Question

Consider two different Compton scattering experiments, in which X-rays and γ rays of wavelength (λ) 1.024Å and 0.049Å, respectively, are scattered from stationary free electrons. The scattered wavelength (λ′) is measured as a function of the scattering angle (θ). If Compton shift is 𝛥λ=λ′−λ, then which of the following statement(s) is/are true:
( h = 6.63 x10^-34J.s, m_e = 9.11x10^-31 kg, c = 3 x 10⁸m/s )

• A. For γ-rays, λ′ _max ≈ 0.098Å
• B. For X-rays, (Δλ)_max is observed at θ= 180°
• C. For X-rays, (Δλ)_max ≈ 1.049Å
• D. For γ-rays, at θ= 90° , λ′ ≈0.049Å

Answer 1

The Correct Option is A, B

The Compton Shift Formula

The Compton shift formula is given by: 

Δλ = λ' − λ = (h / m_ec) (1 − cosθ)

where:

h / m_ec = 2.43 × 10⁻¹² m = 0.0243 Å

For γ-rays (λ = 0.049 Å):

• Maximum shift occurs at θ = 180°, where:
• The maximum scattered wavelength is:
• At θ = 90°:

For X-rays (λ = 1.024 Å):

• Maximum shift occurs at θ = 180°, where:
• The maximum scattered wavelength is:

Conclusion

The correct statements are (A) and (B).