Month: August 2020

Halfway between Einstein’s suggestion about the light quantum in 1905 and the beginning of the acceptance of the light quantum around 1925-6, there is R. A Millikan’s brilliant and puzzling paper on the quantum and the photoelectric effect, published in 1916 in Physical Review.  Millikan is an amazing and baffling figure in the growth of quantum theory and what Buchwald calls “modern physics” – ie a physics that is based on micro-physics and high energy physics with special relativity and without the aether.  In Pais’s biography of Einstein, he notes that in 1948, in honor of Einstein, he had Millikan as the senior contributor to the Festschrift.  In his contribution Millikan said that he spent ten years “testing that 1905 equation of Einstein’s” and in the end he had to  “assert its unambiguous verification in spite of its unreasonableness since it seemed to violate everything we knew about the interference of light (Pais, Subtle is the Lord page 357).”

So let’s look at Millikan’s paper, “A Direct Photoelectric Determination of Planck’s h” and what it verified and then look into Millikan himself as a now rather faded cultural item (after a brief detour to Compton’s early work with Richardson and Thomson and Wilson in 1899). 

Millikan’s paper begins (and I will comment on this first paragraph in more detail):

Quantum theory was not originally developed for the sake of interpreting photoelectric phenomena.  It was solely a theory as to the mechanism of absorption and emission of electromagnetic waves by resonators of atomic or subatomic dimensions.  It had nothing whatever to say about the energy of an escaping electron or about the conditions under which such an electron could make its escape, and up to this day the form of the theory developed by its author has not been able to account satisfactorily for the photoelectric facts presented herewith.  We are confronted, however, by the astonishing situation these facts were correctly and exactly predicted nine years ago by a form of quantum theory that has now been generally abandoned.

The first two sentences describe how Planck’s constant was understood at the time, ie as related to the transfer of energy in relation to blackbody (heat) radiation.  The third sentence brings up the photoelectric effect, ie, that light (ultraviolet and visible light as it was understood at the time) could cause electrons to leave metals – Lithium and Sodium for example.  The observation that the release of electrons was contingent on the wavelength/frequency of the light and not its intensity was known at the time, but not well defined or understood.  The prediction was Einstein’s proposal of the light quantum where  photoelectrons would be emitted only when the light frequency was short enough, and so, powerful enough, to supply enough energy to release the electrons from the specific electromagnetic barrier that varied according to the metal.  This required release energy was called “the work function.”  So, in relation to Planck’s h, Einstein proposed that the maximum kinetic energy of the released electron would be equal to Planck’s constant times the light frequency minus the work function.  Therefore, if you could determine the energy of the electron and the work function, you could determine Planck’s constant as long as you also had good measurements of the light frequencies involved and excluded the effects of reflected light, oxidation and interactions with other metal surfaces.  The last sentence in Millikan’s first paragraph, about the astonishing situation, really is astonishing since I don’t think Einstein ever gave up on the light quantum, though by 1916, he was more involved in completing the theory of General Relativity.  

Still, odd and astonishing as this all was, Millikan’s paper shows why it was so hard to work out what was happening with photoelectrons.

For one thing, at first the controllable light frequencies (produced from sparks, just as in the original discovery of the effect) were only available in a few scattered ranges in the visible and ultraviolent so (as Millikan points out on page 358) energy curves were confined and confused.  Moreover, because the measurements of the energy required for the electrons to leave the metals were unreliable and inaccurate, some experimenters surmised that the energy required was the same for all metals.  Millikan set out to resolve all of the problems by cutting new surfaces in the metals in a vacuum, exposing the metal to light in a vacuum and being very precise about the wavelengths and energies (at the metal surfaces) involved.  This eliminated surface films on the metals and made precise measurement possible.

Nevertheless (as Millikan points out on page 360), that Planck’s constant had some relation to the photoelectric effect was generally assumed – apparently mostly because the presence or absence of emission was related only to the wavelengths of light and not the intensity of light, but this left the question open as to whether the energy of the emitted electrons fitted Einstein’s equation.  The finding that the fit was exact (once Millikan painstakingly eliminated or accounted for major sources of error and extended the measured light frequency range four times beyond what Richardson and Compton had covered in 1912) would seem to suggest something about the possibility of a light quantum – but it did not until Compton demonstrated and explicated the action of light quanta in the context of the Compton Effect.  

Here is the basic form of Millikan’s apparatus for measuring the photoelectric effect in a vacuum.  W is the wheel with the metal samples.  K is a knife for slicing the metal to get fresh surfaces.  F is a movable electromagnet.  Monochromatic light enters at O.  B and C supply current to the Faraday cylinder – which is represented by the dotted lines and the solid line (copper gauze and solid copper) in the region of B, C and O.