In the Compton wavelength shift formula Δλ = (h/(m_e c)) (1 - cos θ), which constants appear in the prefactor?

In the Compton wavelength shift formula Δλ = (h/(m_e c)) (1 - cos θ), which constants appear in the prefactor?

• A. Planck's constant h; electron rest mass m_e; and speed of light c
• B. Gravitational constant G
• C. Boltzmann constant k_B
• D. Elementary charge e

Answer: (A)

The change in wavelength in Compton scattering is governed by a natural length scale set by h divided by the electron’s momentum, m_e c. The prefactor h/(m_e c) comes from combining quantum and relativistic ideas: Planck’s constant h brings in quantum behavior, the electron rest mass m_e sets the inertia of the electron, and the speed of light c brings in relativistic factors. The angular part (1 − cos θ) is dimensionless, so the units of Δλ come entirely from h/(m_e c). This combination is known as the electron Compton wavelength, about 2.43×10^-12 meters. The gravitational constant, Boltzmann constant, or elementary charge do not enter this particular expression.

The change in wavelength in Compton scattering is governed by a natural length scale set by h divided by the electron’s momentum, m_e c. The prefactor h/(m_e c) comes from combining quantum and relativistic ideas: Planck’s constant h brings in quantum behavior, the electron rest mass m_e sets the inertia of the electron, and the speed of light c brings in relativistic factors. The angular part (1 − cos θ) is dimensionless, so the units of Δλ come entirely from h/(m_e c). This combination is known as the electron Compton wavelength, about 2.43×10^-12 meters. The gravitational constant, Boltzmann constant, or elementary charge do not enter this particular expression.