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Compton Scattering Calculator

Find the Compton shift for a scattering angle.

Result

1.2132 pm
1.2132 × 10⁻¹² m

How it is calculated

The shift depends only on the scattering angle, not on the photon's starting energy: Δλ = λc · (1 − cos θ). Here θ is the angle in degrees between the incoming and outgoing photon directions, and λc = h / (mₑc) is the electron's Compton wavelength, which the tool takes as 2.42631023867×10⁻¹² m. The angle is converted to radians internally, and the result is given in picometres (pm) and in metres in scientific notation.

The model assumes the electron is free and at rest before the collision. The result is the increase in wavelength, not the final wavelength of the photon.

Worked example

Take a scattering angle of θ = 60°. Then cos 60° = 0.5, so (1 − cos θ) = 0.5. Multiply by the Compton wavelength: 2.4263 pm × 0.5 ≈ 1.2132 pm. The tool reports a shift of 1.2132 pm (1.2132 × 10⁻¹² m). At 180° the factor is 2 and the shift reaches its largest value, 4.8526 pm.

Try this example →

Common mistakes

  • Entering the angle in radians. The field expects degrees, so π/2 typed as 1.57 gives a tiny angle, not 90°.
  • Reading the result as the new wavelength. It is only the change Δλ; add it to the original wavelength yourself.
  • Confusing the scattering angle with the angle of the electron's recoil. The formula uses the photon's deflection from its original direction.
  • Mixing picometres and metres: 1 pm is 10⁻¹² m, so 1.2132 pm equals 1.2132 × 10⁻¹² m.
  • Expecting the shift to depend on the photon's energy. It does not, though the relative shift is only noticeable for short wavelengths such as X-rays.

About this calculator

This calculator finds the Compton wavelength shift of a photon scattered off a stationary electron, using Δλ = (h/mₑc)(1 − cosθ), where h is Planck's constant, mₑ is the electron's rest mass, c is the speed of light, and θ is the scattering angle. The term h/mₑc is called the Compton wavelength of the electron (about 2.43 picometers), and the shift is zero at θ=0 and maximal (twice the Compton wavelength) at θ=180°, a direct backscatter.

This 1923 discovery by Arthur Compton was historically decisive evidence that light behaves as discrete particles (photons) carrying momentum, not just waves, and it's a staple topic in quantum mechanics and modern physics courses.

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Comments (1)

  • Editorial team

    Whether the shift matters depends on the starting wavelength, which this tool does not ask for. The largest possible shift is 4.85 pm: about 7% of a 71 pm X-ray, but only about one part in 100,000 of 500 nm visible light, which is why the effect shows up with X-rays and not with lamps. Compare your shift with the starting wavelength before drawing conclusions. Is this a textbook problem or a lab plan? Tell us which angles you need.

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