Energy of Photoelectrons A 430-nm violet light is incident on a calcium photoelectrode with a work function of 2.71 eV.

Find the energy of the incident photons and the maximum kinetic energy of ejected electrons.

Significance In this experimental setup, photoelectrons stop flowing at the stopping potential of 0.17 V.

Check Your Understanding A yellow 589-nm light is incident on a surface whose work function is 1.20 eV. What is the stopping potential? What is the cut-off wavelength?

• The photoelectric effect occurs when photoelectrons are ejected from a metal surface in response to monochromatic radiation incident on the surface. It has three characteristics: (1) it is instantaneous, (2) it occurs only when the radiation is above a cut-off frequency, and (3) kinetic energies of photoelectrons at the surface do not depend of the intensity of radiation. The photoelectric effect cannot be explained by classical theory.
• We can explain the photoelectric effect by assuming that radiation consists of photons (particles of light). Each photon carries a quantum of energy. The energy of a photon depends only on its frequency, which is the frequency of the radiation. At the surface, the entire energy of a photon is transferred to one photoelectron.
• The maximum kinetic energy of a photoelectron at the metal surface is the difference between the energy of the incident photon and the work function of the metal. The work function is the binding energy of electrons to the metal surface. Each metal has its own characteristic work function.

Conceptual Questions

For the same monochromatic light source, would the photoelectric effect occur for all metals?

In the interpretation of the photoelectric effect, how is it known that an electron does not absorb more than one photon?

Explain how you can determine the work function from a plot of the stopping potential versus the frequency of the incident radiation in a photoelectric effect experiment. Can you determine the value of Planck’s constant from this plot?

from the slope

Suppose that in the photoelectric-effect experiment we make a plot of the detected current versus the applied potential difference. What information do we obtain from such a plot? Can we determine from it the value of Planck’s constant? Can we determine the work function of the metal?

Speculate how increasing the temperature of a photoelectrode affects the outcomes of the photoelectric effect experiment.

Answers may vary

Which aspects of the photoelectric effect cannot be explained by classical physics?

Is the photoelectric effect a consequence of the wave character of radiation or is it a consequence of the particle character of radiation? Explain briefly.

the particle character

The metals sodium, iron, and molybdenum have work functions 2.5 eV, 3.9 eV, and 4.2 eV, respectively. Which of these metals will emit photoelectrons when illuminated with 400 nm light?

A photon has energy 20 keV. What are its frequency and wavelength?

The wavelengths of visible light range from approximately 400 to 750 nm. What is the corresponding range of photon energies for visible light?

What is the longest wavelength of radiation that can eject a photoelectron from silver? Is it in the visible range?

What is the longest wavelength of radiation that can eject a photoelectron from potassium, given the work function of potassium 2.24 eV? Is it in the visible range?

Estimate the binding energy of electrons in magnesium, given that the wavelength of 337 nm is the longest wavelength that a photon may have to eject a photoelectron from magnesium photoelectrode.

The work function for potassium is 2.26 eV. What is the cutoff frequency when this metal is used as photoelectrode? What is the stopping potential when for the emitted electrons when this photoelectrode is exposed to radiation of frequency 1200 THz?

Estimate the work function of aluminum, given that the wavelength of 304 nm is the longest wavelength that a photon may have to eject a photoelectron from aluminum photoelectrode.

What is the maximum kinetic energy of photoelectrons ejected from sodium by the incident radiation of wavelength 450 nm?

A 120-nm UV radiation illuminates a gold-plated electrode. What is the maximum kinetic energy of the ejected photoelectrons?

A 400-nm violet light ejects photoelectrons with a maximum kinetic energy of 0.860 eV from sodium photoelectrode. What is the work function of sodium?

A 600-nm light falls on a photoelectric surface and electrons with the maximum kinetic energy of 0.17 eV are emitted. Determine (a) the work function and (b) the cutoff frequency of the surface. (c) What is the stopping potential when the surface is illuminated with light of wavelength 400 nm?

a. 1.89 eV; b. 459 THz; c. 1.21 V

The cutoff wavelength for the emission of photoelectrons from a particular surface is 500 nm. Find the maximum kinetic energy of the ejected photoelectrons when the surface is illuminated with light of wavelength 600 nm.

Find the wavelength of radiation that can eject 2.00-eV electrons from calcium electrode. The work function for calcium is 2.71 eV. In what range is this radiation?

Find the wavelength of radiation that can eject 0.10-eV electrons from potassium electrode. The work function for potassium is 2.24 eV. In what range is this radiation?

Find the maximum velocity of photoelectrons ejected by an 80-nm radiation, if the work function of photoelectrode is 4.73 eV.

Photoelectric Effect Copyright © by Samuel J. Ling; Jeff Sanny; and William Moebs is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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• Table Of Contents

photoelectric effect , phenomenon in which electrically charged particles are released from or within a material when it absorbs electromagnetic radiation . The effect is often defined as the ejection of electrons from a metal plate when light falls on it. In a broader definition, the radiant energy may be infrared , visible, or ultraviolet light, X-rays , or gamma rays ; the material may be a solid, liquid, or gas; and the released particles may be ions (electrically charged atoms or molecules) as well as electrons. The phenomenon was fundamentally significant in the development of modern physics because of the puzzling questions it raised about the nature of light—particle versus wavelike behaviour—that were finally resolved by Albert Einstein in 1905. The effect remains important for research in areas from materials science to astrophysics , as well as forming the basis for a variety of useful devices.

The photoelectric effect was discovered in 1887 by the German physicist Heinrich Rudolf Hertz . In connection with work on radio waves, Hertz observed that, when ultraviolet light shines on two metal electrodes with a voltage applied across them, the light changes the voltage at which sparking takes place. This relation between light and electricity (hence photoelectric ) was clarified in 1902 by another German physicist, Philipp Lenard . He demonstrated that electrically charged particles are liberated from a metal surface when it is illuminated and that these particles are identical to electrons, which had been discovered by the British physicist Joseph John Thomson in 1897.

Further research showed that the photoelectric effect represents an interaction between light and matter that cannot be explained by classical physics, which describes light as an electromagnetic wave. One inexplicable observation was that the maximum kinetic energy of the released electrons did not vary with the intensity of the light, as expected according to the wave theory, but was proportional instead to the frequency of the light. What the light intensity did determine was the number of electrons released from the metal (measured as an electric current ). Another puzzling observation was that there was virtually no time lag between the arrival of radiation and the emission of electrons.

Consideration of these unexpected behaviours led Albert Einstein to formulate in 1905 a new corpuscular theory of light in which each particle of light, or photon , contains a fixed amount of energy, or quantum , that depends on the light’s frequency. In particular, a photon carries an energy E equal to h f , where f is the frequency of the light and h is the universal constant that the German physicist Max Planck derived in 1900 to explain the wavelength distribution of blackbody radiation—that is, the electromagnetic radiation emitted from a hot body. The relationship may also be written in the equivalent form E = h c /λ, where c is the speed of light and λ is its wavelength, showing that the energy of a photon is inversely proportional to its wavelength.

Einstein assumed that a photon would penetrate the material and transfer its energy to an electron . As the electron moved through the metal at high speed and finally emerged from the material, its kinetic energy would diminish by an amount ϕ called the work function (similar to the electronic work function ), which represents the energy required for the electron to escape the metal. By conservation of energy , this reasoning led Einstein to the photoelectric equation E k = h f − ϕ, where E k is the maximum kinetic energy of the ejected electron.

Although Einstein’s model described the emission of electrons from an illuminated plate, his photon hypothesis was sufficiently radical that it was not universally accepted until it received further experimental verification. Further corroboration occurred in 1916 when extremely accurate measurements by the American physicist Robert Millikan verified Einstein’s equation and showed with high precision that the value of Einstein’s constant h was the same as Planck’s constant . Einstein was finally awarded the Nobel Prize for Physics in 1921 for explaining the photoelectric effect.

In 1922 the American physicist Arthur Compton measured the change in wavelength of X-rays after they interacted with free electrons, and he showed that the change could be calculated by treating X-rays as made of photons. Compton received the 1927 Nobel Prize for Physics for this work. In 1931 the British mathematician Ralph Howard Fowler extended the understanding of photoelectric emission by establishing the relationship between photoelectric current and temperature in metals. Further efforts showed that electromagnetic radiation could also emit electrons in insulators , which do not conduct electricity, and in semiconductors , a variety of insulators that conduct electricity only under certain circumstances.

According to quantum mechanics , electrons bound to atoms occur in specific electronic configurations . The highest energy configuration (or energy band) that is normally occupied by electrons for a given material is known as the valence band , and the degree to which it is filled largely determines the material’s electrical conductivity. In a typical conductor (metal), the valence band is about half filled with electrons, which readily move from atom to atom, carrying a current. In a good insulator , such as glass or rubber, the valence band is filled, and these valence electrons have very little mobility . Like insulators, semiconductors generally have their valence bands filled, but, unlike insulators, very little energy is required to excite an electron from the valence band to the next allowed energy band—known as the conduction band , because any electron excited to this higher energy level is relatively free. For example, the “bandgap” for silicon is 1.12 eV ( electron volts ), and that of gallium arsenide is 1.42 eV. This is in the range of energy carried by photons of infrared and visible light, which can therefore raise electrons in semiconductors to the conduction band. (For comparison, an ordinary flashlight battery imparts 1.5 eV to each electron that passes through it. Much more energetic radiation is required to overcome the bandgap in insulators.) Depending on how the semiconducting material is configured, this radiation may enhance its electrical conductivity by adding to an electric current already induced by an applied voltage ( see photoconductivity ), or it may generate a voltage independently of any external voltage sources ( see photovoltaic effect ).

Photoconductivity arises from the electrons freed by the light and from a flow of positive charge as well. Electrons raised to the conduction band correspond to missing negative charges in the valence band, called “holes.” Both electrons and holes increase current flow when the semiconductor is illuminated.

In the photovoltaic effect , a voltage is generated when the electrons freed by the incident light are separated from the holes that are generated, producing a difference in electrical potential. This is typically done by using a p - n junction rather than a pure semiconductor. A p - n junction occurs at the juncture between p -type (positive) and n -type (negative) semiconductors. These opposite regions are created by the addition of different impurities to produce excess electrons ( n -type) or excess holes ( p -type). Illumination frees electrons and holes on opposite sides of the junction to produce a voltage across the junction that can propel current, thereby converting light into electrical power .

Other photoelectric effects are caused by radiation at higher frequencies, such as X-rays and gamma rays . These higher-energy photons can even release electrons near the atomic nucleus, where they are tightly bound. When such an inner electron is ejected, a higher-energy outer electron quickly drops down to fill the vacancy. The excess energy results in the emission of one or more additional electrons from the atom, which is called the Auger effect .

Also seen at high photon energies is the Compton effect , which arises when an X-ray or gamma-ray photon collides with an electron. The effect can be analyzed by the same principles that govern the collision between any two bodies, including conservation of momentum . The photon loses energy to the electron, a decrease that corresponds to an increased photon wavelength according to Einstein’s relation E = h c /λ. When the collision is such that the electron and the photon part at right angles to each other, the photon’s wavelength increases by a characteristic amount called the Compton wavelength, 2.43 × 10 −12 metre.

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Table of contents.

• Experiment 1 - Magnetic Fields of Coils and Faraday's Law
• Experiment 2 - Microwave Optics
• Experiment 3 - Geometrical Optics
• Experiment 4 - Physical Optics
• Experiment 5 - Fluids and Thermodynamics

Experiment 6 - The Photoelectric Effect

• Experiment 7 - Radioactivity
• Photodiode with amplifier
• Batteries to operate amplifier and provide reverse voltage
• Digital voltmeter to read reverse voltage
• Source of monochromatic light beams to irradiate photocathode
• Neutral filter to vary light intensity

INTRODUCTION

The energy quantization of electromagnetic radiation in general, and of light in particular, is expressed in the famous relation

\begin{eqnarray} E &=& hf, \label{eqn_1} \end{eqnarray}

where \(E\) is the energy of the radiation, \(f\) is its frequency, and \(h\) is Planck's constant (6.63×10 -34 Js). The notion of light quantization was first introduced by Planck. Its validity is based on solid experimental evidence, most notably the photoelectric effect . The basic physical process underlying this effect is the emission of electrons in metals exposed to light. There are four aspects of photoelectron emission which conflict with the classical view that the instantaneous intensity of electromagnetic radiation is given by the Poynting vector \(\textbf{S}\):

\begin{eqnarray} \textbf{S} &=& (\textbf{E}\times\textbf{B})/\mu_0, \label{eqn_2} \end{eqnarray}

with \(\textbf{E}\) and \(\textbf{B}\) the electric and magnetic fields of the radiation, respectively, and μ 0 (4π×10 -7 Tm/A) the permeability of free space. Specifically:

No photoelectrons are emitted from the metal when the incident light is below a minimum frequency, regardless of its intensity. (The value of the minimum frequency is unique to each metal.)

Photoelectrons are emitted from the metal when the incident light is above a threshold frequency. The kinetic energy of the emitted photoelectrons increases with the frequency of the light.

The number of emitted photoelectrons increases with the intensity of the incident light. However, the kinetic energy of these electrons is independent of the light intensity.

Photoemission is effectively instantaneous.

Consider the conduction electrons in a metal to be bound in a well-defined potential. The energy required to release an electron is called the work function \(W_0\) of the metal. In the classical model, a photoelectron could be released if the incident light had sufficient intensity. However, Eq. \eqref{eqn_1} requires that the light exceed a threshold frequency \(f_{\textrm{t}}\) for an electron to be emitted. If \(f > f_{\textrm{t}}\), then a single light quantum (called a photon ) of energy \(E = hf\) is sufficient to liberate an electron, and any residual energy carried by the photon is converted into the kinetic energy of the electron. Thus, from energy conservation, \(E = W_0 + K\), or

\begin{eqnarray} K &=& (1/2)mv^2 = E - W_0 = hf - W_0. \label{eqn_3} \end{eqnarray}

When the incident light intensity is increased, more photons are available for the release of electrons, and the magnitude of the photoelectric current increases. From Eq. \eqref{eqn_3}, we see that the kinetic energy of the electrons is independent of the light intensity and depends only on the frequency.

The photoelectric current in a typical setup is extremely small, and making a precise measurement is difficult. Normally the electrons will reach the anode of the photodiode, and their number can be measured from the (minute) anode current. However, we can apply a reverse voltage to the anode; this reverse voltage repels the electrons and prevents them from reaching the anode. The minimum required voltage is called the stopping potential \(V_{\textrm{s}}\), and the “stopping energy” of each electron is therefore \(eV_{\textrm{s}}\). Thus,

\begin{eqnarray} eV_{\textrm{s}} &=& hf - W_0, \label{eqn_4} \end{eqnarray}

\begin{eqnarray} V_{\textrm{s}} &=& (h/e)f - W_0/e. \label{eqn_5} \end{eqnarray}

Eq. \eqref{eqn_5} shows a linear relationship between the stopping potential \(V_{\textrm{s}}\) and the light frequency \(f\), with slope \(h/e\) and vertical intercept \(-W_0/e\). If the value of the electron charge \(e\) is known, then this equation provides a good method for determining Planck's constant \(h\). In this experiment, we will measure the stopping potential with modern electronics.

THE PHOTODIODE AND ITS READOUT

The central element of the apparatus is the photodiode tube. The diode has a window which allows light to enter, and the cathode is a clean metal surface. To prevent the collision of electrons with air molecules, the diode tube is evacuated.

The photodiode and its associated electronics have a small “capacitance” and develop a voltage as they become charged by the emitted electrons. When the voltage across this “capacitor” reaches the stopping potential of the cathode, the voltage difference between the cathode and anode (which is equal to the stopping potential) stabilizes.

To measure the stopping potential, we use a very sensitive amplifier which has an input impedance larger than 10 13 ohms. The amplifier enables us to investigate the minuscule number of photoelectrons that are produced.

It would take considerable time to discharge the anode at the completion of a measurement by the usual high-leakage resistance of the circuit components, as the input impedance of the amplifier is very high. To speed up this process, a shorting switch is provided; it is labeled “Push to Zero”. The amplifier output will not stay at 0 volts very long after the switch is released. However, the anode output does stabilize once the photoelectrons charge it up.

