Einsteins photoelectric equation

In 1905 Albert Einstein (1879-1955) published a paper modestly entitled 'On a Heuristic Point of View Concerning the Generation and Transformation of Light'. The word 'heuristic' implied that the matter was not necessarily in its final form and that alternative explanations were possible. He proposed that if the photon was localised in space it could transfer its entire energy to an electron. This energy could then be used by the electron to escape from the metal. Whatever energy was left over would appear as kinetic energy of the 'liberated electron' according to the equation hf = W + (KE)max Einstein's equation where hf is the energy of the incoming photon, W is the work function of the metal, which is the minimum work needed to overcome the restraining forces which bind the electron to the metal, and KEmax is the energy of the most energetic emitted electron.

Einstein was a great thinker, but he did not do experiments. It remained for others to submit the equation to the rigorous test of experiment. If the equation was correct, one would have to observe the following:

1. The energy, hf, of the 'light bullets' should depend only on the frequency of the light (f), and nothing else. This in turn should be reflected in the energy of the electrons which have been ejected.

2. The number of electrons emitted per second should depend on the number of photons per second striking the surface, i.e. on the intensity of the light, and nothing else.

3. Emission would be instantaneous.

The American physicist Robert A. Millikan (1868-1953) is perhaps best known for his work which showed that electric charge comes in discrete indivisible units. An electron carries one such fundamental unit of charge, which he measured in his 'oil drop experiment' published in 1912. It was natural that he should also turn his attention to a quantitative study of the characteristics of electrons emitted in the photoelectric effect. His first step was to measure the energies of electrons emitted by light of various frequencies shining on different metals. As early as 1908, at the Boston meeting of the American Physical Society, he had announced that he intended to measure the kinetic energy of these electrons by a determination of the stopping potential. This is the adverse electrical potential required to prevent them from reaching a second metallic plate at the end of an evacuated tube. Essentially he would give the electrons an 'electrical hill' to climb, and investigate how high this hill must be to completely stop the photoelectric current, for different values of the frequency of the incoming light.

At first Millikan was quite sceptical of Einstein's theory, and his original intention was as much to disprove as to confirm the validity of the equation. 'I scarcely expected that the answer, when it came, would be positive, but the question was very vital, and an answer of some sort had to be found.'

The principles of Millikan's experiment were quite straightforward, but in practice the work was long and tedious, and it took some years to complete. When his results confirmed Einstein's theory Millikan he was generous in giving due credit to Einstein and admitting that his original scepticism had been unfounded.

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