In Compton scattering, the change in wavelength is Δλ = (h / (m_e c)) (1 - cos θ). What is the physical significance of Δλ?

In Compton scattering, the change in wavelength is Δλ = (h / (m_e c)) (1 - cos θ). What is the physical significance of Δλ?

• A. It is the energy change of the photon
• B. It is the wavelength shift of the scattered photon due to electron recoil
• C. It is the scattering angle
• D. It is the momentum transfer

Answer: (B)

The change in wavelength in Compton scattering represents the wavelength shift that the scattered photon undergoes because it loses energy to the electron as the two particles recoil from the collision. The formula Δλ = h/(m_e c) (1 − cos θ) shows that this shift depends on the scattering angle, with the electron’s Compton wavelength h/(m_e c) setting the scale (about 2.43 × 10^-12 m). So the photon ends up with a longer wavelength (lower energy) after the collision, and the amount of that shift grows with the scattering angle, reaching a maximum for backscattering (θ = 180°). This is why Δλ is best understood as the wavelength shift of the scattered photon due to electron recoil. While the energy change and the momentum transfer are related to this process, Δλ specifically encodes the observable change in the photon’s wavelength, not the angle itself.

The change in wavelength in Compton scattering represents the wavelength shift that the scattered photon undergoes because it loses energy to the electron as the two particles recoil from the collision. The formula Δλ = h/(m_e c) (1 − cos θ) shows that this shift depends on the scattering angle, with the electron’s Compton wavelength h/(m_e c) setting the scale (about 2.43 × 10^-12 m). So the photon ends up with a longer wavelength (lower energy) after the collision, and the amount of that shift grows with the scattering angle, reaching a maximum for backscattering (θ = 180°). This is why Δλ is best understood as the wavelength shift of the scattered photon due to electron recoil. While the energy change and the momentum transfer are related to this process, Δλ specifically encodes the observable change in the photon’s wavelength, not the angle itself.