There are two 9-volt batteries already installed in the photodiode housing. To check the batteries, you can use a voltmeter to measure the voltage between the output ground terminal and each battery test terminal. The battery test points are located on the side panel. You should replace the batteries if the voltage is less than 6 volts.

THE MONOCHROMATIC LIGHT BEAMS

This experiment requires the use of several different monochromatic light beams, which can be obtained from the spectral lines that make up the radiation produced by excited mercury atoms. The light is formed by an electrical discharge in a thin glass tube containing mercury vapor, and harmful ultraviolet components are filtered out by the glass envelope. Mercury light has five narrow spectral lines in the visible region — yellow, green, blue, violet, and ultraviolet — which can be separated spatially by the process of diffraction. For this purpose, we use a high-quality diffraction grating with 6000 lines per centimeter. The desired wavelength is selected with the aid of a collimator, while the intensity can be varied with a set of neutral density filters. A color filter at the entrance of the photodiode is used to minimize room light.

The equipment consists of a mercury vapor light housed in a sturdy metal box, which also holds the transformer for the high voltage. The transformer is fed by a 115-volt power source from an ordinary wall outlet. In order to prevent the possibility of getting an electric shock from the high voltage, do not remove the cover from the unit when it is plugged in.

To facilitate mounting of the filters, the light box is equipped with rails on the front panel. The optical components include a fixed slit (called a light aperture) which is mounted over the output hole in the front cover of the light box. A lens focuses the aperture on the photodiode window. The diffraction grating is mounted on the same frame that holds the lens, which simplifies the setup somewhat. A “blazed” grating, which has a preferred orientation for maximal light transmission and is not fully symmetric, is used. Turn the grating around to verify that you have the optimal orientation.

The variable transmission filter consists of computer-generated patterns of dots and lines that vary the intensity of the incident light. The relative transmission percentages are 100%, 80%, 60%, 40%, and 20%.

INITIAL SETUP

Your apparatus should be set up approximately like the figure above. Turn on the mercury lamp using the switch on the back of the light box. Swing the \(h/e\) apparatus box around on its arm, and you should see at various positions, yellow green, and several blue spectral lines on its front reflective mask. Notice that on one side of the imaginary “front-on” perpendicular line from the mercury lamp, the spectral lines are brighter than the similar lines from the other side. This is because the grating is “blazed”. In you experiments, use the first order spectrum on the side with the brighter lines.

Your apparatus should already be approximately aligned from previous experiments, but make the following alignment checks. Ask you TA for assistance if necessary.

Check the alignment of the mercury source and the aperture by looking at the light shining on the back of the grating. If necessary, adjust the back plate of the light-aperture assembly by loosening the two retaining screws and moving the plate to the left or right until the light shines directly on the center of the grating.

With the bright colored lines on the front reflective mask, adjust the lens/grating assembly on the mercury lamp light box until the lines are focused as sharply as possible.

Roll the round light shield (between the white screen and the photodiode housing) out of the way to view the photodiode window inside the housing. The phototube has a small square window for light to enter. When a spectral line is centered on the front mask, it should also be centered on this window. If not, rotate the housing until the image of the aperture is centered on the window, and fasten the housing. Return the round shield back into position to block stray light.

Connect the digital voltmeter (DVM) to the “Output” terminals of the photodiode. Select the 2 V or 20 V range on the meter.

Press the “Push to Zero” button on the side panel of the photodiode housing to short out any accumulated charge on the electronics. Note that the output will shift in the absence of light on the photodiode.

Record the photodiode output voltage on the DVM. This voltage is a direct measure of the stopping potential.

Use the green and yellow filters for the green and yellow mercury light. These filters block higher frequencies and eliminate ambient room light. In higher diffraction orders, they also block the ultraviolet light that falls on top of the yellow and green lines.

PROCEDURE PART 1: DEPENDENCE OF THE STOPPING POTENTIAL ON THE INTENSITY OF LIGHT

Adjust the angle of the photodiode-housing assembly so that the green line falls on the window of the photodiode.

Install the green filter and the round light shield.

Install the variable transmission filter on the collimator over the green filter such that the light passes through the section marked 100%. Record the photodiode output voltage reading on the DVM. Also determine the approximate recharge time after the discharge button has been pressed and released.

Repeat steps 1 – 3 for the other four transmission percentages, as well as for the ultraviolet light in second order.

Plot a graph of the stopping potential as a function of intensity.

PROCEDURE PART 2: DEPENDENCE OF THE STOPPING POTENTIAL ON THE FREQUENCY OF LIGHT

You can see five colors in the mercury light spectrum. The diffraction grating has two usable orders for deflection on one side of the center.

Adjust the photodiode-housing assembly so that only one color from the first-order diffraction pattern on one side of the center falls on the collimator.

For each color in the first order, record the photodiode output voltage reading on the DVM.

For each color in the second order, record the photodiode output voltage reading on the DVM.

Plot a graph of the stopping potential as a function of frequency, and determine the slope and the \(y\)-intercept of the graph. From this data, calculate \(W_0\) and \(h\). Compare this value of \(h\) with that provided in the “Introduction” section of this experiment.

Procedure Part 1:

Photodiode output voltage reading for 100% transmission =                                              

Approximate recharge time for 100% transmission =                                              

Photodiode output voltage reading for 80% transmission =                                              

Approximate recharge time for 80% transmission =                                              

Photodiode output voltage reading for 60% transmission =                                              

Approximate recharge time for 60% transmission =                                              

Photodiode output voltage reading for 40% transmission =                                              

Approximate recharge time for 40% transmission =                                              

Photodiode output voltage reading for 20% transmission =                                              

Approximate recharge time for 20% transmission =                                              

Photodiode output voltage reading for ultraviolet light =                                              

Approximate recharge time for ultraviolet light =                                              

Plot the graph of stopping potential as a function of intensity using one sheet of graph paper at the end of this workbook. Remember to label the axes and title the graph.

Procedure Part 2:

First-order diffraction pattern on one side of the center:

Photodiode output voltage reading for yellow light =                                              

Photodiode output voltage reading for green light =                                              

Photodiode output voltage reading for blue light =                                              

Photodiode output voltage reading for violet light =                                              

Second-order diffraction pattern on the other side of the center:

Plot the graph of stopping potential as a function of frequency using one sheet of graph paper at the end of this workbook. Remember to label the axes and title the graph.

Slope of graph =                                              

\(y\)-intercept of graph =                                              

\(W_0\) =                                              

\(h\) =                                              

Percentage difference between experimental and accepted values of \(h\) =                

{:instructional:lab_manuals:physics:6c:experiment_7:photo_graph_2.jpg|}}

• Experimental Study of Photoelectric Effect

The photoelectric effect is the name given to the phenomenon of emission of electrons from a metal surface when the light of a suitable frequency is incident on it. What happens when light falls on a metal surface? How can we study it? Let’s find out.

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The aim of the experiment is to study the emission of electrons by light. We also try and measure the energy of the electrons emitted in the process. In addition to this, we will also observe the relation of these electrons with the frequency of light used. To study the effect, we use an evacuated cathode ray tube connected in a circuit as shown below:

Browse more Topics under Dual Nature Of Radiation And Matter

• Electron Emission
• Wave Nature of Matter
• Davisson and Germer Experiment
• Einstein’s Photoelectric Equation: Energy Quantum of Radiation

Apparatus used

Quartz window.

Near one of the plates inside the evacuated tube, there is present a small quartz window. The Quartz window has two functions – it lets light in and it only lets the Ultra Violet light in. Hence by using a Quartz window, we make sure that light of a specific frequency falls on the metal plate inside the evacuated chamber.

The circuit

We connect a voltmeter across the two plates. This measures the potential difference between the plates. Moreover, we have a sensitive galvanometer in the circuit. This measures the photocurrent.

The Collector plate-C emits electrons which are then collected at the collector plate-A. These plates are connected to the battery via the commutator. Let’s switch on this experiment and see what happens!

In The Beginning!

Well, in the beginning, let us have a zero potential. We open the quartz window and observe the reading of the Voltmeter and the Ammeter. Both will give a non-zero reading (say for alkali metals), proving the occurrence of the Photoelectric effect. As we increase the Voltage and change it again, we will make the following observations:

The Effect of Intensity

The number of electrons emitted per second is observed to be directly proportional to the intensity of light. “Ok, so light is a wave and has energy. It takes electrons out of a metal, what is so special about that!” First of all, when the intensity of light is increased, we should see an increase in the photocurrent (number of photoelectrons emitted). Right?

As we see, this only happens above a specific value of frequency, known as the threshold frequency. Below this threshold frequency, the intensity of light has no effect on the photocurrent! In fact, there is no photocurrent at all, howsoever high the intensity of light is.

The graph between the photoelectric current and the intensity of light is a straight line when the frequency of light used is above a specific minimum threshold value.

The Effect of The Potential

Suppose you connect C to a positive terminal and A to a negative terminal. What do you expect will happen to the photocurrent?

Since electrons are negatively charged, if we increase the negative potential at C, more and more electrons will want to escape this region and run to the attractive plate A. So the current should increase. Similarly, if we decrease the negative potential at C, removing electrons will become difficult and the photocurrent will decrease. Hence the maximum current flowing at a given intensity of incoming light is the saturation current.

As you can see in the graph, the value of saturation current is greater for higher intensities, provided the frequency is above the threshold frequency. Imagine you are an electron and you just escaped the metal surface. Now you are merrily accelerating towards A. What if we became mischievous and increased the negative potential at A? You will feel a repulsion and consequently you will lose speed.

What if the potential is very strong? You will not be able to escape the metal surface at all! As a result, we call this value of the potential for which the photocurrent becomes zero as the stopping potential or the retarding potential. The more the negative potential of the collector plate, the more is the effort that an electron has to make if it wants to escape successfully from the metal surface.

Thus we will get the following relationship between the stopping potential and the photocurrent.

Effect of Frequency

We see that for higher frequency values like ν 3 , stopping potential is more negative or greater than the stopping potential for smaller frequencies like ν 1 . What does this mean? This means that there should be a relationship between the frequency and energy.

We can sum up the observations as follows:

• For a given metal (photosensitive material), the photoelectric current is directly proportional to the intensity of the light used, above a minimum value of frequency called the threshold frequency.
• The saturation current depends on the intensity for a known value of frequency. At the same time, we see that the stopping potential does not depend on the intensity over a specific value of frequency.
• The Photoelectric effect does not occur below a certain frequency. This is the threshold frequency. If the frequency of light is above the threshold frequency, the stopping potential is directly proportional to the frequency. In other words, to stop an electron emitted by a higher frequency, we require more energy. The stopping potential provides this energy.
• All of this happens instantaneously. As soon as we open the quartz window, electron emission starts.

All this is beautifully explained by the Einstein’s Photoelectric equation.

Solved Examples For You

On reducing the wavelength of light incident on a metal, the velocity of emitted photoelectrons will become

A) Zero                              B) Less

C) More                             D) Remains Unchanged

Solution: C) It will become more.

We know that the energy of photoelectrons increases as we increase the frequency. This means that their kinetic energy will be more. Hence higher frequency means a greater speed of a photoelectron. We also know that λ = c/ν. Hence if the wavelength is increased, the frequency will be decreased and vice-versa. So lesser wavelength means greater frequency and greater speed of the photoelectrons.

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The Photoelectric Effect

Hertz finds maxwell's waves: and something else.

The most dramatic prediction of Maxwell's theory of electromagnetism, published in 1865, was the existence of electromagnetic waves moving at the speed of light, and the conclusion that light itself was just such a wave. This challenged experimentalists to generate and detect electromagnetic radiation using some form of electrical apparatus. The first clearly successful attempt was by Heinrich Hertz in 1886. He used a high voltage induction coil to cause a spark discharge between two pieces of brass, to quote him, " Imagine a cylindrical brass body, 3 cm in diameter and 26 cm long, interrupted midway along its length by a spark gap whose poles on either side are formed by spheres of 2 cm radius ." The idea was that once a spark formed a conducting path between the two brass conductors, charge would rapidly oscillate back and forth, emitting electromagnetic radiation of a wavelength similar to the size of the conductors themselves.

To prove there really was radiation emitted, it had to be detected. Hertz used a piece of copper wire 1 mm thick bent into a circle of diameter 7.5 cm, with a small brass sphere on one end, and the other end of the wire was pointed, with the point near the sphere. He added a screw mechanism so that the point could be moved very close to the sphere in a controlled fashion. This "receiver" was designed so that current oscillating back and forth in the wire would have a natural period close to that of the "transmitter" described above. The presence of oscillating charge in the receiver would be signaled by a spark across the (tiny) gap between the point and the sphere (typically, this gap was hundredths of a millimeter). (It was suggested to Hertz that this spark gap could be replaced as a detector by a suitably prepared frog's leg, but that apparently didn't work.)

The experiment was very successful — Hertz was able to detect the radiation up to fifty feet away, and in a series of ingenious experiments established that the radiation was reflected and refracted as expected, and that it was polarized. The main problem — the limiting factor in detection — was being able to see the tiny spark in the receiver. In trying to improve the spark's visibility, he came upon something very mysterious. To quote from Hertz again (he called the transmitter spark A , the receiver B ): " I occasionally enclosed the spark B in a dark case so as to more easily make the observations; and in so doing I observed that the maximum spark-length became decidedly smaller in the case than it was before. On removing in succession the various parts of the case, it was seen that the only portion of it which exercised this prejudicial effect was that which screened the spark B from the spark A. The partition on that side exhibited this effect, not only when it was in the immediate neighborhood of the spark B, but also when it was interposed at greater distances from B between A and B. A phenomenon so remarkable called for closer investigation ."

Hertz then embarked on a very thorough investigation. He found that the small receiver spark was more vigorous if it was exposed to ultraviolet light from the transmitter spark. It took a long time to figure this out - he first checked for some kind of electromagnetic effect, but found a sheet of glass effectively shielded the spark. He then found a slab of quartz did not shield the spark, whereupon he used a quartz prism to break up the light from the big spark into its components, and discovered that the wavelength which made the little spark more powerful was beyond the visible, in the ultraviolet.

In 1887, Hertz concluded what must have been months of investigation: "… I confine myself at present to communicating the results obtained, without attempting any theory respecting the manner in which the observed phenomena are brought about ."

Hallwachs' Simpler Approach

The next year, 1888, another German physicist, Wilhelm Hallwachs, in Dresden, wrote:

" In a recent publication Hertz has described investigations on the dependence of the maximum length of an induction spark on the radiation received by it from another induction spark. He proved that the phenomenon observed is an action of the ultraviolet light. No further light on the nature of the phenomenon could be obtained, because of the complicated conditions of the research in which it appeared. I have endeavored to obtain related phenomena which would occur under simpler conditions, in order to make the explanation of the phenomena easier. Success was obtained by investigating the action of the electric light on electrically charged bodies ."

He then describes his very simple experiment: a clean circular plate of zinc was mounted on an insulating stand and attached by a wire to a gold leaf electroscope, which was then charged negatively. The electroscope lost its charge very slowly. However, if the zinc plate was exposed to ultraviolet light from an arc lamp, or from burning magnesium, charge leaked away quickly. If the plate was positively charged, there was no fast charge leakage. (We showed this as a lecture demo, using a UV lamp as source.)

Questions for the reader : Could it be that the ultraviolet light somehow spoiled the insulating properties of the stand the zinc plate was on? Could it be that electric or magnetic effects from the large current in the arc lamp somehow caused the charge leakage?

Although Hallwach's experiment certainly clarified the situation, he did not offer any theory of what was going on.

J.J. Thomson Identifies the Particles

In fact, the situation remained unclear until 1899, when Thomson established that the ultraviolet light caused electrons to be emitted, the same particles found in cathode rays. His method was to enclose the metallic surface to be exposed to radiation in a vacuum tube, in other words to make it the cathode in a cathode ray tube. The new feature was that electrons were to be ejected from the cathode by the radiation, rather than by the strong electric field used previously.

By this time, there was a plausible picture of what was going on. Atoms in the cathode contained electrons, which were shaken and caused to vibrate by the oscillating electric field of the incident radiation. Eventually some of them would be shaken loose, and would be ejected from the cathode. It is worthwhile considering carefully how the number and speed of electrons emitted would be expected to vary with the intensity and color of the incident radiation. Increasing the intensity of radiation would shake the electrons more violently, so one would expect more to be emitted, and they would shoot out at greater speed, on average. Increasing the frequency of the radiation would shake the electrons faster, so might cause the electrons to come out faster. For very dim light, it would take some time for an electron to work up to a sufficient amplitude of vibration to shake loose.

