The Photoelectric Effect

Assessment Task Topic: The Photoelectric Effect

1. Introduction

The photoelectric effect is the name given to the phenomenon whereby electrons are emitted from a metal when exposed to electromagnetic radiation of the appropriate frequency. It was first discovered by Heinrich Hertz in 1887, but remained a conundrum to many scientists who sought to explain it, as it clearly contradicted the accepted principles of classical physics such as James Clerk Maxwell’s Theory of Electromagnetic Waves. This phenomenon, unable to be explained by the wave model of light, was finally explained by Albert Einstein in 1905 with the inception of his Quantum Theory, a concept that would completely revolutionise scientific thought. The photoelectric effect has played and continues to play an important role in mankind’s scientific development.

2. Discovery of the Photoelectric Effect: Hertz

The original observation of the photoelectric effect can be traced back to the German scientist Heinrich Hertz. In 1887, in an attempt to generate and detect electromagnetic radiation, Hertz created a rapidly-oscillating electric field with a high voltage induction coil to cause a spark discharge between two spherical brass electrodes. He observed that when a small length of copper wire with brass spheres attached on either end was bent into a loop, leaving a small gap between the spheres, and held near the sparking induction coil, a spark would jump across the gap at the same time when the brass electrodes in the induction loop sparked. This induced spark occurred despite the copper loop not being connected to any electrical current source. Thus Hertz came to the conclusion that the copper loop was a detector of the electromagnetic waves propagated by the transmitting loop.

This successful experiment was followed up by a series of others, through which Hertz demonstrated that these electromagnetic waves could be reflected from a metal mirror, and refracted as they passed through a prism made from pitch, thus proving that these waves behaved similarly to light waves. He also proved these waves were polarised.

Through the course of his investigations, he discovered a mysterious phenomenon: “I occasionally enclosed the spark B[the detector spark]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 transmitter spark]. The partition on that side exhibited this effect, not only when it was in the immediate neighbourhood 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.”

Upon shielding the detecting loop with glass, the intensity of the spark produced was reduced. However, when a quartz shield (a substance that allows UV rays to pass) was applied, there was no drop in the spark intensity. He then used a quartz prism to separate the light from the transmitter spark into its various components, discovering that the wavelength which made the detector spark more powerful was in the ultraviolet range. Unable to explain this phenomenon, Hertz concluded his series of investigations in 1887, declaring that: “… 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.”

3. Further Investigations: Hallwachs, Thomson, von Lenard

After learning of Hertz’s experiments, another German scientist, Wilhelm Hallwachs, devised a much simpler investigation to demonstrate the photoelectric effect. In his own words: “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.” By placing a zinc plate atop an insulating stand and wiring it to a negatively-charged gold leaf electroscope, he observed a slow loss of charge from the electroscope. However, when he exposed the zinc plate to ultraviolet light from an arc lamp or from burning magnesium, the discharge occurred much quicker. Conversely, a positively-charged electroscope resulted in no fast leakage of charge.

In 1899, British scientist J.J. Thomson finally identified that the light caused the metal surface to emit electrons. He enclosed the metal in an evacuated tube before exposing it to radiation, showing the electrons to be the same particles emitted in cathode ray tubes.

Three years later, German physicist Philipp von Lenard, who had worked with Hertz earlier in Bonn, conducted a series of experiments in which he used a bright carbon arc light to examine how the energy of the emitted electrons varied with the light’s intensity (see Figure 2). By using a vacuum tube, he showed that when electrons emitted by the metal plate upon exposure to light hit another plate, the collector, a small measurable current was produced. By charging the collector negatively so as to repel the electrons, von Lenard discovered that a minimum voltage existed, V_stop, so that only electrons with a certain energy threshold could reach the collector and thus generate a current.

He found that while increasing light intensity caused more electrons to be emitted (as can be gathered from an observed increase in current), it did not affect the amount of energy carried by each electron, as the stopping voltage was constant. On the other hand, increasing the frequency of the light led to an augmentation in the electrons’ kinetic energy, thus finding that for a particular frequency of light, the kinetic energy of the electrons remained constant. Von Lenard also showed that if the frequency was lowered beyond a certain threshold, no current was produced, regardless of the intensity of the light. However, like the scientists preceding him, he was unable to account for these phenomena.

4. Inadequacy of Classical Physics Explanations

The phenomenon observed during the photoelectric effect was in contradiction to classical theory explanations such as Maxwell’s Theory of Electromagnetic Waves which was then commonly accepted by scientists. According to such rules of classical physics, for an electron to gain enough energy to be liberated from the metal, the metal surface would have to be exposed to the light waves for a period of time. However, as observed in experiments of the photoelectric effect, the electrons were freed instantly. The Wave Theory maintains that increasing the intensity of a beam of light also increases the amplitude of the oscillating electric field vector E, thus the amount of electrons emitted should be proportional to the intensity of the light.

