Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [29]
There was another intriguing feature. For any particular metal there was a minimum or 'threshold frequency' below which no electrons were emitted at all, no matter how long or intensively the metal was illuminated. However, once this threshold was crossed, electrons were emitted no matter how dim the beam of light. Einstein's quantum of light supplied the answer once again as he introduced a new concept, the work function.
Einstein envisaged the photoelectric effect as the result of an electron acquiring enough energy from a quantum of light to overcome the forces holding it within the metal surface and to escape. The work function, as Einstein labelled it, was the minimum energy an electron needed to escape from the surface, and it varied from metal to metal. If the frequency of light is too low, then the light-quanta will not possess enough energy to allow an electron to break the bonds that keep it bound within the metal.
Einstein encoded all this in a simple equation: the maximum kinetic energy of an electron emitted from a metal surface was equal to the energy of the light-quanta it absorbed minus the work function. Using this equation, Einstein predicted that a graph of the maximum kinetic energy of the electrons versus the frequency of light used would be a straight line, beginning at the threshold frequency of the metal. The gradient of the line, irrespective of the metal used, would always be exactly equal to Planck's constant, h.
Figure 3: The photoelectric effect – maximum kinetic energy of emitted electrons versus the frequency of light striking the metal surface
'I spent ten years of my life testing that 1905 equation of Einstein's and contrary to all my expectations,' complained the American experimental physicist Robert Millikan, 'I was compelled to assert its unambiguous verification in spite of its unreasonableness, since it seemed to violate everything we knew about the interference of light.'61 Although Millikan won the 1923 Nobel Prize partly in recognition of this work, even in the face of his own data he balked at the underlying quantum hypothesis: 'the physical theory upon which the equation is based is totally untenable.'62 From the very beginning, physicists at large had greeted Einstein's light-quanta with similar disbelief and cynicism. A handful wondered if light-quanta existed at all or whether they were simply a useful fictional contrivance of practical value in calculations. At best some thought that light, and therefore all electromagnetic radiation, did not consist of quanta, but only behaved as such when exchanging energy with matter.63 Foremost among them was Planck.
When in 1913 he and three others nominated Einstein for membership of the Prussian Academy of Sciences, they concluded their testimonial by trying to excuse his light-quanta proposal: 'In sum, it can be said that among the important problems, which are so abundant in modern physics, there is hardly one in which Einstein did not take a position in a remarkable manner. That he might sometimes have overshot the target in his speculations, as for example in his light-quantum hypothesis, should not be counted against him too much. Because without taking a risk from time to time it is impossible, even in the most exact natural science, to introduce real innovations.'64
Two years later, Millikan's painstaking experiments made it difficult to ignore the validity of Einstein's photoelectric equation. By 1922 it was becoming almost impossible, as Einstein was belatedly awarded the 1921 Nobel Prize for physics explicitly for his photoelectric effect