PRELIMINARY SURVEY 
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this hypothesis, the energy of radiation is to be treated as though 
it were done up in bundles, the energy of the bundle or light 
quantum being given by Planck’s expression hv. Further, only 
a single quantum is involved in any single physical change. This 
is sometimes known as Einstein’s law, which may be stated as 
follows : “In every case where there is a mutual transforma 
tion between moving electrons and electromagnetic radiation, a 
single light quantum is utilized or is liberated.” 
One aspect of this reciprocal relation is seen in the photo 
electric effect. When light of sufficiently short wave-length is 
allowed to fall upon a polished metal surface, negative electrons 
are set free with a velocity which depends upon the wave-length 
of the exciting light. The maximum kinetic energy of the 
electrons increases with frequency in accordance with a formula 
first suggested by Einstein in the paper referred to. Einstein’s 
formula is : 
| mv 2 — hv — P 1:4 
Here Imv 2 corresponds to the maximum kinetic energy of the 
emission ; hv corresponds to the energy of the light quantum, 
and P measures the work done when an electron escapes from 
the atom to which it is attached. It is found that this quantity 
P, which is called the “ electron affinity,” can be expressed as 
hv0 where v 0 is a definite frequency characteristic of the metal 
on which the radiation falls. The equation, which has been 
called “ the fundamental law of photo-electric activity,” now 
takes the form 
\ mv 2 = h(v — v 0 ) 1:5 
The kinetic energy of the electron is proportional to the difference 
between the frequency of light and the frequency character 
istic of the particular metal. 
The significance of the relation may best be appreciated by 
considering a particular case. For sodium the characteristic 
or “ threshold ” frequency is about 5*15 x io 14 vibrations per 
second, corresponding to green light. If the light is redder 
than this, it may fall on sodium for centuries without liberating 
any electrons, but if the light is bluer than the specified green 
light, it will at once bring about the separation of electrons and 
the maximum kinetic energy of emission will increase as the 
frequency increases. Einstein’s equation has been verified by 
numerous experimenters—in the first instance by Hughes * 
and by Richardson and Compton,f then by Millikan $ and his 
pupils—indeed Millikan’s experiments based on this relation, 
, 2i p, 677, № * A. LI. Hughes, Phil. Trans., vol. 212, p. 205, 1912. 
f O.W. Richardson and K. T. Compton, PM. Mag., vol. 24, p. 575, 1912. 
X R. A. Millikan, Phys. Rev., vol. 7, p. 355, 1916.