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Thermodynamics

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Compton Effect

In 1923, A.H. Compton was able to show that when a beam of monochromatic X-rays was scattered by a light element such as carbon, the scattered radiations of two components, one of longer wavelength than the incident radiation and the second of the same wavelength as the incident radiation. He further observed that the difference in wavelength of the two scattered radiations increases with the angle of scattering. For the radiation scattered at right angles to the incident beam, the differences in wavelength is independent of the wavelength of the incident beam and also of the nature of the scattering material.

In order to account for the difference in wavelength. Compton assumed that during the scattering process, a collision occurs between the incident photon and the electron in the scattering material. He explained the phenomenon on the basis of quantum theory of the radiation due to the Max-Planck and Einstein.

Theory: Consider the incident radiation as consisting of photons of quanta of energy hv. Each incident photon has an energy hv, momentum hv/c and moves with the velocity of light c.

Suppose the photon of energy hv strikes a free electron at rest. The energy of the incident photon is passed on to the scattered photon and the electron. The scattered photon has energy hv’ and the makes an angle θ with the original direction. The electron acquires a velocity v in a direction making an angle Φ with the original direction.

The principle of conservation of momentum and energy can be applied. As the energy of the recoiling electron is taken from the incident photon, therefore, the scattered photon has less energy than the incident photon and hence a lower frequency or longer wavelength than that of the incident photon.

Energy of the incident photon = hv

Energy of the scattered photon = hv’

Energy of the recoiling electron

where m0 is the rest mass of the electron. Applying the principle of conservation of energy