Question

The Compton wavelength shift depends on
A.Wavelength of the incident photon
B.Material of the scatterer
C.Energy of the incident photon
D.Scattering angle

Answer 1

Hint- The formula for the standard Compton wavelength, $\lambda $, is given by $\lambda = \dfrac{h}{{mc}}$.

Complete step by step solution:
Before solving the question, we need to properly understand the meaning of Compton wavelength.
The Compton wavelength is a quantum mechanical property of a particle. It was first introduced by Arthur Compton. The term was first coined to explain the phenomenon of scattering of photons by electrons in a process known as Compton scattering. Let us discuss what the term means. The Compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the mass of the particle.
Let us now discuss the formula for Compton wavelength.
The standard Compton wavelength, $\lambda $, of a particle is given by,
$\lambda = \dfrac{h}{{mc}}$
While its frequency is given by,
$f = \dfrac{{m{c^2}}}{h}$
Where h is the Planck’s constant, m is the particle’s rest mass, and c is the speed of light.
For example, The value for Compton wavelength of the electron is $2.42631023867(73) \times {10^{ - 12}}\,m$
The Compton effect occurs for most of the atomic electrons.
In the Compton effect, individual photons collide with single electrons that are free or quite loosely bound in atoms of matter.
The formula for shift in Compton effect is given by,
$\lambda - {\lambda ^1} = \dfrac{h}{{{m_e}c}}(1 + \cos \theta )$
Where, $\theta $ is the scattering angle.

So the answer is option (d) i.e., the scattering angle.

Note: Before solving the sum, students need to understand the meaning of the Compton effect. Also, after knowing the meaning students also need to be able to derive the formula for shift in Compton effect.