Question

1) What is Compton scattering?

2) Derive an equation for the wavelength of a photon scattered from a nearly free electron in some target material.

3) Why is Compton scattering not observed for visible wavelengths?

Answer 1

(i) What is Compton scattering?

Compton scattering is a collision between a photon and a loosely bound outer-shell orbital electron of an atom.

The photon does not disappear in Compton scattering. Instead, it is deflected through a scattering angle. Part of its energy is transferred to the recoil electron. Thus, the photon loses energy in this process.

Compton scattering is strictly a photon-electron interaction.

(ii) Derive an equation for the wavelength of photon scattered from a nearly free electron in some target material.

Compton derived the mathematical relationship between the shift in wavelength and the scattering angle of X-rays by assuming that each scattered X-ray photon interacted with only one electron.

Compton published the following equation which are given below as :

' - = (h / m_e c) (1 - cos )

where, ' = initial wavelength

= wavelength after scattering

h = Planck constant

m_e = mass of an electron

c = speed of light

= scattering angle

The quantity (h / m_e c) is known as the "Compton wavelength" of an electron. It is equal to a value of 2.43 x 10^-12 m.

The wavelength shift (' - ) is at least zero (for = 0⁰) & at most twice the Compton wavelength of electron (for = 180°).

(iii) Why is Compton scattering not observed for visible wavelengths?

In Compton effect, the energy of photon should be greater than binding energy of electron in metals.

The threshold frequency is equal to that of ultraviolet light.

The visible light energy is low.

So, Compton scattering effect is not observed in visible lights.

The Compton effect is an ionizing effect. Visible light does not have sufficient energy to effect ionization of an atom. Visible light does engage in photochemical reactions which might lead to ionization. A photon may be absorbed in a photochemical reaction and a lower energy photon may be emitted in the process.