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D.  Three quantum phenomena

In fluorescence, matter absorbs light waves of a high frequency and then emits light of the same or lower frequency.  This process was studied and named by George Gabriel Stokes in the mid-19^th century.  Today, fluorescence is familiar to us from fluorescent light bulbs.  A fluorescent bulb's filament produces ultraviolet light, which is absorbed by the bulb's inner coating, which then emits lower-frequency visible light-more visible light than an incandescent bulb produces with the same wattage.

According to the hypothesis of light quanta, during fluorescence an atom absorbs a quantum of light whose energy is proportional to the light wave's frequency.  If the atom doesn't supply any extra energy of its own, the light quantum emitted should either have the same energy or less energy than the quantum it absorbs.  This means that the emitted light's frequency is either the same or lower.  Einstein also saw that, if light quanta really existed, there might be deviations from this process.  If we exposed an atom to so many quanta at once that it could readily absorb more than one at a time, the atom might combine the energies of the quanta to emit one single quantum of higher frequency.  Deviations might also happen if either the absorbed or the emitted light had a low enough frequency, since Einstein's analysis had begun by assuming the light waves' frequencies were high enough for Figure 3's lower curve to accurately describe their intensity.

Another of Einstein's deductions relates to the way ultraviolet light can generate positive and negative electric charges when it shines through gases.  If light moved as individual quanta, this process also ought to work a certain way; positive and negative charges within a gas molecule would separate once the molecule absorbed a sufficiently energetic quantum of ultraviolet light.  The energy would have to be enough for the charges to completely overcome their mutual attraction and move apart.  Since some minimum amount of energy would be required, the light wave would have to have at least a minimum frequency.  Furthermore, since the energy to separate positive and negative charges in one molecule would require one light quantum, the amount of light required to separate charges in a given amount of gas should be directly proportional to the amount of gas.  Einstein noted that checking this proportionality with experiments would be an important test of the light-quantum hypothesis.

Einstein also described one other deduction from the quantum hypothesis related to the photoelectric effect by which light shining on the surface of a metal produces electrons.  This deduction was especially significant since others had already found certain features of this effect hard to explain if the energy of light waves were distributed uniformly.

The electrons of a nonmetallic material are bound within atoms of the material.  In a metal, some of the electrons are less tightly bound, and are free to move around throughout the volume of the metal instead of remaining within a particular atom.  However, these electrons are still bound to the rest of the metal as a whole.  They could escape from the metal if they had enough energy to overcome its attraction.  Shining a light on the metal can supply extra energy.

It turns out that the electrons will only acquire enough energy if the light shining on them has at least a minimum frequency.  Maxwellian theory offers no obvious explanation for this, but it is easy to explain in terms of light quanta.  Suppose each light quantum is absorbed by one electron.  Since the energy of a light quantum is proportional to its frequency, the electron will have enough energy to break free of the metal if the frequency of the quantum is high enough.  If the frequency of the quantum is too low, the electron won't gain enough energy to escape.

The required minimum frequency of the light waves can be raised by increasing the metal's attraction to the electrons.  Since electrons have a negative charge, we can attract them more strongly by applying extra positive charge to the metal.  Einstein pointed out that certain conclusions follow from this fact, at least if the light has high enough frequencies for lower curve in Figure 3 to be accurate.  If each quantum transfers its energy to electrons independently of all other quanta, the positive charge required to stop electrons from leaving the metal should not depend on the intensity of the light, while the number of electrons that would leave if the metal had a lower voltage should increase at a fixed rate with the intensity of the light.

These predictions were verified in detail in experiments performed about a decade later by Robert Millikan and his students.  But the underlying ideas about light quanta gained acceptance more slowly among physicists.

Today, Einstein is most famous for relativity.  But of all the papers Einstein was publishing in 1905, it was his paper on light quanta that he regarded as the revolutionary one.  For while his special relativity theory revealed a surprising connection between space and time, that connection could be logically deduced from known facts and existing physical theory.  There was no obvious way to account for light quanta in Maxwell's theory.

