9.4.B - Photoelectric Effect


In the 1870s, a Scottish mathematician and physicist by the name of James Clarke-Maxwell put forward some revolutionary ideas about electromagnetism. Among them he suggested that there were other waves other than light with different frequencies and wavelengths that belonged to a spectrum of waves that all travelled at the same speed.

In the 1880s, a German physicist by the name of Heinrich Hertz successfully produced and detected a radio wave and measured its speed, confirming Maxwell's predictions. In doing so he also discovered the photoelectric (PE) effect in that the electricity he was measuring was more intense when light was shone onto the metal he was using.

In the 1890s, other scientists were treating electromagnetic (EM) radiation as if it was a wave and getting some experimental results that they could not explain and in 1897, Thomson confirmed the existence of the electron. Planck proposed that if black body radiation was thought of as a particle rather than a wave, it would make some erroneous experimental results of the time perfectly easy to explain. He solved a very real problem, but experimental evidence for this hypothesis did not come until 1902 until a student of Hertz, Phillip Lenard made measurements of the PE effect. These data were not easily explained by physicists at the time who were still clinging to a wave model for EM radiation. In 1905, Einstein used Lenard's experimental data to show that in the PE effect, EM radiation was behaving as though it was a particle. Still physicists were not convinced and it wasn't until 16 years later in 1921 that the significance of Einstein's contribution to our understanding of the wave-particle duality and quantum physics was recognised and he was awarded a Nobel prize.

In this unit you wil learn about:

  • Hertz' discovery of radio waves,
  • Planck's hypothetical solution to the ultraviolet catastrophe, and
  • Einstein's explanation of the photoelectric effect.

Hertz' Discovery of Radio Waves and the PE Effect

In 1865, James Clark-Maxwell predicted the existence of electromagnetic waves. He suggested that an oscillating charge would produce a changing electric field that would in turn produce a changing magnetic field. By Faraday’s law, this changing magnetic field would in turn produce a changing electric field and so on. He showed mathematically that such fields would propagate through space as a transverse wave with a speed of 3 x 10 ms-1. This speed agreed so closely with values of the speed of light measured by Fizeau in 1849 and Foucault in 1862 that Maxwell became convinced that light was a form of electromagnetic radiation.

The apparatus used by Hertz to generate and detect a radio wave.

Heinrich Hertz, a German physicist, achieved the first experimental demonstration of electromagnetic waves in 1887. Hertz used an induction coil to produce oscillating electric sparks between two brass balls connected to two brass plates. The brass plates acted as an aerial system. He used a small loop of wire with a tiny gap in it as the receiver. As sparks jumped across the gap between the balls, they were also observed jumping the gap in the receiver. Hertz reasoned that the spark discharge oscillating backwards and forwards between the brass balls set up changing electric and magnetic fields that propagated as an electromagnetic wave, as postulated by Maxwell. When these waves arrived at the receiver, the changing electric field component caused charges in the loop to oscillate, thus producing the spark across the gap in the receiver. During the course of his many investigations, Hertz' apparatus generated waves with frequencies between
50 and 400 MHz and wavelengths between 6 and 0.7 m respectively.

The apparatus used by Hertz to measure the wavelngth of
the EM waves he had produced.

Hertz carried out a thorough investigation of these waves and showed that they did indeed possess properties similar to light - reflection, polarisation, refraction and diffraction. By setting up an experiment in which he allowed the waves to reflect from a metal sheet and interfere with themselves to produce standing waves, Hertz was able to determine their speed. He calculated the frequency of oscillation of the sparks (and the EM wave) in his transmitter from the known parameters of the circuit. Hertz then formed a standing wave of electromagnetic radiation by reflecting the radio waves from a large flat zinc plate, as shown in the diagram on the right, in which only a standing wave of the electric field is shown. Hertz moved his receiver coil along this wave. A spark in the gap was produced at the anti-nodes but not at the nodes. The distance travelled between nodes or anti-nodes is half a wavelength. Doubling this distance gave the wavelength. Using the wave equation, v = fλ, he calculated the speed of the waves as 3 x 108 ms-1 as predicted by Maxwell. Hertz varied the frequency (and wavelength) of the waves and repeated the experiment to get the same value for the speed of the waves.

