The Compton effect represents another confirmation of the photon theory, and a refutation of the wave theory. One observes it (Compton, 1924) in the scattering of X-rays
by free (or weakly bound) electrons. The wavelength of the scattered radiation exceeds that of the incident radiation. The difference
varies as a function
of the angle
between the direction of propagation of the incident radiation and the direction along which one observes the scattered light, according to Compton's formula:
![]() |
(1) |
where
is the rest mass
of the electron. One notes that
is independent of the incident wavelength. Compton and Debye have shown that the Compton effect is a simple elastic collision
between a photon of the incident light and one of the electrons of the irradiated target.
In order to discuss this corpuscular interpretation it is convenient to state a few properties of photons which derive directly from Einstein's
hypothesis. Since they possess the velocity
,photons are particles of zero mass. The momentum
and the energy
of a photon are thus connected by the relation
![]() |
(2) |
Consider a plane, monochromatic light wave
is a unit vector
in the direction of propagation,
is the wavelength,
the frequency:
. In accordance with Einstein's hypothesis, this wave represents a stream of photons of energy
. The momentum of these photons is evidently directed along
and its absolute value, according to (2), is equal to
This relation is a special case of the relation of L. de Broglie. It is often convenient to introduce the angular frequency
and the wave vector
of he plane wave. The connecting relations are then written:
![]() |
(3) |
The corpuscular theory of the Compton effect consists in writing down that the total energy and momentum are conserved in the elastic collision between the incident photon and the electron. Let
be the initial and final momenta of the photon, respectively,
the recoil momentum of the electron after collision (Figure 1).
The conservation equations are written
![]() |
|||
![]() |
(4) |
According to these equations the collision is completely defined once the initial conditions and the direction of emission of the scattered photon are known. Taking into account the relations in (3), one can easily deduce the Compton formula which is thus explained theoretically. Since the first work
of Compton, all the other predictions of this theory have been confirmed experimentally. The recoil electrons have been observed and the law of their energy variation as a function of the angle of emission
is just the one which one derives from equations (4). Coincidence experiments have shown that the scattered photon and electron are emitted simultaneously, and that the correlation between the emission angles
and
agrees with the theory.
[1] Messiah, Albert. "Quantum mechanics: volume I." Amsterdam, North-Holland Pub. Co.; New York, Interscience Publishers, 1961-62.
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