Lenard Finds Some Surprises

In 1902, Lenard studied how the energy of the emitted photoelectrons varied with the intensity of the light. He used a carbon arc light, and could increase the intensity a thousand-fold. The ejected electrons hit another metal plate, the collector, which was connected to the cathode by a wire with a sensitive ammeter, to measure the current produced by the illumination. To measure the energy of the ejected electrons, Lenard charged the collector plate negatively, to repel the electrons coming towards it. Thus, only electrons ejected with enough kinetic energy to get up this potential hill would contribute to the current. Lenard discovered that there was a well defined minimum voltage that stopped any electrons getting through, we'll call it V stop .  To his surprise, he found that V stop  did not depend at all on the intensity of the light!  Doubling the light intensity doubled the number of electrons emitted, but did not affect the energies of the emitted electrons. The more powerful oscillating field ejected more electrons, but the maximum individual energy of the ejected electrons was the same as for the weaker field.

But Lenard did something else. With his very powerful arc lamp, there was sufficient intensity to separate out the colors and check the photoelectric effect using light of different colors. He found that the maximum energy of the ejected electrons did depend on the color — the shorter wavelength, higher frequency light caused electrons to be ejected with more energy. This was, however, a fairly qualitative conclusion — the energy measurements were not very reproducible, because they were extremely sensitive to the condition of the surface, in particular its state of partial oxidation. In the best vacua available at that time, significant oxidation of a fresh surface took place in tens of minutes. (The details of the surface are crucial because the fastest electrons emitted are those from right at the surface, and their binding to the solid depends strongly on the nature of the surface — is it pure metal or a mixture of metal and oxygen atoms?)

Question: In the above figure, the battery represents the potential Lenard used to charge the collector plate negatively, which would actually be a variable voltage source. Since the electrons ejected by the blue light are getting to the collector plate, evidently the potential supplied by the battery is less than V stop  for blue light. Show with an arrow on the wire the direction of the electric current in the wire.

Einstein Suggests an Explanation

In 1905 Einstein gave a very simple interpretation of Lenard's results.  He just assumed that the incoming radiation should be thought of as quanta of frequency  h f , with f the frequency. In photoemission, one such quantum is absorbed by one electron. The most energetic electrons emitted are found to have energy E depending on the light frequency as

E = h f − W ,  

where  W is a material-dependent constant.

It’s worth thinking carefully about  W . The standard explanation in many textbooks (and earlier versions of this lecture!) was that  W is the minimum work needed to tear the electron out of the emitter in the first place: the  work function  (hence  W ) of the emitter.  But this is wrong!  The voltage  V provided by the battery, or, more realistically, by some variable voltage source, is the voltage difference between  inside the metal  of the emitter and  inside the metal  of the collector.  The photon must provide sufficient energy to the electron to get it from inside the metal of the emitter to a point just  outside  the surface of the collector. But such a point is at a voltage the  collector  work function  W coll higher than that inside the metal of the collector! Therefore, the photon must deliver energy

h f = V + W coll ,  

where, remember,  V is the voltage provided by the battery (or other source of emf).

On cranking up the negative voltage until the current just stops, that is, to  V stop , the photon frequency is given by

e V stop = h f − W coll .  

Thus Einstein's theory makes a very definite quantitative prediction: if the frequency of the incident light is varied, and  V stop plotted as a function of frequency, the slope of the line should be  h / e .

It is also clear that there is a minimum light frequency for a given metal, that for which the quantum of energy is equal to the work function. Light below that frequency, no matter how bright, will not cause photoemission.

Millikan's Attempts to Disprove Einstein's Theory

If we accept Einstein's theory, then, this is a completely different way to measure Planck's constant. The American experimental physicist Robert Millikan , who did not accept Einstein's theory, which he saw as an attack on the wave theory of light, worked for ten years, until 1916, on the photoelectric effect. He even devised techniques for scraping clean the metal surfaces inside the vacuum tube. For all his efforts he found disappointing results: he confirmed Einstein's theory, measuring Planck's constant to within 0.5% by this method. One consolation was that he did get a Nobel prize for this series of experiments.

' Subtle is the Lord...' The Science and Life of Albert Einstein , Abraham Pais, Oxford 1982.

Inward Bound , Abraham Pais, Oxford, 1986

The Project Physics Course, Text , Holt, Rinehart, Winston, 1970

Life of Lenard

Life of Millikan

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Photoelectric effect, light as waves & particles, wavefunctions, nuclear physics.

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Photoelectric Effect: Definition, Equation & Experiment

Everything learned in classical physics was turned on its head as physicists explored ever smaller realms and discovered quantum effects. Among the first of these discoveries was the photoelectric effect. In the early 1900s, the results of this effect failed to match classical predictions and were only explainable with quantum theory, opening up a whole new world for physicists.

Today, the photoelectric effect has many practical applications as well. From medical imaging to the production of clean energy, the discovery and application of this effect now has implications that go well beyond simply understanding the science.

What Is the Photoelectric Effect?

When light, or electromagnetic radiation, hits a material such as a metal surface, that material sometimes emits electrons, called ​ photoelectrons ​. This is essentially because the atoms in the material are absorbing the radiation as energy. Electrons in atoms absorb radiation by jumping to higher energy levels. If the energy absorbed is high enough, the electrons leave their home atom entirely.

This process is sometimes also called ​ photoemission ​ because incident photons (another name for particles of light) are the direct cause of the emission of electrons. Because electrons have a negative charge, the metal plate from which they were emitted is left ionized.

What was most special about the photoelectric effect, however, was that it did not follow classical predictions. The way in which the electrons were emitted, the number that were emitted and how this changed with intensity of light all left scientists scratching their heads initially.

Original Predictions

The original predictions as to the results of the photoelectric effect made from classical physics included the following:

• Energy transfers from incident radiation to the electrons. It was assumed that whatever energy is incident upon the material would be directly absorbed by the electrons in the atoms, regardless of wavelength. This makes sense in the classical mechanics paradigm: Whatever you pour into the bucket fills the bucket by that amount.
• Changes in light intensity should yield changes in kinetic energy of electrons. If it is assumed that electrons are absorbing whatever radiation is incident upon them, then more of the same radiation should give them more energy accordingly. Once the electrons have left the bounds of their atoms, that energy is seen in the form of kinetic energy.
• Very low-intensity light should yield a time lag between light absorption and emission of electrons. This would be because it was assumed that electrons must gain enough energy to leave their home atom, and low-intensity light is like adding energy to their energy “bucket” more slowly. It takes longer to fill, and hence it should take longer before the electrons have enough energy to be emitted.

Actual Results

The actual results were not at all consistent with the predictions. This included the following:

• Electrons were released only when the incident light reached or exceeded a threshold frequency. No emission occurred below that frequency. It didn’t matter if the intensity was high or low. For some reason, the frequency, or wavelength of the light itself, was much more important. 
• Changes in intensity did not yield changes in kinetic energy of electrons. They changed only the number of electrons emitted. Once the threshold frequency was reached, increasing the intensity did not add more energy to each emitted electron at all. Instead, they all ended up with the same kinetic energy; there were just more of them.
• There was no time lag at low intensities. There seemed to be no time required to “fill the energy bucket” of any given electron. If an electron was to be emitted, it was emitted immediately. Lower intensity had no effect on kinetic energy or lag time; it simply resulted in fewer electrons being emitted. 

Photoelectric Effect Explained

The only way to explain this phenomenon was to invoke quantum mechanics. Think of a beam of light not as a wave, but as a collection of discrete wave packets called photons. The photons all have distinct energy values that correspond to the frequency and wavelength of the light, as explained by wave-particle duality.

In addition, consider that the electrons are only able to jump between discrete energy states. They can only have specific energy values, but never any values in between. Now the observed phenomena can be explained as follows:

• Electrons are released only when they absorb very specific sufficient energy values. Any electron that gets the right energy packet (photon energy) will be released. None are released if the frequency of the incident light is too low regardless of intensity because none of the energy packets are individually big enough. 
• Once the threshold frequency is exceeded, increasing intensity only increases the number of electrons released and not the energy of the electrons themselves because each emitted electron absorbs one discrete photon. Greater intensity means more photons, and hence more photoelectrons. 
• There is no time delay even at low intensity as long as the frequency is high enough because as soon as an electron gets the right energy packet, it is released. Low intensity only results in fewer electrons.

The Work Function

One important concept related to the photoelectric effect is the work function. Also known as electron-binding energy, it is the minimum energy needed to remove an electron from a solid.

The formula for the work function is given by:

Where ​ -e ​ is the electron charge, ​ ϕ ​ is the electrostatic potential in the vacuum nearby the surface and ​ E ​ is the Fermi level of electrons in the material.

Electrostatic potential is measured in volts and is a measure of the electric potential energy per unit charge. Hence the first term in the expression, ​ -eϕ ​, is the electric potential energy of an electron near the surface of the material.

The Fermi level can be thought of as the energy of the outermost electron when the atom is in its ground state.

Threshold Frequency

Closely related to the work function is the threshold frequency. This is the minimum frequency at which incident photons will cause the emission of electrons. Frequency is directly related to energy (higher frequency corresponds to higher energy), hence why a minimum frequency must be reached.

Above the threshold frequency, the kinetic energy of the electrons depends on the frequency and not the intensity of the light. Basically the energy of a single photon will be transferred entirely to a single electron. A certain amount of that energy is used to eject the electron, and the remainder is its kinetic energy. Again, a greater intensity just means more electrons will be emitted, not that those emitted will have any more energy.

The maximum kinetic energy of emitted electrons can be found via the following equation:

Where ​ K max ​ is the maximum kinetic energy of the photoelectron, ​ h ​ is Planck's constant = 6.62607004 ×10 -34 m 2 kg/s, ​ f ​ is the frequency of the light and ​ f 0 ​ is the threshold frequency.

Discovery of the Photoelectric Effect

You can think of the discovery of the photoelectric effect as happening in two stages. First, the discovery of the emission of photoelectrons from certain materials as a result of incident light, and second, the determination that this effect does not obey classical physics at all, which led to many important underpinnings of our understanding of quantum mechanics.

Heinrich Hertz first observed the photoelectric effect in 1887 while performing experiments with a spark gap generator. The setup involved two pairs of metal spheres. Sparks generated between the first set of spheres would induce sparks to jump between the second set, thus acting as transducer and receiver. Hertz was able to increase the sensitivity of the setup by shining light on it. Years later, J.J. Thompson discovered that the increased sensitivity resulted from the light causing the electrons to be ejected.

While Hertz’s assistant Phillip Lenard determined that the intensity did not affect the kinetic energy of the photoelectrons, it was Robert Millikan who discovered the threshold frequency. Later, Einstein was able to explain the strange phenomenon by assuming the quantization of energy.

Importance of the Photoelectric Effect

Albert Einstein was awarded the Nobel Prize in 1921 for his discovery of the law of the photoelectric effect, and Millikan won the Nobel Prize in 1923 also for work related to understanding the photoelectric effect.

The photoelectric effect has many uses. One of those is that it allows scientists to probe the electron energy levels in matter by determining the threshold frequency at which incident light causes emission. Photomultiplier tubes making use of this effect were also used in older television cameras.

A very useful application of the photoelectric effect is in the construction of solar panels. Solar panels are arrays of photovoltaic cells, which are cells that make use of electrons ejected from metals by solar radiation to generate current. As of 2018, nearly 3 percent of the world’s energy is generated by solar panels, but this number is expected to grow considerably over the next several years, especially as the efficiency of such panels increases.

But most important of all, the discovery and understanding of the photoelectric effect laid the groundwork for the field of quantum mechanics and a better understanding of the nature of light.

Photoelectric Effect Experiments

There are many experiments that can be performed in an introductory physics lab to demonstrate the photoelectric effect. Some of these are more complicated than others.

A simple experiment demonstrates the photoelectric effect with an electroscope and a UV-C lamp providing ultraviolet light. Place negative charge on the electroscope so that the needle deflects. Then, shine the UV-C lamp. Light from the lamp will release electrons from the electroscope and discharge it. You can tell this happens by seeing the needle’s deflection reducing. Note, however, that if you tried the same experiment with a positively charged electroscope, it wouldn’t work.

There are many other possible ways to experiment with the photoelectric effect. Several setups involve a photocell consisting of a large anode that, when hit with incident light, will release electrons that are picked up by a cathode. If this setup is connected to a voltmeter, for example, the photoelectric effect will become apparent when shining the light creates a voltage.

More complex setups allow for more accurate measurement and even allow you to determine the work function and threshold frequencies for different materials. See the Resources section for links.

Related Articles

• Physics Hypertextbook: Photoelectric Effect
• Georgia State University: HyperPhysics: Photoelectric Effect
• UTK: Lab 2: The Photoelectric Effect
• UCLA Physics and Astronomy: Experiment 6 – The Photoelectric Effect
• Amrita: Photoelectric Effect

About the Author

Gayle Towell is a freelance writer and editor living in Oregon. She earned masters degrees in both mathematics and physics from the University of Oregon after completing a double major at Smith College, and has spent over a decade teaching these subjects to college students. Also a prolific writer of fiction, and founder of Microfiction Monday Magazine, you can learn more about Gayle at gtowell.com.

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Photoelectric Effect

The photoelectric effect is a phenomenon in which electrons are ejected from the surface of a metal when light is incident on it. These ejected electrons are called  photoelectrons . It is important to note that the emission of photoelectrons and the kinetic energy of the ejected photoelectrons is dependent on the frequency of the light that is incident on the metal’s surface. The process through which photoelectrons are ejected from the surface of the metal due to the action of light is commonly referred to as  photoemission .

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The photoelectric effect occurs because the electrons at the surface of the metal tend to absorb energy from the incident light and use it to overcome the attractive forces that bind them to the metallic nuclei. An illustration detailing the emission of photoelectrons as a result of the photoelectric effect is provided below.

History of the Photoelectric Effect Principle Formula Laws Governing the Photoelectric Effect Experimental Study of the Photoelectric Effect Einstien’s Photoelectric Equation Graphs Applications Solved Problems (Numericals)

Recommended Video

Photoelectric effect – basics.

Hertz and Lenard’s Observation

History of the Photoelectric Effect

The photoelectric effect was first introduced by Wilhelm Ludwig Franz Hallwachs in the year 1887, and the experimental verification was done by Heinrich Rudolf Hertz. They observed that when a surface is exposed to electromagnetic radiation at a higher threshold frequency, the radiation is absorbed, and the electrons are emitted. Today, we study the photoelectric effect as a phenomenon that involves a material absorbing electromagnetic radiation and releasing electrically charged particles.

To be more precise, light incident on the surface of a metal in the photoelectric effect causes electrons to be ejected. The electron ejected due to the photoelectric effect is called a photoelectron and is denoted by e – .  The current produced as a result of the ejected electrons is called photoelectric current.

Explaining the Photoelectric Effect: The Concept of Photons

The photoelectric effect cannot be explained by considering light as a wave. However, this phenomenon can be explained by the particle nature of light, in which light can be visualised as a stream of particles of electromagnetic energy. These ‘particles’ of light are called photons . The energy held by a photon is related to the frequency of the light via Planck’s equation .

E = h𝜈 = hc/λ

• E denotes the energy of the photon
• h is Planck’s constant
• 𝜈 denotes the frequency of the light
• c is the speed of light (in a vacuum)
• λ is the wavelength of the light

Thus, it can be understood that different frequencies of light carry photons of varying energies. For example, the frequency of blue light is greater than that of red light (the wavelength of blue light is much shorter than the wavelength of red light). Therefore, the energy held by a photon of blue light will be greater than the energy held by a photon of red light.

Threshold Energy for the Photoelectric Effect

For the photoelectric effect to occur, the photons that are incident on the surface of the metal must carry sufficient energy to overcome the attractive forces that bind the electrons to the nuclei of the metals. The minimum amount of energy required to remove an electron from the metal is called the  threshold energy  (denoted by the symbol Φ). For a photon to possess energy equal to the threshold energy, its frequency must be equal to the  threshold frequency  (which is the minimum frequency of light required for the photoelectric effect to occur). The threshold frequency is usually denoted by the symbol 𝜈 th , and the associated wavelength (called the threshold wavelength) is denoted by the symbol λ th . The relationship between the threshold energy and the threshold frequency can be expressed as follows.

