The Compton wavelength shift depends onA) Wavelength of the incident photonB) Material of the scattererC) Energy of the incident photonD) Scattering angle

Answer: (D) Scattering angle

The Compton wavelength shift refers to the change in the wavelength of a photon when it undergoes Compton scattering (elastic scattering of a photon by a free electron). This shift depends on several factors, but the key factor that determines the wavelength shift is the scattering angle of the photon. Let's analyze each option:
(A) Wavelength of the incident photon:
• The incident photon wavelength does influence the energy of the photon, and indirectly it could affect the wavelength shift in some contexts. However, the Compton shift is typically described in terms of the scattering angle, not the initial wavelength.
• The formula for the Compton shift is independent of the initial wavelength but depends on the scattering angle.
(B) Material of the scatterer:
• The material of the scatterer is not directly relevant to the Compton wavelength shift, provided that the scatterer is an electron or a free particle (or an electron in a material that can be approximated as free for this interaction).
• The Compton shift is mainly dependent on the scattering angle and not on the material properties.
(C) Energy of the incident photon:
• The energy of the incident photon is related to the wavelength via the equation E=hcλE = \frac{hc}{\lambda}. A higher-energy photon (shorter wavelength) will experience a different interaction with the electron than a low-energy photon (longer wavelength).
• However, the Compton shift itself, i.e., the change in wavelength, depends primarily on the scattering angle, not directly on the energy of the incident photon.
(D) Scattering angle:
• The scattering angle (θ\theta) plays a direct role in determining the Compton wavelength shift.
• The change in wavelength (or Compton shift) Δλ\Delta \lambda is given by the equation:
Δλ=λ′−λ=hmec(1−cos⁡θ)\Delta \lambda = \lambda' - \lambda = \frac{h}{m_e c} (1 - \cos \theta)
Where:
o hh is Planck's constant,
o mem_e is the mass of the electron,
o cc is the speed of light,
o θ\theta is the scattering angle.
As shown in the equation, the wavelength shift depends on the scattering angle θ\theta, and it is maximal when the photon is scattered backward (θ=180∘\theta = 180^\circ).
Final Answer:
The Compton wavelength shift depends on the scattering angle. Therefore, the correct option is:
(D) Scattering angle\boxed{\text{(D) Scattering angle}}