The Quantization of Energy 175
by R.A. Millikan (the man who measured the absolute charge of an
electron using oil drops). He verified that the Einstein formula was
correct and that the energy of the photoelectrons was proportional to the
frequency. The constant of proportionality is just Planck’s constant, h,
which Millikan found from his experimental results had the same value
that Planck used when he explained black body radiation. Millikan’s
results confirmed, with great mathematical precision, that the energy of
light is quantized and that light displays particle-like behaviour in the
photoelectric effect.
Another experiment, which followed Millikan’s photoelectric work
also revealed the particle-like behaviour of light. This was the
experiment of Compton in 1922 in which he scattered x-rays using
electrons as the target. When a beam of x-rays is directed at an
amorphous (non-crystalline) solid like graphite, most of the x-rays pass
through the solid unscattered. Some of the x-rays are scattered in all
directions by collisions with the electrons in the solid. Compton noted an
effect, which bears his name, namely those x-rays, which are scattered by
the electrons have a slightly smaller frequency after the collision and that
the greater the angle of scatter, the more the diminution of the frequency.
The Compton effect is easily understood if the beam of x-rays is
treated as a beam of photons. Each photon carries energy and momentum
related to its frequency, f. The energy of the photon is equal to hf and its
momentum to hf/c where c is the velocity of light. The momentum of a
photon is related to energy by the theory of relativity and is equal to its
energy divided by c. Although the electrons in the graphite are bound to
the nucleus, they may be treated as unbound because the energy of
binding is so small compared to the energy of the x-ray photons. In
analyzing his experiment, Compton treated the electron and photon as
two particles colliding with each other. Using this assumption, he was
able to explain all of the details of the Compton effect. Once again,
electromagnetic waves behave as though they are a beam of particles.
Newton’s corpuscular theory of light seems to be valid in certain
circumstances, namely for black body radiation, the photoelectric effect
and the Compton effect. For other situations, however, such as
diffraction, interference and refraction, light behaves as a wave. The dual
nature of light provided physicists with the deepest mystery they had yet
experienced. Light seemed to possess contradictory aspects. The
dilemma was expressed succinctly by William Bragg, who had worked
on the x-ray diffraction experiments, which had shown x-rays behave