Φ = h𝜈 th  = hc/λ th

Relationship between the Frequency of the Incident Photon and the Kinetic Energy of the Emitted Photoelectron

Therefore, the relationship between the energy of the photon and the kinetic energy of the emitted photoelectron can be written as follows:

E photon  = Φ + E electron

⇒  h𝜈 = h𝜈 th  + ½m e v 2

• E photon  denotes the energy of the incident photon, which is equal to h𝜈
• Φ denotes the threshold energy of the metal surface, which is equal to h𝜈 th
• E electron  denotes the kinetic energy of the photoelectron, which is equal to ½m e v 2  (m e = Mass of electron = 9.1*10 -31  kg)

If the energy of the photon is less than the threshold energy, there will be no emission of photoelectrons (since the attractive forces between the nuclei and the electrons cannot be overcome). Thus, the photoelectric effect will not occur if 𝜈 < 𝜈 th . If the frequency of the photon is exactly equal to the threshold frequency (𝜈 = 𝜈 th ), there will be an emission of photoelectrons, but their kinetic energy will be equal to zero. An illustration detailing the effect of the frequency of the incident light on the kinetic energy of the photoelectron is provided below.

From the image, it can be observed that

• The photoelectric effect does not occur when the red light strikes the metallic surface because the frequency of red light is lower than the threshold frequency of the metal.
• The photoelectric effect occurs when green light strikes the metallic surface, and photoelectrons are emitted.
• The photoelectric effect also occurs when blue light strikes the metallic surface. However, the kinetic energies of the emitted photoelectrons are much higher for blue light than for green light. This is because blue light has a greater frequency than green light.

It is important to note that the threshold energy varies from metal to metal. This is because the attractive forces that bind the electrons to the metal are different for different metals. It can also be noted that the photoelectric effect can also take place in non-metals, but the threshold frequencies of non-metallic substances are usually very high.

Einstein’s Contributions towards the Photoelectric Effect

The photoelectric effect is the process that involves the ejection or release of electrons from the surface of materials (generally a metal) when light falls on them. The photoelectric effect is an important concept that enables us to clearly understand the quantum nature of light and electrons.

After continuous research in this field, the explanation for the photoelectric effect was successfully explained by Albert Einstein. He concluded that this effect occurred as a result of light energy being carried in discrete quantised packets. For this excellent work, he was honoured with the Nobel Prize in 1921.

According to Einstein, each photon of energy E is

Where E = Energy of the photon in joule

h = Plank’s constant (6.626 × 10 -34 J.s)

ν = Frequency of photon in Hz

Properties of the Photon

• For a photon, all the quantum numbers are zero.
• A photon does not have any mass or charge, and they are not reflected in a magnetic and electric field.
• The photon moves at the speed of light in empty space.
• During the interaction of matter with radiation, radiation behaves as it is made up of small particles called photons.
• Photons are virtual particles. The photon energy is directly proportional to its frequency and inversely proportional to its wavelength.
• The momentum and energy of the photons are related, as given below

E = p.c where

p = Magnitude of the momentum

c = Speed of light

Definition of the Photoelectric Effect

Principle of the photoelectric effect.

The law of conservation of energy forms the basis for the photoelectric effect.

Minimum Condition for Photoelectric Effect

Threshold frequency (γ th ).

It is the minimum frequency of the incident light or radiation that will produce a photoelectric effect, i.e., the ejection of photoelectrons from a metal surface is known as the threshold frequency for the metal. It is constant for a specific metal but may be different for different metals.

If γ = Frequency of the incident photon and γ th = Threshold frequency, then,

• If γ < γ Th , there will be no ejection of photoelectron and, therefore, no photoelectric effect.
• If γ = γ Th , photoelectrons are just ejected from the metal surface; in this case, the kinetic energy of the electron is zero.
• If γ > γ Th , then photoelectrons will come out of the surface, along with kinetic energy.

Threshold Wavelength (λ th )

During the emission of electrons, a metal surface corresponding to the greatest wavelength to incident light is known as threshold wavelength.

λ th  = c/γ th

For wavelengths above this threshold, there will be no photoelectron emission. For λ = wavelength of the incident photon, then

• If λ < λ Th , then the photoelectric effect will take place, and ejected electron will possess kinetic energy.
• If λ = λ Th, then just the photoelectric effect will take place, and the kinetic energy of ejected photoelectron will be zero.
• If λ > λ Th, there will be no photoelectric effect.

Work Function or Threshold Energy (Φ)

The minimal energy of thermodynamic work that is needed to remove an electron from a conductor to a point in the vacuum immediately outside the surface of the conductor is known as work function/threshold energy.

Φ = hγ th  = hc/λ th

The work function is the characteristic of a given metal. If E = energy of an incident photon, then

• If E < Φ, no photoelectric effect will take place.
• If E = Φ, just a photoelectric effect will take place, but the kinetic energy of ejected photoelectron will be zero
• If E > photoelectron will be zero
• If E > Φ, the photoelectric effect will take place along with the possession of the kinetic energy by the ejected electron.

Photoelectric Effect Formula

According to  Einstein’s explanation of the photoelectric effect ,

The energy of photon = Energy needed to remove an electron + Kinetic energy of the emitted electron

i.e., hν = W + E

• ν is the frequency of the incident photon
• W is a work function
• E is the maximum kinetic energy of ejected electrons: 1/2 mv²

Laws Governing the Photoelectric Effect

• For a light of any given frequency,; (γ > γ Th ), the photoelectric current is directly proportional to the intensity of light.
• For any given material, there is a certain minimum (energy) frequency, called threshold frequency, below which the emission of photoelectrons stops completely, no matter how high the intensity of incident light is.
• The maximum kinetic energy of the photoelectrons is found to increase with the increase in the frequency of incident light, provided the frequency (γ > γ Th ) exceeds the threshold limit. The maximum kinetic energy is independent of the intensity of light.
• The photo-emission is an instantaneous process.

Experimental Study of the Photoelectric Effect

Photoelectric Effect: Experimental Setup

The given experiment is used to study the photoelectric effect experimentally. In an evacuated glass tube, two zinc plates, C and D, are enclosed. Plates C acts as an anode, and D acts as a photosensitive plate.

Two plates are connected to battery B and ammeter A. If the radiation is incident on plate D through a quartz window, W electrons are ejected out of the plate, and current flows in the circuit. This is known as photocurrent. Plate C can be maintained at desired potential (+ve or – ve) with respect to plate D.

Characteristics of the Photoelectric Effect

• The threshold frequency varies with the material, it is different for different materials.
• The photoelectric current is directly proportional to the light intensity.
• The kinetic energy of the photoelectrons is directly proportional to the light frequency.
• The stopping potential is directly proportional to the frequency, and the process is instantaneous.

Factors Affecting the Photoelectric Effect

With the help of this apparatus, we will now study the dependence of the photoelectric effect on the following factors:

• The intensity of incident radiation.
• A potential difference between the metal plate and collector.
• Frequency of incident radiation.

Effects of Intensity of Incident Radiation on Photoelectric Effect

The potential difference between the metal plate, collector and frequency of incident light is kept constant, and the intensity of light is varied.

The electrode C, i.e., the collecting electrode, is made positive with respect to D (metal plate). For a fixed value of frequency and the potential between the metal plate and collector, the photoelectric current is noted in accordance with the intensity of incident radiation.

It shows that photoelectric current and intensity of incident radiation both are proportional to each other. The photoelectric current gives an account of the number of photoelectrons ejected per sec.

Effects of Potential Difference between the Metal Plate and the Collector on the Photoelectric Effect

The frequency of incident light and intensity is kept constant, and the potential difference between the plates is varied.

Keeping the intensity and frequency of light constant, the positive potential of C is increased gradually. Photoelectric current increases when there is a positive increase in the potential between the metal plate and the collector up to a characteristic value.

There is no change in photoelectric current when the potential is increased higher than the characteristic value for any increase in the accelerating voltage. This maximum value of the current is called saturation current.

Effect of Frequency on Photoelectric Effect

The intensity of light is kept constant, and the frequency of light is varied.

For a fixed intensity of incident light, variation in the frequency of incident light produces a linear variation of the cut-off potential/stopping potential of the metal. It is shown that the cut-off potential (Vc) is linearly proportional to the frequency of incident light.

The kinetic energy of the photoelectrons increases directly proportionally to the frequency of incident light to completely stop the photoelectrons. We should reverse and increase the potential between the metal plate and collector in (negative value) so the emitted photoelectron can’t reach the collector.

Einstein’s Photoelectric Equation

According to Einstein’s theory of the photoelectric effect, when a photon collides inelastically with electrons, the photon is absorbed completely or partially by the electrons. So if an electron in a metal absorbs a photon of energy, it uses the energy in the following ways.

Some energy Φ 0  is used in making the surface electron free from the metal. It is known as the work function of the material. Rest energy will appear as kinetic energy (K) of the emitted photoelectrons.

Einstein’s Photoelectric Equation Explains the Following Concepts

• The frequency of the incident light is directly proportional to the kinetic energy of the electrons, and the wavelengths of incident light are inversely proportional to the kinetic energy of the electrons.
• If γ = γ th or λ =λ th then v max = 0
• γ < γ th  or λ > λ th : There will be no emission of photoelectrons.
• The intensity of the radiation or incident light refers to the number of photons in the light beam. More intensity means more photons and vice-versa. Intensity has nothing to do with the energy of the photon. Therefore, the intensity of the radiation is increased, and the rate of emission increases, but there will be no change in the kinetic energy of electrons. With an increasing number of emitted electrons, the value of the photoelectric current increases.

Different Graphs of the Photoelectric Equation

• Photoelectric current vs Retarding potential for different voltages
• Photoelectric current vs Retarding potential for different intensities
• Electron current vs Light Intensity
• Stopping potential vs Frequency
• Electron current vs Light frequency
• Electron kinetic energy vs Light frequency

Applications of the Photoelectric Effect

• Used to generate electricity in solar panels. These panels contain metal combinations that allow electricity generation from a wide range of wavelengths.
• Motion and Position Sensors: In this case, a photoelectric material is placed in front of a UV or IR LED. When an object is placed in between the Light-emitting diode (LED) and sensor, light is cut off, and the electronic circuit registers a change in potential difference
• Lighting sensors, such as the ones used in smartphones, enable automatic adjustment of screen brightness according to the lighting. This is because the amount of current generated via the photoelectric effect is dependent on the intensity of light hitting the sensor.
• Digital cameras can detect and record light because they have photoelectric sensors that respond to different colours of light.
• X-Ray Photoelectron Spectroscopy (XPS): This technique uses X-rays to irradiate a surface and measure the kinetic energies of the emitted electrons. Important aspects of the chemistry of a surface can be obtained, such as elemental composition, chemical composition, the empirical formula of compounds and chemical state.
• Photoelectric cells are used in burglar alarms.
• Used in photomultipliers to detect low levels of light.
• Used in video camera tubes in the early days of television.
• Night vision devices are based on this effect.
• The photoelectric effect also contributes to the study of certain nuclear processes. It takes part in the chemical analysis of materials since emitted electrons tend to carry specific energy that is characteristic of the atomic source.

Photoelectric Effect – JEE Advanced Concepts and Problems

Problems on the Photoelectric Effect

1. In a photoelectric effect experiment, the threshold wavelength of incident light is 260 nm and E (in eV) = 1237/λ (nm). Find the maximum kinetic energy of emitted electrons.

⇒ K max  = (1237) × [(380 – 260)/380×260] = 1.5 eV

Therefore, the maximum kinetic energy of emitted electrons in the photoelectric effect is 1.5 eV.

2. In a photoelectric experiment, the wavelength of the light incident on metal is changed from 300 nm to 400 nm and (hc/e = 1240 nm-V). Find the decrease in the stopping potential.

hc/λ 1  = ϕ + eV 1 . . . . (i)

hc/λ 2  = ϕ + eV 2 . . . . (ii)

Equation (i) – (ii)

hc(1/λ 1 – 1/λ 2 ) = e × (V 1 – V 2 )

= (1240 nm V) × 100nm/(300nm × 400nm)

=12.4/12 ≈ 1V

Therefore, the decrease in the stopping potential during the photoelectric experiment is 1V.

3. When ultraviolet light with a wavelength of 230 nm shines on a particular metal plate, electrons are emitted from plate 1, crossing the gap to plate 2 and causing a current to flow through the wire connecting the two plates. The battery voltage is gradually increased until the current in the ammeter drops to zero, at which point the battery voltage is 1.30 V. 

a) What is the energy of the photons in the beam of light in eV?

b) What is the maximum kinetic energy of the emitted electrons in eV?

Assuming that the wavelength corresponds to the wavelength in the vacuum.

f = 1.25 × 10 15 Hz

The energy of photon E = hf

E = (4.136 × 10 -15 )( 1.25 × 10 15)   

Note: Planck’s constant in eV s = 4.136 × 10 -15  eV s

E = 5.17 eV.

b) The maximum kinetic energy related to the emitted electron is stopping potential. In this case, the stopping potential is 1.30V. So the maximum kinetic energy of the electrons is 1.30V.

Also Check out:  JEE Main Photoelectric Effect Previous Year Questions with Solutions

Important Points to Remember

• If we consider the light with any given frequency, the photoelectric current is generally directly proportional to the intensity of light. However, the frequency should be above the threshold frequency in such a case.
• Below threshold frequency, the emission of photoelectrons completely stops despite the high intensity of incident light.
• A photoelectron’s maximum kinetic energy increases with an increase in the frequency of incident light. In this case, the frequency should exceed the threshold limit. Maximum kinetic energy is not affected by the intensity of light.
• Stopping potential is the negative potential of the opposite electrode when the photo-electric current falls to zero.
• The threshold frequency is described as the frequency when the photoelectric current stops below a particular frequency of incident light.
• The photoelectric effect establishes the quantum nature of radiation. This has been taken into account to be proof in favour of the particle nature of light.

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21.2 Einstein and the Photoelectric Effect

Section learning objectives.

By the end of this section, you will be able to do the following:

• Describe Einstein’s explanation of the photoelectric effect
• Describe how the photoelectric effect could not be explained by classical physics
• Calculate the energy of a photoelectron under given conditions
• Describe use of the photoelectric effect in biological applications, photoelectric devices and movie soundtracks

Teacher Support

The learning objectives in this section will help your students master the following standards:

• (D) : explain the impacts of the scientific contributions of a variety of historical and contemporary scientists on scientific thought and society.
• (A) : describe the photoelectric effect and the dual nature of light.

Section Key Terms

The Photoelectric Effect

[EL]Ask the students what they think the term photoelectric means. How does the term relate to its definition?

When light strikes certain materials, it can eject electrons from them. This is called the photoelectric effect , meaning that light ( photo ) produces electricity. One common use of the photoelectric effect is in light meters, such as those that adjust the automatic iris in various types of cameras. Another use is in solar cells, as you probably have in your calculator or have seen on a rooftop or a roadside sign. These make use of the photoelectric effect to convert light into electricity for running different devices.

[BL] [OL] Discuss with students what may cause light to eject electrons from a material. Are there certain materials that are more susceptible to having electrons ejected?

[AL] Ask students why a light meter would be useful in a camera. How could the number of electrons emitted from the light meter control the camera’s iris? Have students draw a diagram of the camera that may demonstrate this effect.

Revolutionary Properties of the Photoelectric Effect

When Max Planck theorized that energy was quantized in a blackbody radiator, it is unlikely that he would have recognized just how revolutionary his idea was. Using tools similar to the light meter in Figure 21.5 , it would take a scientist of Albert Einstein ’s stature to fully discover the implications of Max Planck’s radical concept.

Through careful observations of the photoelectric effect, Albert Einstein realized that there were several characteristics that could be explained only if EM radiation is itself quantized . While these characteristics will be explained a bit later in this section, you can already begin to appreciate why Einstein’s idea is very important. It means that the apparently continuous stream of energy in an EM wave is actually not a continuous stream at all. In fact, the EM wave itself is actually composed of tiny quantum packets of energy called photons .

