. Equat- 
v 2 ) = m 2 c 
.(52-2). 
d quanta, 
(52-31), 
(52-32). 
n contain- 
a,ve-length 
le incident 
It is not 
to experi- 
f high fre- 
natter can 
rmula. It 
sctron can 
e-length is 
such as to 
ust be just 
)f Planck’s 
re consider 
QUANTUM THEORY 
Denote the electric force in the electromagnetic oscillations which 
constitute the radiation by X. Acting on an electron of charge — e and 
mass m, it will produce an acceleration 
r = — eX/m. 
hjow according to classical electromagnetic theory an accelerated electron 
should radiate energy at the rate 
§e 2 r 2 /c 3 = §e 4 Z 2 /w 2 c 3 (53-1). 
This radiation is not in the direction of the incident beam and is scattered 
radiation. By the conservation of energy it must be supplied at the expense 
of the incident beam. 
If we have a screen containing N electrons per sq. cm. the radiation 
scattered per second will be 
2Ne* x - 
3 m 2 c 3 
where the mean value of X 2 is to be taken. This assumes that the conditions 
are such that the electrons scatter independently, and that there is no 
systematic phase relation of the wavelets from the separate electrons. The 
energy of the incident radiation is Z 2 / 4?7 per cu. cm. (half electric and half 
magnetic) ; hence the amount incident on the N electrons in 1 second is 
cZ2/47t (53-3). 
Dividing (53-2) by (53-3), the fraction of the incident radiation scattered 
by the screen is 
877 Ne* 8n , t , 
3 ra 2 c 4 3 v n 
where b = e 2 jmc 2 = 2-81 . 10 -13 cm.* 
The usual definition of a scattering coefficient is the proportion scattered 
by a screen containing 1 gm. per sq. cm.; but since we are not likely to 
meet with a screen composed wholly of free electrons we prefer to modify 
the definition in this case. Instead of a gram of electrons we take the 
electrons contained in 1 gm. of matter, assuming (as is roughly true for 
all elements except hydrogen) that there is one electron for every two units 
of atomic weight, and therefore 3-01 . 10 23 electrons per gm. The scattering 
coefficient is then by (53-4) 
As with the Compton effect this scattering coefficient has been verified 
experimentally by using hard X rays which act on the bound electrons 
of the lighter elements practically as if they were free. When the wave 
length is comparable with the diameter of the atom the scattering is much