COMPTON EFFECT topics

Einstein's photoelectric discussion of 1905 and his other work including "Special Relativity" led physicists to speculate on the "momentum" of these "packets" of light which became known as "photons". Arthur Compton and Debye both provided in 1922 a very simple mathematical framework for the momentum of these photons with Compton having experimental evidence from firing X-Rays of known frequency into graphite and looking at recoil electrons.

Let E = mc^{2}
= hf for a photon, where f is frequency,
and "m" is the mass "equivalent" of the photon given they
have no "rest mass". (It is important to recognise that stopping a
photon to measure its mass eliminates it -so it has no "at rest" mass
- crucial in Special Relativity where, to travel at the speed of light, mass
would otherwise become infinite.)

Having "rigged" this mass problem,

p = momentum = mc (mass x velocity) = hf /c = E / c = h / l

The experiment shows that X-Rays and electrons behave exactly like ball bearings colliding on a table top using the same 2D vector diagrams. They enter the graphite at one wavelength and leave at a longer wavelength as they have transfered both momentum and kinetic energy to an electron. Momentum and energy are conserved in the collision if we accept the equation above for momentum of light.

When the photon enters at l_{0}
and leaves at l_{1},
its energy has changed from E_{0} to E_{1}
and momentum from E_{0} / c to E_{1}
/ c with a change in direction of q. The electron
gains E_{k} = E_{0}
-E_{1}

Using the cos rule on the diagram above, the energy equation, with some Special Relativity (or by approximation) one can derive the change in wavelength as a function of scattered angle q.

Dl = ( h / mc )( 1 - cosq ) "m" here is the electron mass and the term h / mc is called the "Compton wavelength".

This was corroborated and forced doubting physicists to take the whole photon thing very seriously - which they had not up to this point.