Hertz’s experiment confirmed Maxwell’s prediction of EM waves and provided strong experimental support for the idea that light was a form of transverse EM wave. The waves produced by Hertz eventually became known as radio waves and his research led to the development of radio communications. As Hertz suspected it was indeed oscillating charges that produced the EM waves. Today we know that radio waves are produced when an oscillating voltage applied to an antenna causes free electrons to oscillate along that antenna. This generates an EM wave that spreads out from the transmitter at 3 x 108 ms-1. When the EM wave strikes a receiving antenna it forces charges in the antenna to oscillate at the same frequency as the wave. This oscillating electrical signal is then converted into an audio-frequency signal by diodes in appropriately tuned electronic circuits.

Discovery of the PE Effect

While conducting his initial experiments Hertz often placed the receiver loop in a darkened box to make it easier to see the tiny sparks in the gap. He noticed that the sparks across the gap in the receiver were distinctly weaker when the receiver was in the box. After much effort Hertz discovered that the sparks jumping the gap in the receiver were more vigorous when the receiver was exposed to the ultraviolet light coming from the sparks in the gap of the transmitter. Although this was a most amazing discovery, Hertz did not further investigate the phenomenon but confined his research to the production and study of EM waves. What Hertz had discovered but failed to investigate further was the photoelectric effect.

 

Planck's Solution to the Ultraviolet Catastrophe

The Ultraviolet Catastrophe

When an object such as the filament in a light globe is heated (but not burned) it glows with different colours: black, red, yellow, blue-white, as it gets hotter. To understand how radiation is emitted for all bodies and how the radiation varies with temperature, creative experiments involving the behaviour of standard objects called ‘black bodies’ were being performed in the 1890s. Physicists of the time engaged in such experiments to assist in their understanding of light. A black body is one that absorbs and re-emits all radiation that falls onto its surface. The use of black bodies was necessary because all objects behave slightly differently in terms of the radiation they absrorb and emit at different temperatures. Scientists were using standard black bodies in experiments to study the nature of radiation emitted at different temperatures.

Typical emitted radiation curves for black body radiation at different
temperatures.

As an example of an object used to model a black body, imagine you drilled a very small hole through the wall of an induction furnace (an efficient oven in which the temperature can be set to known values). At a temperature of 1000°C for example, the walls of such a model black body will emit all types of radiation, including visible light and infrared and ultra-violet radiation, but they will not be able to escape the furnace except through the small hole. They will be forced to bounce around in the furnace cavity until the walls of the furnace absorb them. As the walls absorb the radiation they increase in energy. As such, the walls to release radiation of a different wavelength, eventually establishing an equilibrium situation. The walls absorb all radiation applied to the black body, so the radiation leaving the hole in the side of the furnace is characteristic of the equilibrium temperature that exists in the furnace cavity. This emitted radiation is given the name black body radiation. As the graph on the right shows, the radiation emitted from a black body extends over all wavelengths of the EM spectrum. However, the relative intensity varies considerably and is characteristic of a specific temperature. Black bodies absorb all radiation that falls on them and that energy is spread throughout the object. At higher equilibrium temperatures, the emission of more intense, shorter wavelength radiation from the cavity occurs.

A comparison of the experimental results from black bodies compared
with the theoretical predictions that cause the ultraviolet catastrophe.

Physicists used a spectrometer to measure how much light of each colour, or wavelength, was emitted from the hole in the side of the black body models they constructed. The shape of the radiation versus intensity curves on the graphs that they created presented a problem for the physicists attempting to explain the intensity and wavelength variations that occurred quantitatively. The problem was how to explain the results theoretically using classical wave theory. The traditional mathematics based on thermodynamics and classical wave theory predicted that the pattern of radiation should be different to that which the physicists found occurred. The classical wave theory of light predicted that, as the wavelength of the radiation emitted becomes shorter, the energy it carries would increase. In fact, it would increase without limit. This would mean that, as the energy (that was emitted from the walls of the black body and then re-absorbed) decreased in wavelength from the visible into the ultraviolet portion of the spectrum, energy of the radiation emitted from the hole in the black body would approach infinity. This increase in energy would violate the principle of conservation of energy and could not be explained by existing theories. This effect was called the ultraviolet catastrophe. The experimental data from black body experiments indicated that the radiation intensity curve corresponding to a given temperature has a definite peak, passing through a maximum and then declining. This experimental data could not be explained using classical physics, hence the catastrophe.