However, according to the observations made, the current flow was independent of light intensity, yet varied according to the frequency of the light, and was non-existent when the frequency decreased beyond a certain level, regardless of the intensity. Von Lenard’s experiment confirmed the existence of a threshold frequency in the photoelectric effect, another phenomenon unable to be explained with a classical physics approach. Thus the belief in light being completely wavelike in nature was incompatible with the experimental observations of the photoelectric effect.

5. Black Body Radiation and Planck’s Hypothesis

A black body cavity can be defined as a perfect cavity that absorbs all radiation that falls onto it and then perfectly radiates all energy absorbed until it is at equilibrium with its surroundings. The intensity of various wavelengths emitted by the black body changes according to its temperature, forming black body radiation curves (see diagram on right). Experimental data showed that the intensity of radiation emitted increased with decreasing wavelength, until a definite peak is reached, after which lower wavelengths of radiation are emitted at lower intensities.

Yet, according to the classical wave theory of light, as the wavelength of the radiation emitted shortened, the intensity should increase, thus as the wavelength tends to zero, intensity would approach infinity. However, this would be a gross violation of the principle of conservation of energy. Hence it remained an inexplicable conundrum for scientists for a long time, who gave this effect the name ‘ultraviolet catastrophe’.

In 1900, German scientist Max Planck came up with a revolutionary explanation for this phenomenon. He made the assumption that the radiant energy may be treated statistically not as continuous waves but rather as discrete ‘packets’ of energy, each of which he called a ‘quantum’. Based on this radical assumption of light as particles, he formulated a mathematical equation by which this phenomenon could be exemplified. He proposed this relation that calculated the energy of a quantum for radiation of a certain frequency: E= hf,Ebeing the energy in joules, fthe frequency in Hertz, and ha small constant (6.626 x 10^-34Js) now known as Planck’s constant. Figure 4 is a graph of experimental results that confirms Planck’s equation, with the gradient corresponding to h. He proposed that any quanta of a particular frequency (and thus wavelength) would carry the same amount of energy. However, he did not attribute any physical significance to this postulation, merely perceiving it as a mathematical trick by which the corresponding answer could be obtained.

6. Quantum Theory: Einstein’s Explanation

Due to the inadequacies of classical physics in explaining the photoelectric effect, in 1905 Albert Einstein further developed upon Planck’s hypothesis to come up with a new ground-breaking theory to explain the photoelectric effect. He proposed that light was made up not of continuous waves but rather of discrete bundles of energy which he termed ‘photons’. He wrote in the renowned journal Annalen der Physik: “It seems to me that the observations on ‘black-body radiation’, photoluminescence, the production of cathode rays by ultraviolet light and other phenomena involving the emission or conversion of light can be better understood on the assumption that the energy of light is distributed discontinuously in space.

According to the assumption considered here, when a light ray starting from a point is propagated, the energy is not continuously distributed over an ever increasing volume, but it consists of a finite number of energy quanta, localised in space, which move without being divided and which can be absorbed or emitted only as a whole.”

Einstein used Planck’s equation that each photon had an energy E=hf, and proposed that light intensity was proportional to the number of photons. The higher the frequency of the electromagnetic radiation, the greater the energy carried by its photons. Einstein provided a comprehensive explanation for the photoelectric effect. When an electron is liberated from the metal surface, the energy in the light photons must be great enough to overcome the forces that bind the electrons to the surface. This minimum energy required to liberate an electron from a metal surface is known as the work function, represented by the symbol ¢, and is dependent solely on the material of the metal.

The corresponding minimum frequency required for the photons to contain the required energy is called the threshold frequency (f₀). If the energy of the photon is greater than the work function of the metal (i.e. E> hf₀), than the difference in their energy levels will provide the kinetic energy for the photoelectrons (electrons released from interaction with a photon), allowing them to travel and thus generate an electric current. Einstein’s quantum theory explains the existence of a threshold frequency for the light below which no electrons would be emitted from the metal, an experimental observation that had puzzled scientists up to that time.

Einstein established that when different metal surfaces are illuminated with monochromatic light, photoelectrons are emitted by the metal surface. The magnitude of the forces by which electrons are held varies with different metals. Thus the work functions of each different metal are also varied. Below is a table of the work functions of various metals.

Figure 6:Work Functions for Various Metals

Source: Nave, CR. HyperPhysics: Photoelectric Effect

According to Einstein’s theory a single photon collides with an electron in the metal, transferring all its energy to the electron, thus liberating the (photoelectron from the metal surface. This concept successfully explained the instantaneity of the electron emission upon light exposure, another phenomenon that classical wave theory was unable to account for.

