Question

Consider an x-ray beam with λ = 10 × 10-12 m is scattered from an atom at angle π/3 from its initial path, in such case the value of Compton shift will be ________.
1. 1.2 picometer
2. 1.4 picometer
3. 1.6 picometer
4. 2.0 picometer

Answer 1

Correct Answer - Option 1 : 1.2 picometer

Concept:

Compton effect:

• Compton effect is defined as the effect that is observed when x-rays or gamma rays are scattered on a material with an increase in wavelength.
• Arthur Compton studied this effect in the year 1922.
• During the study, Compton found that wavelength is not dependent on the intensity of incident radiation.
• It is dependent on the angle of scattering and on the wavelength of the incident beam.
• It is given in the following mathematical form:

​\(⇒ λ'-λ=\frac{h}{m_0c}\left(1-cosϕ\right)\)

Where λ' and λ = radiation spectrum peaks, mo = rest mass of an electron, h = Planck's constant, ϕ = angle at which radiation scattered and \(\frac{h}{m_0c}\)= Compton wavelength of the electron

Calculation:

Given ϕ = 60°, mo = 9.1 × 10-31 kg, c = 3×108 m/sec and h = 6.6 × 10-34 J-sec

The Compton shift for X-rays is given as,

\(⇒ λ'-λ=\frac{h}{m_0c}\left(1-cosϕ\right)\)

\(⇒ λ'-λ=\frac{6.6×10^{-34}}{9.1×10^{-31}×3×10^8}\left(1-cos \ 60\right)\)

⇒ λ' - λ = 0.12 × 10-11

⇒ λ' - λ = 1.2 × 10-12

⇒ λ' - λ = 1.2 picometer​

Hence, option 1 is correct.