Planck's Solution to the Ultraviolet Catastrophe

Max Planck pulls a quantum rabbit out
of a hat.

In 1900, Max Planck, a German physicist, came up with a solution to the ultraviolet catastrophe which ascribed particle status to EM radiation. In the quantum equivalent of pulling a rabbit out of a hat, he showed that an accurate equation for the spectrum could be derived as long as one new assumption was added to those of classical physics. He assumed that the oscillators in the walls of the black body that emit the electromagnetic radiation can only have discrete energies. Each oscillator can have zero energy or some multiple of a fixed amount (quantum) which depends on the frequency, f, of oscillation according to the formula, E=nhf, where n is an integer such as 1, 2, 3, etc., and h is a new constant
(6.626 x 10-34 Js) now known as Planck’s constant.

How does this fix the ultraviolet catastrophe? The shorter wavelengths correspond to higher frequencies, so the oscillators responsible for radiation in this part of the spectrum need a lot more energy even to get into the first vibration state than those emitting radiation at a lower wavelength (lower frequency). Thermal energy is randomly distributed, so the chance that high-frequency oscillators will get enough energy to start vibrating (at least hf) is much less likely than for lower frequency oscillators. The result is that if energy is quantised in this way, the high frequency oscillators are ‘switched off’ and the intensity of the spectrum at high frequencies drops rapidly down to zero – exactly as observed by experiment.

According to Planck’s theory, an oscillating charge in the walls of a black body can only have a certain specific or discrete values for frequency. The energy it produces will be proportional to the frequency with which it is oscillating and, therefore, the energy it produces as a result of the oscillation will also be in discrete packets or quanta. In classical physics remember that all frequencies of oscillation would have been excited and the cumulative effect was the ultraviolet catastrophe. The quanta are not the same size for all colours. They are tiny for infrared, small for green and big for ultraviolet. Consider the furnace again with the energy traffic inside being emitted from the small hole in the side. The quantum restriction will make itself felt at the ultraviolet end of the spectrum where the quanta are big. Infrared will continue to pour out in a copious stream of tiny quanta, too tiny and too continuous to modify the traffic. Ultraviolet light must be emitted in big quanta or not at all. Blue, violet, and above all, ultraviolet will be seriously limited and the ultraviolet catastrophe averted.

Equation - Photon Energy
E = hf

E

f

f

energy carries by a photon

frequency

Planck's constant

joules (J)

hertz (Hz)

6.626 x 10-34 Js

You should use this equation when calculating the energy carried by an individual photon.


If your head is about to explode then think of it like this. Planck suggested that radiation was emitted from the walls of a black body in discrete energy packets rather than the continuous stream of energy carried by a wave. The thermal equivalent of being blasted with tiny balls of energy from your heater rather than a continuous flow of warmth. In addition, Planck suggested that these energy packets couldn't have any and every value for energy. The energy packets were discrete in that they could only carry energy that was a whole number integer multiple of hf or their frequency. This was the birth of quantum physics!

Planck changed the picture of radiation from a smooth stream like the wind to a grainy stream like like a sand blast. Planck and other physicists were uneasy about this new idea but there seemed to be no other way to explain the black body spectrum. The inescapable conclusion was that electromagnetic radiation is emitted in discrete energy packets or quanta rather than a smooth wave like everyone thought.

 

Einstein's Explanation of the PE Effect

In the photoelectric effect, light with a sufficiently
high frequency ejects electrons from a metal surface.
These photoelectrons, as they are called, are drawn
to the positive collector, thus producing a current.

