Compton Scattering Calculator Formula

Understand the math behind the compton scattering calculator. Each variable explained with a worked example.

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Formulas Used

Wavelength Shift

wavelength_shift = (6.626e-34 / (9.109e-31 * 2.998e8)) * (1 - cos(scattering_angle * pi / 180))

Shift (pm)

shift_pm = (6.626e-34 / (9.109e-31 * 2.998e8)) * (1 - cos(scattering_angle * pi / 180)) * 1e12

Variables

VariableDescriptionDefault
scattering_angleScattering Angle(deg)90

How It Works

Compton Scattering

When a photon scatters off a free electron, its wavelength increases. The shift depends only on the scattering angle.

Formula

delta_lambda = lambda_C * (1 - cos theta)

where lambda_C = h / (m_e c) = 2.426 pm is the Compton wavelength of the electron.

Maximum shift (2 lambda_C = 4.85 pm) occurs at 180 degrees (backscattering).

Worked Example

Photon scattered at 90 degrees.

scattering_angle = 90
  1. 01delta_lambda = lambda_C * (1 - cos 90)
  2. 02lambda_C = 6.626e-34 / (9.109e-31 * 2.998e8) = 2.426e-12 m
  3. 03cos(90) = 0
  4. 04delta_lambda = 2.426e-12 * (1 - 0) = 2.426 pm

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