In equation form, Einstein found the energy of a photon or photoelectron to be

where E is the energy of a photon of frequency f and h is Planck’s constant. A beam from a flashlight, which to this point had been considered a wave, instead could now be viewed as a series of photons, each providing a specific amount of energy see Figure 21.6 . Furthermore, the amount of energy within each individual photon is based upon its individual frequency, as dictated by E = h f . E = h f . As a result, the total amount of energy provided by the beam could now be viewed as the sum of all frequency-dependent photon energies added together.

It is important for students to be comfortable with the material to this point before moving forward. To ensure that they are, one task that you may have them do is to draw a few pictures similar to Figure 21.6 . Have the students draw photons leaving a low intensity flashlight vs. a high intensity flashlight, a high frequency flashlight vs. a low frequency flashlight, and a high wavelength flashlight vs. a low wavelength flashlight. These diagrams will help ensure the students understand fundamental concepts before moving to the difficult proofs that follow.

Just as with Planck’s blackbody radiation, Einstein’s concept of the photon could take hold in the scientific community only if it could succeed where classical physics failed. The photoelectric effect would be a key to demonstrating Einstein’s brilliance.

Consider the following five properties of the photoelectric effect. All of these properties are consistent with the idea that individual photons of EM radiation are absorbed by individual electrons in a material, with the electron gaining the photon’s energy. Some of these properties are inconsistent with the idea that EM radiation is a simple wave. For simplicity, let us consider what happens with monochromatic EM radiation in which all photons have the same energy hf .

• If we vary the frequency of the EM radiation falling on a clean metal surface, we find the following: For a given material, there is a threshold frequency f 0 for the EM radiation below which no electrons are ejected, regardless of intensity. Using the photon model, the explanation for this is clear. Individual photons interact with individual electrons. Thus if the energy of an individual photon is too low to break an electron away, no electrons will be ejected. However, if EM radiation were a simple wave, sufficient energy could be obtained simply by increasing the intensity.
• Once EM radiation falls on a material, electrons are ejected without delay . As soon as an individual photon of sufficiently high frequency is absorbed by an individual electron, the electron is ejected. If the EM radiation were a simple wave, several minutes would be required for sufficient energy to be deposited at the metal surface in order to eject an electron.
• The number of electrons ejected per unit time is proportional to the intensity of the EM radiation and to no other characteristic. High-intensity EM radiation consists of large numbers of photons per unit area, with all photons having the same characteristic energy, hf . The increased number of photons per unit area results in an increased number of electrons per unit area ejected.
• If we vary the intensity of the EM radiation and measure the energy of ejected electrons, we find the following: The maximum kinetic energy of ejected electrons is independent of the intensity of the EM radiation . Instead, as noted in point 3 above, increased intensity results in more electrons of the same energy being ejected. If EM radiation were a simple wave, a higher intensity could transfer more energy, and higher-energy electrons would be ejected.
• The kinetic energy KE of an ejected electron equals the photon energy minus the binding energy BE of the electron in the specific material. An individual photon can give all of its energy to an electron. The photon’s energy is partly used to break the electron away from the material. The remainder goes into the ejected electron’s kinetic energy. In equation form, this is given by

where K E e K E e is the maximum kinetic energy of the ejected electron, h f h f is the photon’s energy, and BE is the binding energy of the electron to the particular material. The binding energy is also often called the work function of the material. This equation explains the properties of the photoelectric effect quantitatively and demonstrates that BE is the minimum amount of energy necessary to eject an electron. If the energy supplied is less than BE, the electron cannot be ejected. The binding energy can also be written as B E = h f 0 , B E = h f 0 , where f 0 f 0 is the threshold frequency for the particular material. Figure 21.8 shows a graph of maximum K E e K E e versus the frequency of incident EM radiation falling on a particular material.

Show students Figure 21.8 . What would be the kinetic energy of an electron if f is less than f 0 ? What does this mean? Why would this be the case? These questions aim to help students internalize the concept of binding energy.

Tips For Success

The following five pieces of information can be difficult to follow without some organization. It may be useful to create a table of expected results of each of the five properties, with one column showing the classical wave model result and one column showing the modern photon model result.

The table may look something like Table 21.1

It may be useful to complete the table above as a class. This material takes some time to interpret, so encourage students to move slowly. Once completed, your table may look like Table 21.2 .

Virtual Physics

Photoelectric effect.

In this demonstration, see how light knocks electrons off a metal target, and recreate the experiment that spawned the field of quantum mechanics.

Grasp Check

In the circuit provided, what are the three ways to increase the current?

• increase the intensity, increase the wavelength, alter the target
• decrease the intensity, increase the wavelength, alter the target
• decrease the intensity, decrease the wavelength, alter the target
• increase the intensity, decrease the wavelength, alter the target

Worked Example

Photon energy and the photoelectric effect: a violet light.

(a) What is the energy in joules and electron volts of a photon of 420-nm violet light? (b) What is the maximum kinetic energy of electrons ejected from calcium by 420 nm violet light, given that the binding energy of electrons for calcium metal is 2.71 eV?

To solve part (a), note that the energy of a photon is given by E = h f E = h f . For part (b), once the energy of the photon is calculated, it is a straightforward application of K E e = h f − B E K E e = h f − B E to find the ejected electron’s maximum kinetic energy, since BE is given.

Photon energy is given by

E = h f . E = h f .

Since we are given the wavelength rather than the frequency, we solve the familiar relationship c = f λ c = f λ for the frequency, yielding

Combining these two equations gives the useful relationship

Now substituting known values yields

Converting to eV, the energy of the photon is

Finding the kinetic energy of the ejected electron is now a simple application of the equation K E e = h f − B E K E e = h f − B E . Substituting the photon energy and binding energy yields

The energy of this 420 nm photon of violet light is a tiny fraction of a joule, and so it is no wonder that a single photon would be difficult for us to sense directly—humans are more attuned to energies on the order of joules. But looking at the energy in electron volts, we can see that this photon has enough energy to affect atoms and molecules. A DNA molecule can be broken with about 1 eV of energy, for example, and typical atomic and molecular energies are on the order of eV, so that the photon in this example could have biological effects, such as sunburn. The ejected electron has rather low energy, and it would not travel far, except in a vacuum. The electron would be stopped by a retarding potential of only 0.26 eV, a slightly larger KE than calculated above. In fact, if the photon wavelength were longer and its energy less than 2.71 eV, then the formula would give a negative kinetic energy, an impossibility. This simply means that the 420 nm photons with their 2.96 eV energy are not much above the frequency threshold. You can see for yourself that the threshold wavelength is 458 nm (blue light). This means that if calcium metal were used in a light meter, the meter would be insensitive to wavelengths longer than those of blue light. Such a light meter would be completely insensitive to red light, for example.

Practice Problems

What is the longest-wavelength EM radiation that can eject a photoelectron from silver, given that the bonding energy is 4.73 eV ? Is this radiation in the visible range?

• 2.63 × 10 −7 m; No, the radiation is in microwave region.
• 2.63 × 10 −7 m; No, the radiation is in visible region.
• 2.63 × 10 −7 m; No, the radiation is in infrared region.
• 2.63 × 10 -7 m; No, the radiation is in ultraviolet region.

What is the maximum kinetic energy in eV of electrons ejected from sodium metal by 450-nm EM radiation, given that the binding energy is 2.28 eV?

Technological Applications of the Photoelectric Effect

While Einstein’s understanding of the photoelectric effect was a transformative discovery in the early 1900s, its presence is ubiquitous today. If you have watched streetlights turn on automatically in response to the setting sun, stopped elevator doors from closing simply by putting your hands between them, or turned on a water faucet by sliding your hands near it, you are familiar with the electric eye , a name given to a group of devices that use the photoelectric effect for detection.

All these devices rely on photoconductive cells. These cells are activated when light is absorbed by a semi-conductive material, knocking off a free electron. When this happens, an electron void is left behind, which attracts a nearby electron. The movement of this electron, and the resultant chain of electron movements, produces a current. If electron ejection continues, further holes are created, thereby increasing the electrical conductivity of the cell. This current can turn switches on and off and activate various familiar mechanisms.

One such mechanism takes place where you may not expect it. Next time you are at the movie theater, pay close attention to the sound coming out of the speakers. This sound is actually created using the photoelectric effect! The audiotape in the projector booth is a transparent piece of film of varying width. This film is fed between a photocell and a bright light produced by an exciter lamp. As the transparent portion of the film varies in width, the amount of light that strikes the photocell varies as well. As a result, the current in the photoconductive circuit changes with the width of the filmstrip. This changing current is converted to a changing frequency, which creates the soundtrack commonly heard in the theater.

Work In Physics

Solar energy physicist.

According to the U.S. Department of Energy, Earth receives enough sunlight each hour to power the entire globe for a year. While converting all of this energy is impossible, the job of the solar energy physicist is to explore and improve upon solar energy conversion technologies so that we may harness more of this abundant resource.

The field of solar energy is not a new one. For over half a century, satellites and spacecraft have utilized photovoltaic cells to create current and power their operations. As time has gone on, scientists have worked to adapt this process so that it may be used in homes, businesses, and full-scale power stations using solar cells like the one shown in Figure 21.9 .

Solar energy is converted to electrical energy in one of two manners: direct transfer through photovoltaic cells or thermal conversion through the use of a CSP, concentrating solar power, system. Unlike electric eyes, which trip a mechanism when current is lost, photovoltaic cells utilize semiconductors to directly transfer the electrons released through the photoelectric effect into a directed current. The energy from this current can then be converted for storage, or immediately used in an electric process. A CSP system is an indirect method of energy conversion. In this process, light from the Sun is channeled using parabolic mirrors. The light from these mirrors strikes a thermally conductive material, which then heats a pool of water. This water, in turn, is converted to steam, which turns a turbine and creates electricity. While indirect, this method has long been the traditional means of large-scale power generation.

There are, of course, limitations to the efficacy of solar power. Cloud cover, nightfall, and incident angle strike at high altitudes are all factors that directly influence the amount of light energy available. Additionally, the creation of photovoltaic cells requires rare-earth minerals that can be difficult to obtain. However, the major role of a solar energy physicist is to find ways to improve the efficiency of the solar energy conversion process. Currently, this is done by experimenting with new semi conductive materials, by refining current energy transfer methods, and by determining new ways of incorporating solar structures into the current power grid.

Additionally, many solar physicists are looking into ways to allow for increased solar use in impoverished, more remote locations. Because solar energy conversion does not require a connection to a large-scale power grid, research into thinner, more mobile materials will permit remote cultures to use solar cells to convert sunlight collected during the day into stored energy that can then be used at night.

Regardless of the application, solar energy physicists are an important part of the future in responsible energy growth. While a doctoral degree is often necessary for advanced research applications, a bachelor's or master's degree in a related science or engineering field is typically enough to gain access into the industry. Computer skills are very important for energy modeling, including knowledge of CAD software for design purposes. In addition, the ability to collaborate and communicate with others is critical to becoming a solar energy physicist.

What role does the photoelectric effect play in the research of a solar energy physicist?

• The understanding of photoelectric effect allows the physicist to understand the generation of light energy when using photovoltaic cells.
• The understanding of photoelectric effect allows the physicist to understand the generation of electrical energy when using photovoltaic cells.
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How Well Do Popular Bicycle Helmets Protect from Different Types of Head Injury?

• S.I. : Concussions II
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• Published: 19 September 2024

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• C. E. Baker   ORCID: orcid.org/0000-0001-9729-6087 1 ,
• X. Yu 1 , 2 ,
• B. Lovell 1 ,
• S. Patel 1 &
• M. Ghajari 1  

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Bicycle helmets are designed to protect against skull fractures and associated focal brain injuries, driven by helmet standards. Another type of head injury seen in injured cyclists is diffuse brain injuries, but little is known about the protection provided by bicycle helmets against these injuries. Here, we examine the performance of modern bicycle helmets in preventing diffuse injuries and skull fractures under impact conditions that represent a range of real-world incidents. We also investigate the effects of helmet technology, price, and mass on protection against these pathologies. 30 most popular helmets among UK cyclists were purchased within 9.99–135.00 GBP price range. Helmets were tested under oblique impacts onto a 45° anvil at 6.5 m/s impact speed and four locations, front, rear, side, and front-side. A new headform, which better represents the average human head’s mass, moments of inertia and coefficient of friction than any other available headforms, was used. We determined peak linear acceleration (PLA), peak rotational acceleration (PRA), peak rotational velocity (PRV), and BrIC. We also determined the risk of skull fractures based on PLA (linear risk), risk of diffuse brain injuries based on BrIC (rotational risk), and their mean (overall risk). Our results show large variation in head kinematics: PLA (80–213 g), PRV (8.5–29.9 rad/s), PRA (1.6–9.7 krad/s 2 ), and BrIC (0.17–0.65). The overall risk varied considerably with a 2.25 ratio between the least and most protective helmet. This ratio was 1.76 for the linear and 4.21 for the rotational risk. Nine best performing helmets were equipped with the rotation management technology MIPS, but not all helmets equipped with MIPS were among the best performing helmets. Our comparison of three tested helmets which have MIPS and no-MIPS versions showed that MIPS reduced rotational kinematics, but not linear kinematics. We found no significant effect of helmet price on exposure-adjusted injury risks. We found that larger helmet mass was associated with higher linear risk. This study highlights the need for a holistic approach, including both rotational and linear head injury metrics and risks, in helmet design and testing. It also highlights the need for providing information about helmet safety to consumers to help them make an informed choice.

Avoid common mistakes on your manuscript.

Introduction

Cycling is an active mode of mobility with significant health and environmental benefits. In England, there has been a significant upward trend in cycling since 2002 [ 1 ]. Despite many health, environmental, and independent travel benefits, there can be a risk of trauma in bicycle falls and collisions. In Great Britain, cyclists had a reduction in fatalities in 2021 (down 21%) compared with a significant peak during the 2020 COVID-19 pandemic. Despite this reduction, cyclist fatalities in 2021 remained higher than the 2017 to 2019 average (increase of 17%) [ 2 ]. Head injuries are a key cause of fatal and life-changing injuries in cyclists [ 3 ]. Some cyclists choose to wear a helmet as a key line of defense against head injuries if they are involved in a collision or fall. Several previous studies, including a large meta-analysis of data relating to 64,000 cyclists, have shown that helmets have a protective effect to the head against head injury (including serious and fatal injury) and facial injury in cycle incidents, such as collisions and falls [ 3 , 4 ]. In particular, helmet use has been found to reduce the risk of skull fractures, hemorrhages (extradural, subdural, subarachnoid, intraparenchymal, and intraventricular) and facial fractures when a cyclist is involved in a collision or fall event [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 ].

All helmets which come to market must pass a minimum safety threshold, set out by standards [ 14 , 15 , 16 , 17 , 18 , 19 , 20 ]. At the time of publication, current standards use metrics based on linear motion of the head to assess the safety of helmets. These metrics can assess the protection of helmets against head injuries caused by linear mechanisms, such as skull fractures and associated focal injuries, including extradural haematoma [ 21 ]. Rotational motion is also a known head injury mechanism, leading to diffuse brain injuries and hemorrhage [ 22 , 23 , 24 ]. New initiatives in the injury biomechanics field have led to a better understanding of rotational effects on brain injury outcomes, particularly diffuse brain injuries which are seen in cyclists [ 3 ]. Injured cyclists are commonly reported to lose consciousness [ 25 , 26 ]. Loss of consciousness (LOC) is associated with rotational motion [ 23 , 27 ]. LOC can occur across a broad range of head injury severities, with a range of long-term outcomes. In more severe instances, cyclists can sustain another rotationally driven injury, diffuse axonal injury (DAI), which often results in unfavorable long-term outcomes [ 28 , 29 , 30 ]. Cyclists also sustain subdural haematoma, which is strongly associated with rotational motion [ 11 , 13 , 22 , 31 ]. Despite the importance of rotational effects and the broad range of head injuries sustained by cyclists, which can be attributed to them, rotational motion is not yet assessed in current standards.

A few recent studies have assessed the performance of bicycle helmets under oblique impacts, which better represent real-world incidents and produces larger head rotation [ 32 , 33 , 34 , 35 ]. These studies show a wide range of performance measured with metrics based on head translation and rotation, including peak linear acceleration (PLA), peak rotational acceleration (PRA), peak rotational velocity (PRV), and the brain injury criterion (BrIC) [ 36 ]. However, these studies use the HIII headform, which has biofidelity shortcomings. For example, the HIII headform has a large coefficient of friction, leading to overprediction of head rotational metrics [ 37 ]. A state-of-the-art, more biofidelic headform that can measure linear and rotational motion of the head more accurately has been developed recently. The key physical properties of this headform, including coefficient of friction, mass, and mass moments of inertia, better represent those of the medium human head than the HIII headform [ 37 ]. Hence, the new headform is better able to assess head protection performance of helmets. The development of the headform has been underpinned by international groups of experts at the CEN/TC158/WG11 working group to shape future helmet standards like cycle helmet standard, EN1078. This biofidelic headform provides a new opportunity for assessing the performance of bicycle helmets using more biofidelic lab test methods.