You will remember than in his experiment to produce and detect radio waves Hertz noticed that light increased the intensity of the spark across the gap in the receiver. He called this the photoelectric effect which is now used in electric eyes, in a photographer's light meter and in picking up sound from the sound track of motion pictures. Light shining on a negatively charged photosensitive metal surface liberates electrons. The liberated electrons are attracted to the positive plate and produce a measurable current. If we instead charge the plate with just enough negative charge that it repels electrons, the current can be stopped. This is called the stopping voltage and represents the energy needed to stop photoemission from the metal surface. We can then calculate the energies of the ejected electrons from the easily measured potential difference between the plates.

The photoelectric effect was not particularly surprising to early investigators. They thought they could explain it using the classical wave model of EM radiation that was widely accepted at the time. This theory suggested that the energy in an electromagnetic wave could be transferred to the delocalilsed electrons in the metal and givs them enough kinetic energy to escape the surface of the metal. If you increased the intensity or brightness of the light (the amplitude of the wave), it would carry more energy and you would expect to see the electrons leaving the metal surface with a greater kinetic energy or velocity. Changing the frequency of the wave should have no effect on the amount of energy it carried so it should not affect the velocity of the electrons leaving the metal – but not so!

In 1902, the physicist Phillip Lenard is hysterical because he discovered experimentally that there was no relationship between the kinetic energy of electrons leaving the surface of the metal and the incident light intensity. It appeared that giving the electrons more energy by increasing the intensity of the light did not change their kinetic energies or velocities leaving the metal surface. All it did was make more electrons leave the metal at the same velocity as shown by an increased current in the circuit. Also, increasing the frequency of the light did increase the kinetic energy of the electrons leaving the surface of the metal. Even more puzzling, there was a threshold frequency below which no electrons were ejected. These findings did not fit the classical wave model of light. Was Phil a total troublemaker physicist or had he opened the proverbial can of photons that would lead to the birth of quantum theory?

Einstein's explanation of the PE effect showing EM
radiation as photons rather than a wave.

Einstein produced the answer in 1905, the same year he explained Brownian motion and came up with his theory of special relativity. His clue was Planck's quantum theory of radiation. Planck had assumed that the emission of light in quanta was due to restrictions on the vibrating atoms that produced the light. That is, he assumed that energy in matter is quantized, but that radiant energy is continuous. Einstein, on the other hand, attributed quantum properties to light itself and viewed radiation as a shower of particles. To emphasise this particle aspect, we speak of photons (by analogy with electrons, protons, and neutrons) whenever we are thinking of the particle nature of light. One photon is completely absorbed by each electron ejected from the metal. The absorption is an all or nothing process and is immediate, so there is no delay as wave energies build up. A light wave has a broad front and its energy is spread out along this front. For the light wave to eject a single electron from a metal surface, all its energy would somehow have to be concentrated on that one electron. But this is as improbable as an ocean wave hurling a surfer a few hundred metres inland with energy equal to that of the whole wave. Therefore, instead of thinking of light encountering a surface as a continuous train of waves, the photoelectric effect suggests we conceive of light encountering a surface or any detector as a succession of discrete packets of energy, or photons. The number of photons in a light beam controls the brightness (intensity) of the whole beam, whereas the frequency of the light controls the energy carried by each individual photon.

The results of an experiment where the frequency of incident light
is changed (independent variable) and the KE of emitted electrons is
measured (ependant variable). The y-intercept is the work function
and the x-intercept is the threshold frequency. The slope of the line
represents Planck's constant.

The energy carried by a photon was given by Planck as E = hf. A beam of light consisted of a stream of photons with energies given by whole number ratios of hf. The photons carry this energy into the surface of the metal. If they collide with an electron, part of their energy is transferred to the electron to be used to overcome the attraction between the nucleus and allow it to escape from the metal surface. We will call this energy Eo, which is known as the work function of the material. Any remaining energy from the photon can be given to the electron as kinetic energy. If the energy of the photon is equal to or less than the work function of the material, no electrons will be ejected. The frequency corresponding to this work function energy is the threshold frequency of the material. The energy involved can be summarised as:

hf = Eo + KE

KE = hf - Eo

The PE effect for different metals. Metals with
higher electronegativities have higher threshold
frequencies but the same gradient because of
Planck's constant.

