Modern Physics

Compton Scattering

λ′−λ=hmec(1−cos⁡θ)\lambda' - \lambda = \frac{h}{m_e c}(1 - \cos\theta)

Wavelength shift of photons scattered by electrons. Confirms particle nature of light.

Variables

Δλ
Wavelength shift
Allowed values: 0 or more
m
λ'
Scattered wavelength
m
λ
Incident wavelength
Allowed values: greater than 0
m
h
Planck constant
Allowed values: greater than 0
J·s
me
Electron mass
Allowed values: greater than 0
kg
c
Speed of light
Allowed values: greater than 0
m/s
θ
Scattering angle
°

Derivation

Derived by treating collision as relativistic particle interaction.

Your notes

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Constants in this formula

h
6.626 070 15 × 10⁻³⁴. Exact by definition.
J·s
me
9.109 × 10⁻³¹. Measured (CODATA 2018).
kg
c
299,792,458. Exact by definition.
m/s

Other modern physics formulas with the same quantities

Where this formula is listed

Common questions

What is the Compton Scattering formula?

Compton Scattering is written λ′ − λ = (h/(m_e c))(1 − cos θ). Wavelength shift of photons scattered by electrons. Confirms particle nature of light. It belongs to Modern Physics, under Quantum Mechanics.

What are the units in λ′ − λ = (h/(m_e c))(1 − cos θ)?

In SI units, Δλ is wavelength shift, measured in m; λ′ is scattered wavelength, measured in m; λ is incident wavelength, measured in m; h is planck constant, measured in J·s; m_e is electron mass, measured in kg; c is speed of light, measured in m/s; θ is scattering angle, measured in °.

How is the Compton Scattering formula derived?

Derived by treating collision as relativistic particle interaction. The result is λ′ − λ = (h/(m_e c))(1 − cos θ).