The aim of this study is to determine the performance of a range of bicycle helmets under oblique impacts using the new, biofidelic headform. We provide the ranges of linear and rotational head kinematics for 30 popular helmets used by cyclists in the UK. A widely adopted head rotation management technology is MIPS (Multi-direction Impact Protection System). Previous work with the Hybrid III headform has shown MIPS to provide protection against rotation [ 38 , 39 ]. Here, we test whether this remains the case with the newly adopted headform, which has a lower coefficient of friction and more accurate moments of inertia than the HIII headform. In the absence of more objective ways to compare helmet performance, consumers may rely on helmet price as the indicator of safety [ 40 , 41 ]. Hence, we also test whether there is a relationship between helmet price and its linear, rotational and overall performance. Mass is a factor considered to be important in the road cycling community. We therefore investigate whether mass influences linear, rotational or overall risk.

An overview of the test method is shown in Fig. 1 . The following sections explain each component of the test method.

The test method summary. a The Cellbond-CEN 2022 headform. b Each helmet was tested at four locations. c For each test, three components of head linear acceleration and rotational velocity time-history were recorded. The rotational velocities were differentiated to obtain the rotational accelerations. d Data were analyzed to derive kinematics-based injury metrics, two of which were used to calculate the linear risk and rotational risk, with mean of these risks representing the overall risk

The New Headform

For testing helmets, we used a new headform manufactured by Cellbond, a division of Encocam Limited, under the instruction of the European Committee for Standardization Working Group 11 (CEN/TC158/WG11). The Cellbond-CEN headform is made of nylon through an injection molding process. The significant advantage of this headform over previous headforms, such as the Hybrid III and EN960 headform, is its improved biofidelity in terms of the moments of inertia (MoIs) and coefficient of friction (CoF) of the headform surface (for more details please see [ 37 ]). MoIs and CoF of the headform are key factors in determining its rotational motion during helmeted head impacts [ 37 , 42 , 43 , 44 ]. In a recent study, we compared the kinematics of an earlier version of the Cellbond-CEN headform with the Hybrid III headform in various oblique impact scenarios while wearing helmets [ 37 ]. The Cellbond-CEN headform produced much lower peak rotational kinematics than the Hybrid III headform. These results emphasize the importance of incorporating realistic MoIs and CoF to accurately assess helmet performance.

In this study, we used a version of the Cellbond-CEN headform, manufactured in 2022, which includes two further improvements (Fig. 1 a): (i) the headform has a realistic head and face geometry derived from data of a large human population [ 37 ] and (ii) the headform has a small portion of the neck, in contrast to the HIII headform, ensuring a more realistic interaction between the chin strap and the neck. The physical properties of this version of the headform are provided in Table 1 .

Helmet Impact Conditions

The impact test conditions involved three factors: impact speed, impact angle, and impact location [ 46 ]. The values of these three factors were aligned with previous studies and supported by the findings in our recent, extensive literature review investigating cyclist head injury and impact characteristics [ 3 , 32 , 37 , 45 , 47 ]. Our literature review revealed that the head impact speed resulted from cyclist-ground impacts is concentrated around 6.5 m/s. In addition, the reviewed literature showed that the head impact angle (the angle between the impact velocity and the ground) is often between 30° and 60°. Hence, we chose a 6.5 m/s impact speed and a 45° impact angle.

Supported by previous studies and our literature review, we conducted helmet testing at four specific locations [ 3 , 48 , 49 , 50 ]: left (pXR configuration), front (pYR configuration), rear (nYR configuration), and front-left (pZR configuration), as illustrated in Fig. 1 b. Each impact location induced rotational motions predominantly about the specific axis of the headform which the impact location is named after.

Helmet Impact Test Method

The oblique impact tests were conducted with the drop tower helmet test rig at the Human Experience, Analysis and Design (HEAD) Lab, Imperial College London. The test rig has been purposely built and previously used for testing helmets under various conditions [ 37 , 46 , 51 ]. The bicycle helmet (with visor attached if applicable) was securely fitted onto the headform following the manufacturer’s instructions. To ensure consistency, a distance of 27.5 mm was maintained between the edge of the helmet and the upper edge of the eye orbit marked on the headform (Fig. 1 ). The chin strap was then tightened in accordance with normal usage. Prior to tightening, a rigid cylinder with a diameter of 10 mm was placed between the chin and the strap and subsequently removed once the strap was tightened.

Next, the helmeted headform was positioned on a free-falling U-shape testing platform. To ensure proper alignment, we used an inclinometer to adjust the orientation of the headform (Fig. 1 a). The goal across all test configurations was to achieve a nearly horizontal position with an inclination of 0° ± 1° for pXR/pYR/nYR or an inclination of 65° ± 1° for the pZR test. We then used a gripper to hold the helmet onto the platform, maintaining the helmet’s position and orientation during the free fall (Fig. 1 a). The gripper was released by a mechanical trigger just prior to the helmet-anvil impact.

Helmets were dropped onto a metal anvil, with a 130 mm diameter and 45° inclined surface. The anvil was covered with an 80-grit abrasive paper to simulate the road surface, as suggested in previous studies and helmet test standards [ 46 , 52 , 53 , 54 ]. The impact speed was recorded using a photoelectric sensor trigger system, which also triggered the video capture. A high-speed video camera was placed behind the anvil to record the impacts at a rate of 3500 frames per second. Following each test, the high-speed video was examined to verify that the helmet maintained its intended orientation and position on the platform until impact with the anvil.

For each helmet model, we conducted the four impact tests using two helmet samples. pXR and pYR were performed on helmet sample 1, and nYR and pZR were performed on helmet sample 2. The closest impact points (i.e., nYR and pZR) are at least 135° apart from each other. This is to ensure that the impact locations were separated from each other to minimize the influence of accumulated damage on the subsequent tests. To enhance the reliability of our results, each test was repeated three times using three different samples. Therefore, each helmet required 12 tests performed on 6 samples.

Kinematic Data Capture and Processing

The headform was equipped with a DTS 6DX PRO sensor package along with a wireless datalogger system. This sensor package enabled the measurement of linear accelerations and rotational velocities along the three axes (Fig. 1 c). Linear accelerations and rotational velocities were measured for 0.5 s either side of the time of impact at a sampling frequency of 20 kHz. All linear accelerations were filtered at CFC600 and rotational velocities were filtered at CFC180 according to ISO 6487 [ 55 ]. All signals were filtered before they were combined or used to derive other kinematic metrics, including calculating the resultant values and obtaining rotational acceleration via differentiating rotational velocity (Fig. 1 d). We investigated N-point moving average to differentiate the filtered rotational velocity to obtain rotational acceleration. There was minimal difference between the peak rotational acceleration values obtained via the 1-point (no smoothing), 3-point, and 5-point moving averages, and therefore 1-point was adopted. Python was used to filter and differentiate the test data and perform subsequent analysis. The filtering was conducted using a fourth order Butterworth phaseless digital filter function (written according to SAE J211-1) [ 56 ]. The differentiation was done without any smoothing using the numpy library “gradient” function [ 57 ]. We extracted peak values of linear and rotational acceleration (PLA and PRA), rotational velocity (PRV), and BrIC. The mean value, averaged across all repeats for a given helmet and test configuration, were calculated as well as the standard deviation and coefficient of variation (CV).

Injury Risk Calculation

Helmeted cyclists sustain both focal and diffuse brain injuries [ 3 , 4 ]. Hence, we incorporated methods for evaluating the risk of these injuries from the measured head kinematics (Fig. 1 d). We used the peak linear acceleration (PLA) to predict the risk of skull fractures and associated focal injuries. The focal injury risk function was based on a recent work where 30 elderly vulnerable road user collisions were reconstructed and a risk function for PLA at AIS4+ severity was produced [ 58 ]. Out of the 20 cases with AIS4+, 19 suffered skull fracture, SAH or contusions, which were predicted by PLA. Since the risk function was established using data from older casualties (60+), we adjusted it by multiplying PLA by the ratio of PLA of older population to the general population at 50% risk of AIS4+. We used the threshold adopted by helmet standards for the latter, i.e., 250 g [ 59 ] and 200 g for the former [ 60 ], leading to the following risk function:

\({a}_{x}(t)\) , \({a}_{y}(t)\) , and \({a}_{z}\left(t\right)\) represent the components of the head linear acceleration measured at the CoG.

We also used the injury metric based on head rotational velocities, BrIC, to predict the risk of diffuse injuries [ 36 ]. It has been shown that BrIC has a strong correlation with the maximum principal strain within the brain, produced in cycle helmet oblique impacts [ 61 ]. In addition, brain strain is shown to predict diffuse brain injuries, including white matter damage [ 62 , 63 , 64 , 65 ]. Risk functions have been developed for BrIC based on different definitions of brain strain (maximum principal strain, or MPS, and cumulative strain damage metric). These risk curves have been produced based on large animal experiments scaled to the human. The original risk curves were developed for severe diffuse brain injuries observed in animals, which were assumed to be of AIS4+ severity. These curves were scaled to obtain risk curves for other severities. We used the MPS-based BrIC risk function for AI2+ severity to evaluate the performance of helmets in preventing diffuse brain injuries [ 36 ]. This function is as follows:

\({\omega }_{x}\left(t\right)\) , \({\omega }_{y}\left(t\right)\) , and \({\omega }_{z}\left(t\right)\) are the components of the head rotational velocity. \({\omega }_{xC}\) = 66.25 rad/s, \({\omega }_{yC}\) = 56.45 rad/s, and \({\omega }_{zC}\) = 42.87 rad/s are the critical values of rotational velocity. These critical values were calculated such that they corresponded to 50% risk of severe diffuse axonal injuries in large animals [ 36 ].

After evaluating the risk of focal (linear) and diffuse (rotational) injuries for each impact location, we combined them to obtain an overall risk for each impact location. As there is currently insufficient data available to provide accurate weighting of these two types of injuries [ 3 ], we allocated them a 0.5 weighting to determine an overall injury risk for each impact location:

Finally, we used the weighting of each impact location determined from a meta-analysis of real-world cycle incident data to determine the overall injury risk for the helmet:

The meta-analysis included three studies that followed the same convention for defining the impact location, with a total number of 815 impact locations recorded [ 3 ]. The analysis provided the impact frequency for different helmet regions, namely front, side, rear, and crown. It showed that the crown is the least frequently impacted area. We used the weighting for the four impact configurations, pXR, pYR, nYR, and pZR. The pYR and pZR are both within the front region of the helmet as defined in the meta-data analysis. Hence, we equally split the weighting of front impacts between them. The weightings are provided in Table 2 .

Selecting Popular Helmets

Two approaches were combined to select a cohort of 30 helmets that included the most popular helmets purchased by UK consumers. Firstly, we used best-selling lists of major retailers, which yielded 10 helmets. 3 additional helmets with an additional protective technology, MIPS, were selected from the best-selling list to provide comparison. We additionally surveyed a broad cyclist population to yield a further 17 helmets. Importantly, all these helmets meet the European standard EN 1078.

Helmets Selected from Popular Retailers’ Best-Selling Lists

Halfords and Decathlon are two of the largest in-store and online helmet providers in the UK. On each respective retailer’s website, adult cycling helmets were sorted using the “Best-Selling” function and the popularity of each helmet by website was recorded accordingly as a “Selling Rank” (as accessed in May 2022). Mountain biking-only, full-face, and time-trial helmets were removed from the longlist, resulting in a list of 76 helmets. The top 10 best-selling helmets were identified from the combined best-selling list (Table 3 ). In addition, 3 helmets from the top 10 had counterpart models which use MIPS, namely Lazer Compact DLX MIPS, Giro Angon MIPS, and Lazer Tonic MIPS. These helmets were additionally included to allow direct comparison between MIPS and non-MIPS versions of the same helmet.

Cyclist Helmet Use Survey Design and Distribution for Helmet Selection

We surveyed UK cyclists to determine more information about their cycling habits, including helmet use and preferences. In line with Imperial College London’s ethics requirements, a survey was approved by the Head of Department for the Dyson School of Design Engineering and Research Governance Integrity Team (RGIT). The survey was circulated widely across various social media platforms to a large range (> 50) of online groups designed for cyclists. A significant effort was made to distribute the survey to groups attracting and consisting of a range of geographic locations, ages, genders, races, and other demographics. The survey invited any cyclists who owned or wore a helmet any proportion of the time to list the helmet make and model they use (if known). The following questions were used to obtain information about UK cyclist helmet-related preferences:

Do you wear a helmet when you cycle?

Do you own a cycling helmet?

What is the retail price of your current helmet?

What is the model name and brand of your current cycle helmet?

Cyclist Helmet Survey Responses Informing Helmet Selection: Helmets and Their Prices

Of 1132 respondents, 1060 (93.6%) wore a helmet at least some of the time. Interestingly, a greater proportion owned a helmet (1083, 95.7%) all of whom provided information about the current retail price of the helmet. Around half (532/1083, 49.1%) of respondents who owned helmets provided information about the make or model of helmet. A frequency distribution was created, resulting in a list of popular helmets among survey respondents. Seven of the helmets already selected via the best-selling lists were present. Secondly, the survey results were used to better understand the price of helmets commonly worn by respondents. For each unique listed helmet, a corresponding retail price at the time of purchase selection (May 2022) was identified. The continuous distribution was subsequently classified into price bands, allowing for a distribution of cycling helmet prices to be obtained. This price distribution was then populated with the most popular road cycling helmets highlighted in the survey. Further details including figures can be found in the Appendix. The Btwin 100 City (£9.99) ranked eighth was unable to be purchased. This was replaced with another popular helmet, the Specialized Tactic MIPS (shown at the bottom of Table 4 ).

Statistical Analysis

The mean value, averaged across all repeats for a given helmet, were calculated as well as the standard deviation and coefficient of variation (CV). The CV was used to assess helmet test variability across all kinematic metrics. To directly compare a cohort of helmets composed of the same helmets with and without MIPS, the Mann-Whitney U test was used due to its ability to account for non-parametric data.

Ordinary least square (OLS) linear models from the Python package ‘statsmodels’ were used to investigate the influence of different factors on injury risk [ 66 ]. Three separate OLS models were considered. The first OLS model investigates the influence of impact location, mass, price, presence of MIPS, and distinct helmet model on the location-specific overall risk of injury associated with each test repeat, referred to previously as \(P\left(\text{injury }@ \text{location}\right)\) . This enables the influence of impact location to be understood in conjunction with other listed factors. The input data included all test repeats collected from 360 tests (all helmets, impact locations and repeats). The mean overall risk at a specific location was used as a baseline for the inter-helmet comparison. In order to compare the influence of impact location, the non-exposure-weighted overall risk was used. The pXR impact location was selected as the baseline impact location as it occurs most frequently in real-world impacts [ 3 ]. The second OLS model investigates the influence of almost the same parameters (only impact location is necessarily excluded) on the helmet-specific risk, referred to earlier as \(P\left(\text{injury }@\text{ helmet}\right)\) . The third OLS model investigates how individual parameters (e.g., purchase price and mass) are affected by linear and/or rotational motion. The helmet mass was taken from online vendors of the helmets. In all instances, we ensure that the assumptions of OLS models (linearity, no multicollinearity, no autocorrelation, homoscedasticity, and a normal distribution of errors) are upheld via the Omnibus and Jarque-Bera tests [ 67 , 68 , 69 , 70 ].

Overview of the Head Kinematics

Figure 2 shows a snapshot from high-speed footage at 20 ms following the helmet/anvil contact initiation. The headform rotation about the x -axis at this time point is noticeable. This figure shows the difference in headform rotation across different helmets, e.g., a large rotation of the headform fitted with helmet 16 compared with helmet 27.