Planck had understood light quanta to be units of energy, but not as having particular locations in space; Einstein brought the latter concept to light.  Einstein's predictions about the photoelectric effect were widely accepted among physicists after Millikan and his students verified them about a decade later, but it would be about one more decade before the concept behind those predictions became similarly accepted.  By then, further extensions of the light-quantum concept into related ideas about matter had demonstrated their value for understanding the behavior of the atoms and subatomic particles of which matter is made.  The value of these ideas, known as quantum theory, is much clearer today, since atoms and particles are increasingly the focus of practical technologies.

While the Nobel Prize awarded to Einstein in 1922 implicitly recognized his now-famous theory of relativity, it specifically mentioned only his accomplishment in describing how energies from photoelectrons depend on light frequency, and how the number of photoelectrons depends on light intensity.  The presentation speech did describe Einstein's work on Brownian motion and the relativity theory (pointing out how, at that time, some philosophers challenged this theory while others acclaimed it), but Einstein's photoelectric theory was the main topic.  In fact, the award diploma declared the prize was awarded to Einstein "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect".

References, Links, and Comments:  

"The Nobel Prize in Physics 1921" [exit federal site]
[exit federal site]The 1921 Nobel Prize in Physics was actually awarded a year later, at the same ceremony where Niels Bohr received the Physics prize for 1922.  The presentation speech describes the law of the photoelectric effect and Einstein's concept of how the effect works. 

"The Photoelectric Effect" [exit federal site] by Walter Fendt
A Java applet simulating a Millikan-type experiment.  

The Old Quantum Theory, edited by D. ter Haar
Contains English translations of the December 1900 paper by Max Planck cited above ("On the Theory of the Energy Distribution Law of the Normal Spectrum") and of the paper in which Albert Einstein published the discoveries described in this article ("On a Heuristic Point of View about the Creation and Conversion of Light").  

"A Scientific Autobiography" (English translation of "Wissenschaftliche Selbstbiographie"), in Scientific Autobiography and Other Papers by Max Planck.
Among other things, describes how and why Planck worked out the relation between intensity and frequency of the cavity radiation described above, also known as black-body radiation.  

The Rise of the New Physics by Abraham D'Abro
The section "The Wave Theory of Light" (pp. 276-281) describes the theory proposed by Christiaan Huygens in the 17^th century and its later development by others, as well as experiments by Huygens and later physicists demonstrating light's wave character. The chapter "Planck's Original Quantum Theory" (pp. 447-471) is a detailed discussion of Planck's theory of cavity radiation and its predecessors; the section "Rayleigh's Erroneous Law of Radiation" (pp. 454-456) tells why the older theory of light leads to the erroneous upper curve in Figure 2.  

Treatise on Light [exit federal site] by Christiaan Huygens (Silvanus P. Thompson, trans.)  "The 8 January 1690".
Chapter V, "On the Strange Refraction of Iceland Crystal", [exit federal site] contains a section [exit federal site] describing a polarization phenomenon perpendicular to the way light travels through the crystal-which was later understood to be the direction of the light's vibrating force fields. 

"George Gabriel Stokes", [exit federal site] The MacTutor History of Mathematics [exit federal site] archive, School of Mathematics and Statistics, [exit federal site] University of St Andrews, Scotland [exit federal site]
Short biography of the discoverer of fluorescence.

The Strange Story of the Quantum by Banesh Hoffmann
Heinrich Hertz' experiments with electromagnetic waves are described early in this book. Interestingly, as this book shows, it was Hertz, during this demonstration of the correctness of  Maxwell's theory, who discovered the photoelectric effect, which presented a new problem for that same theory.  

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Prepared by Dr. William Watson, Physicist
DOE Office of Scientific and Technical Information