This model explains Phil’s observations rather nicely. Thanks Albert for your input! A more intense beam of light simply contains more photons with the same energies. This means that more electrons will be ejected from the metal but at the same kinetic energy or velocity.

Increasing the frequency of the incident light ray means that the photons will have more energy so the ejected electrons will be ejected with greater kinetic energies and velocities.

The American physicist Robert Millikan made experimental verification of Einstein’s explanation of the PE effect 11 years later. Every aspect of Einstein's interpretation was confirmed, including the direct proportionality of photon energy to frequency. It was for this (and not for his theory of relativity) that Einstein received the Nobel prize in 1921.

 

 



An introduction to the PE effect in the poshest English accent you've ever heard!


The PE effect proves conclusively that light has particle properties. We cannot conceive of the PE effect on the basis of waves. On the other hand, we have seen that the phenomenon of interference demonstrates convincingly that light has wave properties. We cannot conceive of interference in terms of particles. In classical physics, this appears to be and is contradictory. From the point of view of quantum physics, light has properties resembling both. It is like a wave or just like a particle, depending on the particular experiment. So we think of light as both, as a wave packet. How about "wavicle"? Quantum physics calls for a new way of thinking.



A video explaining how a quantum mechanical model of radiation was developed in response to the ultraviolet
catastrophe and the anomalous results of PE effect experiments. An excellent summary of the material
covered in this section.

 

Planck and Einstein's Differing Views

Max Planck presents Albert Einstein
with the Max Planck medal of the
German Physical Society, June 28,
1929 in Berlin.

Max Planck and Albert Einstein shared many similarities. Both were men who devoted their lives to science, both were leaders in their field and both were born in Germany. They differed in their opinions as to the reality of the concept of the quantum and its application to light, but eventually they agreed on that.

On the surface it should seem that these two men would probably share ideals and maybe even nationalist goals for their native land. The incomplete picture below will highlight that many other aspects of their careers, personalities and political ideals were different. Planck was a patriot for his native Germany. Einstein sought to leave it from an eariy age and to take up Swiss citizenship. Planck was respected by the state and was a very stoic and proper man; a gentleman who was working for his native Germany. In many respects Planck was for all intents and purposes a patriotic nationalist. Einstein was more liberal in outlook, and was not apparently loyal to any government. These differences were never highlighted more than at the beginning of World War I. In 1914, Germany had invaded Belgium, the war propaganda machine in Germany was in full operation. A document was produced called later the Manifesto ofthe ninety-three German intellectuals to the civilized world. This document was designed to tell the German public that the role Germany was taking in the war was justified. Planck was one of the first to sign the document supporting the role of the state in the war. He then supported research to support the war effort. Einstein was also invited to sign the Manifesto of the ninety-three German intellectuals to the civilized world. He refused to accept the role of the state in war and the nationalist view that it was the role of the scientist to support the war effort. This was despite the fact that he was working in Berlin Germany at the time.

Einstein refused to sign. His views were those of a pacifist. He could not accept the role of science in killing his fellow human beings. Einstein even went as far as signing a rival document that supported the rights of all people to a peaceful world called the Manifesto to the European. This anti-nationalist view was to remain with Einstein all his life. Einstein saw clearly the role of science as something for the good of man that was not to be manipulated for the good of the state.

An interesting sideline to this story of the differences between these two scientists is that they were in fact friends. After the war Einstein fought hard to have the rights of German scientists returned when some would have taken them away. It was Planck who supported Einstein's appointment to the research institute where he worked in Berlin.

To learn more about the lives of Planck and Einstein and their respective views on whether science research is removed from social and political forces, including English translations of the Manifesto of the ninety-three German intellectuals to the civilized world and the Manifesto to the European, see pages on the physics website page at:

http://www.lmpc.edu.au/science