High-speed footage showing helmet response to impact at 20 ms following the helmet/anvil contact initiation. The pXR configuration is shown

The head kinematic distributions of the whole tested helmet population for all impact locations and repeats are shown in Fig. 3 . Each low transparency line represents one helmet drop. The variation in the headform kinematics can be seen by the faded distributions. This figure shows that the duration of impacts is 10–15 ms. It also shows some trends across impact locations. For instance, larger variation in linear acceleration can be seen in nYR impacts than other impact locations. In addition, when looking at the rotational velocity curves, the results are more homogenous for the pZR impact than the other three impact locations. This figure shows that some helmets produce distinctly lower rotational velocities than the rest of the helmets in pYR, pXR, and nYR impacts.

Time-history of head kinematics, showing resultant linear acceleration, resultant rotational acceleration and resultant rotational velocity for all helmets and impact locations

Good Repeatability of the Tests

The coefficient of variation (CV) was below 10% for the majority of helmets, impact locations, and kinematic metrics (Fig. 4 ). 86.9% (417/480) of CVs across all metrics were below 10%, which includes 93.3% of PLA CVs, 91.7% of PRV and BrIC CVs, and 70.8% of PRA CVs. 98.5% (473/480) of CVs across all metrics were below 20%. The CV is generally higher for PRA than other metrics [CV PLA < CV PRA: U  = 3483.0, p  < 0.000; CV PRV < CV PRA: U  = 3511.0, p  < 0.0001; CV BrIC < CV PRA: U  = 3328.0, p  < 0.0001]. Except for a few helmets and impact locations, the CV for the other metrics was low and does not differ significantly between any other kinematics metrics, showing the good test repeatability.

The coefficient of variation of head kinematics metrics for all helmets and impact locations

Different test locations had different CV distributions. In general, nYR and pYR tests had lower CV across all metrics, while pXR and pZR were higher. For all metrics, pYR had the lowest variability [pYR < pXR: U  = 4905.0, p  < 0.0001; pYR < pZR: U  = 4414.0, p  < 0.0001; pYR < nYR: U  = 6213.0, p  = 0.0333]. In addition, nYR variability was lower when compared to pXR and pZR [nYR < pXR: U  = 5710.0, p  = 0.0028; nYR < pZR U  = 5040.0, p  < 0.0001]. When using a linear model to investigate the interaction between impact location and kinematic metric on CV, the pXR and pZR tests in addition to PRA increased the CV [location = pXR, t  = 2.629, p  < 0.001; location = pZR, t  = 2.897, p  = 0.004; metric = PRA, t  = 7.448, p  < 0.001]. A full summary can be found in “ Appendix 2 ”.

Head Kinematics Metrics and Injury Risks for Different Helmets

The head kinematics metrics and injury risks vary across the different helmets and impact locations, as shown in Figs. 5 and 6 . The ranges of head kinematics and injury risks are provided in Table 5 for each impact location and across all locations, showing large differences between lowest and highest values recorded across all kinematics metrics and injury risks.

The head kinematics metrics for all helmets and impact locations; the mean value and standard deviation are shown

The head injury risks for all helmets and impact locations. The linear risk is based on PLA, the rotational risk is based on BrIC, and the overall risk is the average of these risks

Distinct Effect of Impact Location on Head Kinematic Metrics and Injury Risks

The mean PLA across all helmets and repeats was highest in the pXR impact location (159.9 g) than other impact locations (pYR: 147.7 g, pZR: 134.3 g, nYR: 131.1 g) (Fig. 7 ). The PLA across all tests in the pXR impact location was significantly higher than the tests in the other three impact locations [pXR > pYR: U  = 5255.0, p  = 0.0003; pXR > pZR: U  = 6299.0, p  < 0.0001; pXR > nYR: U  = 6184.0, p  < 0.0001]. Additionally, the PLA in the pYR impact location was significantly higher than in the nYR and pZR locations [nYR < pYR: U  = 2857.0, p  = 0.0003; pZR < pYR: U  = 2761.0, p  = 0.0001].

The distributions of head kinematics and risk metrics separated by impact location. The risks shown are not exposure-weighted and follow the definition of \(\text{P}\left(\text{injury }@\text{ location}\right)\) set out in the method section

The mean PRA across all helmets and repeats was highest in the pZR (6.31 krad/s 2 ) impact location, followed by the pYR (5.94 krad/s 2 ), nYR (4.69 krad/s 2 ), and finally lowest in the pXR impact location (4.15 krad/s 2 ). Statistically, the PRA across all tests at pXR was lower when compared to test conducted at the other three impact locations [pXR < pYR: U  = 1630.0, p  < 0.0001; pXR < pZR: U  = 1054.0, p  < 0.0001; pXR < nYR: U  = 2975.0, p  = 0.0010]. The PRA of the nYR tests was lower than for the pZR and the pYR tests [nYR < pZR: U  = 6131.0, p  < 0.0001; nYR < pYR: U  = 2407.0, p  < 0.0001].

The mean PRV for the nYR location was highest (24.4 rad/s), followed by pYR (24.1 rad/s), pZR (22.8 rad/s) and finally pXR (17.2 rad/s). Statistically, the PRV across all repeats and helmets was significantly lower for pXR than the other three impact locations [pXR < pYR: U  = 686.0, p  < 0.0001; pXR < pZR: U  = 1263.0, p  < 0.0001; pXR < nYR: U  = 832.0, p  < 0.0001]. The PRV was lower across all tests at pZR than the nYR and pYR locations [pZR < nYR: U  = 2761.0, p  = 0.0001; pZR < pYR: U  = 2958.0, p  = 0.0008].

The mean BrIC across all helmets and repeats was highest in the pZR (0.523) impact location, followed by the pYR (0.450), nYR (0.436), and finally lowest in the pXR impact location (0.272). When comparing all tests at a given impact location statistically, pZR tests produced higher BrIC across all tests [pZR > nYR: U  = 6254.0, p  < 0.0001; pZR > pYR: U  = 6434.0, p  < 0.0001; pXR < pZR: U  = 91.0, p  < 0.0001].

Since the linear and rotational injury risks are monotonic functions of PLA and BrIC, respectively, the impact location has the same effect on these risks as it has on PLA and BrIC. Most notably, the largest linear risk was seen in pXR impacts [pXR > pYR: U  = 5255.0, p  = 0.0003; pXR > pZR: U  = 6299.0, p  < 0.0001; pXR > nYR: U  = 6184.0, p  < 0.0001] (Fig. 7 ). The largest rotational risk was seen in pZR impacts [pZR > nYR: U  = 6254.0, p  < 0.0001; pZR > pYR: U  = 6434.0, p  < 0.0001; pZR > pXR: U  = 91.0, p  < 0.0001]. The largest overall risk was seen in pZR impacts [pZR > nYR: U  = 6215.0, p  < 0.0001; pZR > pYR: U  = 6079.0, p  < 0.0001; pZR > pXR: U  = 563.0, p  < 0.0001].

The OLS model built to investigate the influence of impact location, helmet type, mass, price, and presence of MIPS on non-exposure-adjusted overall risk, \(P\left(\text{injury}@\text{location}\right)\) , confirmed that pYR, nYR, and pZR all differed significantly from pXR. Significantly higher overall risk was seen in pYR [coefficient: 0.0960, t  = 16.7, p  < 0.001], nYR [coefficient: 0.0883, t  = 15.3, p  < 0.001] and pZR [coefficient: 0.1635, t  = 16.7, p  < 0.001] when compared to the pXR baseline. The coefficients show that the overall risk is approximately 0.1 higher for pYR and nYR compared to pXR, and 0.17 higher for pZR (the location with the highest associated risk). The findings related to other OLS model parameters are detailed within the relevant sections.

Exposure Weighted Linear, Rotational, and Overall Injury Risk: Ranking of Helmets

Finally, we used the impact location weighting to calculate one value for the linear, rotational, and overall risk for each helmet type, \(P(\text{injury}@\text{helmet})\) and rank them based on the overall risk (Table 6 ). We observed a larger variation in rotational risk than the linear risk, as shown in Fig. 8 . The worst performing helmet of the 30 cohort (rank #30) had a 2.62 times higher overall injury risk compared to the best performing helmet (rank #1). When considering the linear and rotational components of the overall worst and best performing helmets, this ratio was 1.76 for the linear risk and 4.21 for the rotational risk.

A visualization of the influence of linear and rotational risk on the overall risk rank and values. The first subplot shows (from left to right) linear, overall, and rotational risk ranks while the second subplot shows (from left to right) linear, overall, and rotational risk values including their distributions. The colored table at the base acts as a color-coded reference to the helmets on the plot

Of the 9 helmets which had rotational risk lower than the mean rotational risk of 0.256, 6 (66.7%) were also below the mean linear risk of 0.175, including the 6 helmets with the lowest rotational and overall risks. However, of the 15 helmets that had linear risk lower than the mean linear risk of 0.175, only 6 (40%) were also below the mean rotational risk of 0.257. A single variate OLS model predicting rotational risk using linear risk suggests there is a trend toward lower rotational risk being associated with lower linear risk, significant at p  = 0.10 level but not p  = 0.05 level [coefficien t  = 0.173, t  = 2.0, p  = 0.055].

MIPS Reduces Rotational Kinematics and Risk

Ten of the top eleven most protective helmets in terms of overall risk had the MIPS add-on technology (Table 6 ). MIPS was a factor included in the non-exposure-weighted OLS model that also included helmet model, price, and mass. The presence of MIPS reduced overall non-location weighted risk by 0.0729 [ t  = − 21.3, p  < 0.001].

To investigate whether MIPS was causal in this protective effect, we compared the three helmets which had models with and without MIPS using Mann–Whitney U tests (Table 7 ). Across all 72 tests conducted at different impact locations for the three helmets with and without MIPS, MIPS significantly reduced PRV by 19% [ U  = 263.0, p  < 0.0001], PRA by 27.6% [ U  = 302.0, p  < 0.0001], and BrIC by 18.5% [ U  = 336.0, p  = 0.0002] but not PLA [ U  = 545.0, p  = 0.1242]. The significance holds when considering the helmet models with and without MIPS individually. The Giro Angon MIPS had significantly lower PRV [ U  = 42.0, p  = 0.044] and PRA [ U  = 37.0, p  = 0.023] but not BrIC [ U  = 58.0, p  = 0.218] or PLA [ U  = 47.0, p  = 0.079] compared to the Giro Angon (without MIPS). The Lazer Tonic MIPS had significantly lower PRV [ U  = 21.0, p  = 0.002], PRA [ U  = 26.0, p  = 0.004], and BrIC [ U  = 27.0, p  = 0.005] but not PLA [ U  = 57.0, p  = 0.201] compared to the Lazer Tonic (without MIPS). The Lazer Compact with MIPS demonstrated significantly lower PRV [ U  = 25.0, p  = 0.004], PRA [ U  = 29.0, p  = 0.007], and BrIC [ U  = 27.0, p  = 0.005] but not PLA [ U  = 61.0, p  = 0.272].

Linear, rotational and overall risk were also compared across the three helmets which had MIPS and no-MIPS versions. Helmets with MIPS significantly reduced the overall risk by 33.8% [ U  = 1.0, p  = 0.0003] and rotational risk by 53.8% [ U  = 0.0, p  = 0.0002] but not the linear risk [ U  = 29.0, p  = 0.1657]. When comparing individual helmets, the overall and rotational risks were reduced for the Giro Angon, Lazer Compact, and Lazer Tonic models when MIPS was included [all U  = 0.0, p  = 0.0404]. The linear risk was reduced for the Lazer Compact and Giro Angon [both U  = 0.0, p  = 0.0404], but not the Lazer Tonic [ U  = 2.0, p  = 0.1914].

No Influence of Price on Protection

The price of helmets in our cohort varied between £9.99 and £135.00 (GBP). A visual summary of price vs linear and rotational risk does not indicate any association between them (Fig. 9 ). This was confirmed using the OLS models. Predicting overall, linear and rotational risk from price showed that there was not a significant influence of price on protection [overall risk: p  = 0.755; linear risk: p  = 0.263; rotational risk: p  = 0.799]. The same conclusions were reached when considering all three risk values in conjunction to predict price [overall risk: p  = 0.755; linear risk: p  = 0.790; rotational risk: p  = 0.747].

A scatter plot showing helmet purchase price vs overall risk for all thirty tested helmets

This differed slightly when considering non-exposure-weighted risk. The OLS model combining helmet model, impact location, presence of MIPS, price, and mass showed that price had a small influence on non-exposure-weighted location-specific overall risk. For every 1GBP increase in price, the overall non-location-weighted risk increased by 0.0007 [ t  = 7.6, p  < 0.001]. The difference between the cheapest (£10) and most expensive helmet (£135) in the sample is £125, which based on the OLS output corresponds to a difference of 0.0875 in risk, with more expensive helmets associated with a higher risk. Note that it was not possible to repeat this analysis for overall risk (adjusted for exposure) due to the assumptions of OLS modeling not being upheld in that instance. Details of this model can be found in “ Appendix 3 ”.

Mass of Helmet Significantly Affects Linear Protection

Helmet masses in our cohort varied between 230 and 560 g. A visual summary of mass vs overall risk is shown in Fig. 10 . In single variate OLS models, we observed no significant effect of mass on rotational risk [ t  = − 1.135, p  = 0.266] or on overall risk [ t  = − 0.060, p  = 0.952], which can also be seen in Fig. 10 . However, there was a relationship between linear risk and mass [ t  = 2.307, 0.029], inferring that heavier helmets were associated with higher linear risk. An OLS model which assessed the combined effect of linear and rotational risk in relation to mass showed that mass depended on both the rotational risk and linear risk, in different directions [rotational risk can predict mass: t  = − 2.297, p  = 0.030; linear risk can predict mass: t  = 3.118, p  = 0.004]. This infers that increasing rotational risk was associated with decreasing mass and conversely, that increasing linear risk is associated with increasing mass.

A scatter plot showing the mass of the helmet in grams (taken from vendor or manufacturer websites) vs the overall risk for all thirty tested helmets

When considering non-exposure-weighted overall risk, the OLS model combining helmet model, impact location, presence of MIPS, price, and mass showed that mass had a small influence on non-weighted location-specific overall risk. For every gram increase in mass, the overall non-location weighted risk increased by 0.0004 [ t  = 6.9, p  < 0.001]. The 330 g difference between the lightest and heaviest helmet corresponds to a difference of 0.132 non-location adjusted overall risk, with heavier helmets associated with higher risk. Note that it was not possible to repeat this analysis for overall risk (adjusted for exposure) due to the assumptions of OLS modeling not being upheld in that instance.

We presented the protection performance of 30 most popular bicycle helmets against skull fractures associated with the head linear motion and diffuse brain injuries associated with the head rotational motion. We used the new biofidelic headform for testing the helmets, allowing us to predict head linear and rotational responses more accurately [ 37 ]. In addition, we used an evidence-based test protocol enabling to assess performance under representative impact conditions [ 3 ]. Head kinematics and overall, linear, and rotational injury risks varied substantially across helmets, demonstrating that there are large differences in their protection, although all helmets had passed the standard impact tests of the EN1078 standard. Interestingly, we observed a greater difference in rotational compared to linear risk protection. The ratio between the highest and lowest rotational risk was over two folds the ratio between the highest and lowest linear risk. This suggests that the helmets tested are better optimized for managing head linear motion than rotational motion. This is likely due to the absence of rotational testing in helmet standards to date, an area that needs to be addressed in future standards in order to improve the protection of helmets against injuries caused by head rotation, particularly diffuse brain injuries.

MIPS was equipped to the top 9 and 11th overall most protective helmets, 8 of which were helmets with the lowest rotational risk (0.074–0.242). MIPS has been shown to be effective in reducing rotational motion when testing with the Hybrid III (HIII) headform across a range of headform surface conditions, including bare, with a stocking to reduce the coefficient of friction and with hair [ 71 ]. This study is the first to show that MIPS remains effective at mitigating rotational motion with the new headform that is more biofidelic than the HIII headform in terms of two key factors affecting head rotation, the coefficient of friction and moments of inertia [ 37 , 72 , 73 ]. Importantly, in the direct comparison between matched helmet models with and without MIPS, we found that linear acceleration was not significantly reduced by MIPS. While MIPS drives overall risk down by reducing rotational risk, it does not drive a reduction in linear risk. Interestingly, the helmet with the Wavecel technology, designed for rotational risk mitigation [ 74 ], produced the lowest linear risk (0.141) in our cohort of 30 helmets, although its overall rank was #13 due to the high rotational risk (0.301). These results show that it is vital to design helmets holistically to reduce both linear and rotational kinematics metrics to protect against a range of different head injury types caused by different mechanisms.

