Q.16. Explain Compton Effect and show that
Compton shift depends only on angle of scattering and its independent of the
wavelength of the incident photons. (AKTU. 2002-03)
Related
Questions -
Q. Discuss Compton Effect and derive the
expression for Compton shift. (AKTU. 2009-10)
Q. Derive an expression for Compton
shift showing dependency on angle of scattering. (AKTU. 2013 - 14)
Ans. Compton Effect: -
Compton discovered that when X-rays of a sharply
defined frequency were incident on a material of low atomic number like carbon,
they suffered a change of frequency on scattering. Compton observed that the
scattered X-rays had wavelength l slightly longer than the wavelength of incidentX-rays l0. This change in wavelength Dl = l - l0 is called
Compton shift, which varies with the scattering angle and it is independent of
the incident frequency, also of the nature of the scatter. This phenomenon of
scattering with the change in frequency is called the Compton Effect.
Let a photon of energy hn incident on an electron at rest. The initial momentum
of the electron is zero and its initial energy is only the rest mass energy
i.e. m0c2. The scattered photon of energy hn¢ moves in a direction inclined at an angle q to the original direction. The electron acquires a
momentum mv and energy mc2 moves at an angle f to the original direction.
According to principle of
conservation of momentum,
In X-direction
+ mvcosf
Þ mvc.cosf = h(n- n¢cosq ) ..........(i)
in Y-direction
..........(ii)
Squaring and adding
eq.(i) and eq.(ii)
m2v2c2 = h2(n2+ n¢2cos2q-2nn¢cosq)+h2n¢2 sin2 q
= h2n2 + h2n¢2 (sin2 q + cos2q) -2h2nn¢cosq
= h2n2 + h2n¢2 - 2h2nn¢cosq ..........(iii)
According to the
principle of conseration of energy
Þ 
..........(iv)
..........(iv)
Substracting eq.(iii)
from eq.(iv)