In Einstein’s own words, “According to the idea that the incident light consists of energy quanta… one can picture the production of cathode rays by light as follows. Energy quanta penetrate into a surface layer of the body, and their energy is at least partly transformed into electron kinetic energy. The simplest picture is that a light quantum transfers all of its energy to a single electron; we shall assume that that happens. We must, however, not exclude the possibility that electrons only receive part of the energy from light quanta.

An electron obtaining kinetic energy inside the body will have lost part of its kinetic energy when it has reached the surface. Moreover, we must assume that each electron on leaving the body must produce work P, which is characteristic for the body. Electrons which are excited at the surface and at right angles to it will leave the body with the greatest normal velocity.”

Einstein formulated an equation, known as Einstein’s Photoelectric Equation, to provide a quantitative explanation for the photoelectric effect:

E= hf= ¢+ E_k

with Ebeing the energy of the photon (thus E= hffrom Planck’s hypothesis),¢the work function of the particular metal (¢= hf₀), and E_kthe photoelectron’s kinetic energy (in Joules or electron volts).

Einstein’s theory also explains the stopping voltage in the photoelectric effect, which von Lenard had discovered earlier. This voltage is a good measure of the kinetic energy of the photoelectrons. It can be demonstrated (see figure 7) by introducing a variable electric potential difference to make the anode negative, thus generating a repelling force against the photoelectrons emitted from the cathode. As this opposing voltage is increased, it will arrive at a point where there is no current flowing in the external circuit as the photoelectrons’ kinetic energy is not enough to overcome the voltage. This stopping potential equals the maximum kinetic energy of the electrons at the cathode, as it is just enough to stop any electron from reaching the anode.

Thus E_{K max}= -qV₀, where E_{K max}is the maximum kinetic energy of the electron in joules, V₀the magnitude of the stopping potential in volts, and q the charge of the electron (-1.60 x 10^-19C). As the unit of the joule is too large to be used effectively for atomic systems, the electron volt (eV) is employed instead, with 1 eV = 1.60 x 10^-19J. Thus the maximum kinetic energy of a photoelectron can be experimentally obtained from the stopping voltage. Radiation with higher frequencies will result in higher stopping voltages, and vice versa.

With his theory of the quantisation of light, Einstein was able to derive Planck’s formula and account directly for such hitherto inexplicable phenomena as the photoelectric effect and black-body radiation. His work overturned the previously accepted, but now proven flawed, wave theory of light, heralding a new era with the concept of wave-particle duality, in which light can be seen both as waves and as particles (quanta). It was “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect” that Einstein was awarded the Nobel Prize for Physics in 1921.

Another notable scientist, the American Robert Millikan, expressed grave doubts about Einstein’s quantum theory and set out to experimentally prove him wrong. However, after a decade of thorough scientific investigations, Millikan’s results confirmed Einstein’s theory in every aspect. He was even able to measure Planck’s constant to within 0.5% accuracy. These travails earned Millikan the Nobel Prize in 1923 and further validated Einstein’s quantum theory in explaining the photoelectric effect.

7. Practical Applications of the Photoelectric Effect

The principle of the photoelectric effect is utilised in many domains. One significant application of the photoelectric effect is the solar cell. This is a device that converts electromagnetic radiation from sunlight into electrical energy. It is generally made up of a series of metallic plates facing the sun, emitting photoelectrons when struck by sunlight. These electrons then flow through an external circuit, thus generating electrical power.

Another practical application is the photomultiplier tube (PMT). When light is shone onto a photosensitive cathode, electrons are emitted, and subsequently accelerated towards a second cathode. This produces more electrons, and is repeated for a number of cathodes, resulting in the multiplication of the number of electrons initially emitted by a factor of a million, to be detected as a current pulse at the final electrode. Thus PMTs are extremely sensitive light detectors, used in scientific applications that require high levels of accuracy, such as emission spectroscopy experiments.

Phototubes also operate on the principle of the photoelectric effect. The electrical characteristics of these devices are dependent on the light that they are exposed to. Thus the current produced from a phototube may be used to operate sensor-based appliances such as automatic doors, sensor taps, alarm systems and light-activated counters.

8. Conclusion

The photoelectric effect has undeniably played a significant role in the development of modern physics ever since its discovery. It has revolutionised mankind’s understanding of the nature of light, its wave-particle duality. It was in the pursuit of an explanation for this phenomenon that Einstein made what was an important great leap forward in the world of science 3/4his conception of quantum theory. In fact the photoelectric effect and the problem of the ultraviolet catastrophe in black-body radiation formed the two experimental foundations upon which quantum theory was built.

Thus the experiments conducted on the photoelectric effect can be considered among the most significant in the history of physics. Three distinguished physicists received the Nobel Prize in part for their work on the photoelectric effect: Max Planck in 1918, Albert Einstein in 1921 and Robert Millikan in 1923. The observations of the photoelectric effect and its subsequent explanations by Einstein can be regarded as directly responsible for the birth of modern physics.

Appendix:A Timeline of the Photoelectric Effect

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