The shift in wavelength upon scattering of light from stationary electrons. The Compton effect, discovered by Compton in 1923, provided the final confirmation of the validity of Planck's quantum hypothesis that electromagnetic radiation came in discrete massless packets (photons) with energy proportional to frequency.
Let a photon
of frequency 
scatter off an electron e at an angle 
. In the collision, it transfers some energy to the electron 
and emerges at a shifted frequency 
as 
. Conservation of momentum gives
But
Plugging (3) and (4) into (2) gives
Conservation of energy gives
Now,
Plugging (7)-(10) into (6) gives
Solving (11) for
gives
Equating (5) and (12) gives
Rewriting,
giving the Compton scattering equation,
The quantity
is known as the Compton wavelength.
Let a photon
of frequency scatter off an electron e at an angle . In the collision, it transfers some energy to the electron and emerges at a shifted frequency as . Conservation of momentum gives (1)
(2)
But
(3)
(4)
Plugging (3) and (4) into (2) gives
(5)
Conservation of energy gives
(6)
Now,
(7)
(8)
(9)
(10)
Plugging (7)-(10) into (6) gives
(11)
Solving (11) for
gives (12)
Equating (5) and (12) gives
(13)
Rewriting,
(14)
(15)
(16)
giving the Compton scattering equation,
(17)
The quantity
is known as the Compton wavelength. 
回复Comments
{commenttime}{commentauthor}
{CommentUrl}
{commentcontent}