We observed a distinct effect of impact location on head kinematics and subsequently the linear and rotational risks calculated from PLA and BrIC, respectively. The largest PLA and linear risk were seen in pXR impacts. The largest BrIC and rotational risks were seen in pZR impacts. Interestingly although both BrIC and PRV are driven from head rotational velocity, the largest PRV was produced in nYR impacts, rather than pZR. This is because BrIC has a lower critical angular velocity for the z axis rotation than x and y , i.e., it exaggerates the effects of rotation about the z axis. A recent study of eight established brain FE models using kinematics data from cycle helmet oblique impacts has shown stronger correlation between BrIC and brain strain, than PRV [ 61 ]. This further supports adopting BrIC for assessing the effects of head rotational motion on the brain in our helmet impacts. Our findings show the particular importance of the pXR and pZR impact locations in producing highest linear and rotational risks, respectively, which should be a target for improving helmet design.

Although we found that there is no relationship between helmet price and the linear, rotational, or overall risk in isolation, our OLS model of non-exposure-weighted overall risk based on helmet model, mass, price, and presence of MIPS suggested an effect of increased price on increased risk. The lack of relationship in the isolated models is in keeping with previous work that has shown a weak negative correlation between cycle helmet price and risk of “concussion” measured under oblique impacts [ 33 , 75 ]. The lack of relationship between price and safety performance is important because in the absence of objective information about helmet safety, consumers may rely on the price to indicate the safety performance [ 40 , 41 ]. Previous work has shown that higher likelihood of helmet use is correlated with higher income and employment status [ 76 ]. Consumers should be able to access clear information about the protection performance of helmets, particularly relating to more affordable options.

Our survey demonstrated that helmet mass is a factor considered to be important in the road cycling community, likely due to lower mass equating to higher speed and comfort. Of 1083 helmet wearers, 890 (82.2%) found helmet mass to be either “very important,” “important,” or “somewhat important” compared to 193 (17.8%) who found mass to be “not important” or “not important at all.” The results of the multivariate OLS models suggested that increasing rotational risk is associated with decreasing mass and conversely, that increasing linear risk is associated with increasing mass (additionally supported by a single variate model). The fact that heavier helmets were associated with higher linear risk is in contrast to one of our incoming hypotheses that heavier helmets have more material and therefore offer better linear protection due to higher potential for the liner to remove energy in an impact. Our second hypothesis that lighter helmets are product of increased research and development, which is associated with better performance, is one possible reason that lighter helmets offered better linear protection. We found no studies on the relationship between bicycle helmet mass and protection, making this a novelty of our study. In one 1996 study of fatal motorcyclist incidents with axial load shift, heavier motorcycle helmets (> 1500 g among a range of 600–2000 g) were associated with higher basilar skull fracture risk [ 77 ]. The authors found no increased risk below 1500 g. Our helmets ranged from 230 to 560 g, making all bicycle helmets we tested lighter than the motorcycle helmet in the previously mentioned study. This previous work additionally assessed risk of a specific injury, whereas we use a combined overall risk metric assessing the risk of diffuse and focal injuries. Importantly, our OLS model shows that increasing mass is associated with increasing overall risk, a finding which may be of interest to the road cycling community who use mass as a purchase factor.

We repeated the tests three times using a new sample. This enabled us to quantify the variation across the tests, which can be attributed to both the test conditions and helmet manufacturing. Such information is missing in previous studies that have assessed helmet performance [ 32 , 33 ]. The coefficient of variation for the peak kinematic values was found to be below 10% for 87% of tests across all metrics, with 99% below 20%. The variation was highest in the peak rotational acceleration, which is likely due to the fact that PRA was obtained by differentiating the filtered rotational velocity. We chose not to apply an additional filter to the rotational acceleration pulse, as this would act as a smoother when filtering for a second time. The CV for the other kinematic metrics was low and did not differ significantly, further demonstrating consistency of the test conditions and helmet samples. The low CV particularly provides more support for the adoption of the new headform in helmet standards and rating systems that use an isolated headform.

The Cellbond-CEN 2022 headform used in this study has further evolved since this study was completed. The focus of the improvements has been on lowering the CoF to fall within the 0.27–0.33 range, which overlaps with the range of CoF reported for the contact between human head and EPS foam (95% CI static CoF = 0.30–0.34, dynamic CoF = 0.26–0.28) and polyester liner (mean ± STD = 0.29 ± 0.07) [ 78 , 79 ]. The mean value of the CoF that we measured for the headform was 0.4 ± 0.01, which is 21% higher than the upper value of the target CoF range. A study of cycle helmet oblique impacts using the HIII and NOCSAE headforms has shown that a 55–58% reduction in CoF to around 0.37–0.38 by adding a skull cap to the headforms had a small effect on PLA, PRA and PRV, decreasing them between 2 and 14% [ 44 ]. It is likely that using a more recent version of the CEN headform with lower CoF, our results will be affected within a range similar to that reported in this previous study.

Different headforms are currently used in standards and research studies, including EN960, NOCSAE, and HIII, but often their CoF or MoI are not reported or controlled, or they do not agree with human data [ 44 ]. Several studies however have investigated helmet response using headforms with more biofidelic MoI or CoF, showing that the headform kinematics is influenced by both [ 37 , 42 , 43 , 44 , 73 , 80 , 81 , 82 ]. The new CEN headform is designed with MoI and CoF that better matches those of the human head, addressing the shortcomings of other headforms used for helmet testing. The adoption of this headform by researchers and test labs will enhance the reproducibility of helmet tests.

One novelty of this study is that injury risk functions developed for skull fractures and associated focal injuries and diffuse brain injuries were used, covering a large range of pathologies reported in helmeted cyclists’ incidents. Using a risk function allows for producing one overall risk for a helmet, in contrast to using kinematics values only [ 32 , 83 ]. Previous studies have used risk functions focused on predicting the risk of “concussion” [ 33 , 39 ]. Here we provided a more comprehensive picture of helmet protection against a range of injuries. A limitation of this approach is that the risks of linear and rotational injuries are averaged, assuming they have equal importance and presence in real-world casualties. With more data on the distribution of these injuries and their consequences, the weighting of these risks should be adjusted in future.

The rotational risk function is based on BrIC. This metric has had the best correlation with the strain predicted by a range of brain FE models [ 61 ]. The BrIC risk function used here was scaled by the developers of BrIC to predict mild diffuse brain injuries, which is a limitation [ 36 ]. A recent study has developed a mild traumatic brain injury risk function for BrIC based on data from professional American Football [ 84 ]. This function however provides zero risk for small values of BrIC. This study assumed that mild TBI is equivalent to “concussion,” an assumption that has been debated by neurologists, who suggest shifting the focus from symptoms to the likelihood of brain structural damage [ 85 ]. Supporting this suggestion, recent work has shown that the count of concussions is not associated with neurodegeneration in American Football players, while cumulative head linear and rotational accelerations can predict neurodegeneration [ 86 ]. Hence, in the absence of a better risk function for BrIC, here we used a more conservative risk function that associates a non-zero risk to small values of BrIC.

In this study, only four impact locations are tested, while real-world head impacts can occur in many different locations. We however ensured to select the locations impacted most frequently based on a meta-analysis of 815 cycle helmets [ 3 ]. We used the results of this analysis to weight the injury risk associated with each impact location for exposure in contrast to previous work [ 33 , 39 ]. The exposure was highest in the pXR (side) impact, followed by the nYR (rear) impact and then the pYR and pZR (frontal) [ 3 ]. We however did not include a crown impact due to it being the lowest exposure impact location based a meta-analysis of 815 cycle helmets. One further recent study assessing head impact location by soft tissue damage also suggests that crown impacts are uncommon, with soft tissue injuries to the parietal region representing the lowest proportion of soft tissue injuries to the head region (excluding the face), at just 15% [ 87 ]. Additionally, all helmets which go to market in Europe and the UK must pass standards, which include impacting the crown region. Therefore, a minimum threshold of protection for impacts to the crown is obtained for all helmets in this cohort.

Consistent use of OLS models was limited due to some datasets violating the assumptions for modeling, in particular non-normal distribution of errors and residuals (identified using the Omnibus and Jarque-Bera tests). This led to an inability to use OLS models to assess the location exposure-adjusted overall risk, \(P(\text{injury}@\text{helmet})\) .

Another limitation of this study is that we tested medium-sized helmets only, as dictated by the physical headform. Although future development will include a range of sizes for the new headform, at the time this study was conducted, the headform corresponds to an average adult (57 cm circumference based on a height of 175 cm) [ 88 ]. Our survey of cyclists showed that on average, males tended to wear medium or large helmets, while females tended to wear small or medium helmets, with a minority of males wearing small helmets and a minority of females wearing large helmets. This corresponds to previous work which demonstrates that head circumference is a function of height, with a slight difference between the sexes, whereby females have a 1.38 cm smaller head circumference at the same height [ 88 ]. Although a large proportion of the adult population do wear a medium helmet, future work should ensure that different helmet sizes are tested, promoting equitable research.

We selected the most popular cycle helmets used on the UK roads. This led to the inclusion of two distinct helmet technologies in the cohort of helmets studied here, MIPS and Wavecel. There are several other helmet technologies that are currently available in commercially available helmets [ 83 ]. Although these technologies were not within the helmets selected here, they warrant testing according to the protocol used in this study, allowing for a comparison between their performance and the performance of the most popular helmets included in this study. An aim of future work should be to provide the opportunity for the developers of new helmet technologies to submit their helmets for assessment by independent test labs, with the results being published for consumers’ information. This approach helps the designers to better understand the comparative performance of their helmets. It also helps consumers to learn about most protective helmet technologies that may not be popular yet.

In summary, we present the protective performance of 30 bicycle helmets which are popular in the UK under oblique impacts using a new, biofidelic headform and evidence-based test protocol enabling to assess performance under representative impact conditions. Below is a summary of the key findings:

The least protective helmet had a 2.62 times higher overall head injury risk than the most protective helmet. There was a lesser spread of linear risk (1.76 times) compared to rotational risk (4.21 times).

The pXR and pZR impact locations produced highest linear and rotational risks, respectively.

The nine helmets offering the best overall injury protection were all equipped with the anti-rotation technology MIPS, which in direct helmet comparisons between models with MIPS and no-MIPS versions, was shown to be effective in reducing rotational kinematics and risk under the impact conditions tested. However, not all helmets equipped with MIPS were the most protective.

Mass and price in isolation did not demonstrate a significant effect on exposure-weighted linear, rotational and overall risk, \(P(\text{injury}@\text{helmet})\) . However, the OLS model predicting non-exposure-weighted overall risk, \(P(\text{injury}@\text{location})\) , using price, mass, presence of MIPS and impact location showed that both price and mass had a small influence on the non-exposure-weighted overall risk, with increased mass and price shown to relate to increased non-exposure-weighted overall risk.

Our study highlights the need for distinct linear and rotational injuries with different mechanisms to be mitigated through continued improvement in helmet test methods and helmet designs. It also supports the need for providing consumers with objective information about helmet impact performance to help them with choosing most appropriate helmet.

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Acknowledgements

This work was funded by the Road Safety Trust and Innovate UK. The authors would like to thank HEXR for purchasing and providing the helmets selected by the authors for this study. MG has a Royal Academy of Engineering Senior Research Fellowship (RCSRF2324-17-19).

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C. E. Baker, X. Yu, B. Lovell, R. Tan, S. Patel & M. Ghajari

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Helmet Selection and Price Distribution

The information about the make or model of helmet was used to inform the selection of the remaining 17 helmets for testing. Firstly, each unique helmet response was listed (collected from respondents via a free-text field), accounting for discrepancies in spelling and capitalisation, resulting in 214 unique helmets. 20 of these were discontinued and 15 could not be found for purchase, resulting in a list of 179 helmets. 121 helmets were only mentioned once, 21 had more than 5 mentions, 6 had more than 10 and 1 helmet had more than 50 mentions.

The retail price distribution shown in Fig. 11 was used to ensure the helmets tested were popular and representative of the prices of helmets of cyclists who chose to own or wear a helmet. Once the 13 already selected helmets were included, the survey responses in order of helmet popularity were used to fit the price bands which were not yet at capacity. In instances of equal popularity, helmets were selected with the aim of increasing the diversity of the list of 30 cycling helmets for testing (Table 8 ).

Histogram showing the frequency of helmets across a range of retail price bands (in GBP, determined as of May 2022) of survey responders cycling helmets, based on 1083 who owned a helmet (out of 1132 collected survey responses)

As such, helmets with distinct features and or technologies were chosen in said instances, for example, foldable helmets and helmets that have LEDs. In the event that there were an insufficient number of helmets within a given price band from the survey responses, the initial helmet long list was used to select the best-selling helmet within that price band. Further information relating to the survey responses and helmet pricing can be found in “ Appendix 1 ”. The final list of 30 helmets selected for testing are shown in Table 4 (Fig. 12 ).

The cumulative price distributions of the 30 helmets selected for testing and the helmet prices obtained via survey responses

A summary of the kinematics of all tests can be found in this section (Table 9 ). The distributions of kinematics are summarized below.

Mean linear risk across all helmets and repeats was highest in the pXR impact location (0.233), but lower across other impact locations (pYR: 0.205, pZR: 0.177, nYR: 0.175). The linear risk, calculated from PLA, across all tests in the pXR impact location was significantly higher than the tests in the other three impact locations [pXR > pYR: U  = 5255.0, p  = 0.0003; pXR > pZR: U  = 6299.0, p  < 0.0001; pXR > nYR: U  = 6184.0, p  < 0.0001]. Additionally, the linear risk in the pYR impact location was significantly higher than in the nYR and pZR locations [nYR < pYR: U  = 2857.0, p  = 0.0003; pZR < pYR: U  = 2761.0, p  = 0.0001].

Mean rotational risk across all helmets and repeats was highest in the pZR impact location (0.494) and lowest in the pXR impact location (0.107). Both YR tests produced similar mean rotational risks (pYR: 0.327, nYR: 0.342). The rotational risk, calculated from BrIC, across all tests in the pXR impact location was significantly lower than the tests in the other three impact locations [pXR < pYR: U  = 520.0, p  < 0.0001; pXR < pZR: U  = 91.0, p  < 0.0001; pXR < nYR: U  = 600.0, p  < 0.0001]. The rotational risk of the pZR tests was higher compared to other test locations [pZR > nYR: U  = 6254.0, p  < 0.0001; pZR > pYR: U  = 6434.0, p  < 0.0001; pXR < pZR: U  = 91.0, p  < 0.0001]. There was no statistically significant difference found across YR tests.

Mean overall risk across all helmets and repeats was highest in the pZR impact location (0.335), lowest in pXR (0.170) and similar across the nYR and nYR test locations (pYR: 0.266, nYR: 0.258). Across all tests, the overall risk was significantly lower in the pXR test configuration [pXR < pYR: U  = 899.0, p  < 0.0001; pXR < pZR: U  = 563.0, p  < 0.0001; pXR < nYR: U  = 1082.0, p  < 0.0001] and significantly higher in the pZR test configuration [pZR > nYR: U  = 6215.0, p  < 0.0001; pZR > pYR: U  = 6079.0, p  < 0.0001; pXR < pZR: U  = 563.0, p  < 0.0001]. There was no statistically significant difference found across YR tests.

OLS Model Summaries

The ordinary least squares (OLS) model output used to explore the relationship between helmet type, impact location, mass, price and presence of MIPS and overall risk not adjusted for location exposure, P(injury@location) is shown (Fig. 13 ).

The OLS model summary is shown for the comprehensive model to predict overall risk not adjusted for location exposure, \(\text{P}\left(\text{injury}@\text{location}\right).\) Helmet type, impact location, mass, price, and presence of MIPS are used as factors

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Baker, C.E., Yu, X., Lovell, B. et al. How Well Do Popular Bicycle Helmets Protect from Different Types of Head Injury?. Ann Biomed Eng (2024). https://doi.org/10.1007/s10439-024-03589-8

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Received : 13 February 2024

Accepted : 25 July 2024

Published : 19 September 2024

DOI : https://doi.org/10.1007/s10439-024-03589-8

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