2006/10/02 | 康普顿效应[Compton Effect]
类别(Ω〖物理〗) | 评论(0) | 阅读(105) | 发表于 11:38
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
(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.
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