Compton Scattering Calculator

Compton scattering proved that photons behave as particles with momentum. When an X-ray collides with an electron, the scattered photon has a longer wavelength, and the shift depends only on the scattering angle.

⚛️ Quantum Physics📐 Δλ = λᶜ(1-cosθ)☢️ X-rays
Incident Wavelength (nm)
Scattering Angle θ (deg)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Wavelength ShiftΔλ(h/mec)(1−cosθ)m
Compton Wavelengthλch/mec = 2.426 pmm
Scattered Wavelengthλ′λ + Δλm
Recoil KEKeEi − EfeV

Step-by-Step Examples

Example 1
90 Degree Scattering

X-ray lambda=0.1 nm (100 pm), theta=90 deg.

  • delta_lambda = 2.426*(1-cos90) = 2.426*1 = 2.426 pm
  • lambda' = 100 + 2.426 = 102.43 pm
✓ 102.43 pm scattered wavelength
Example 2
Backscatter (180 deg)

Maximum shift at 180 degrees.

  • delta_lambda = 2.426*(1-(-1)) = 4.852 pm
  • lambda' = 100 + 4.852 = 104.85 pm
  • Max possible shift: 2*lambda_C = 4.85 pm
✓ Maximum shift = 4.85 pm at backscatter
Example 3
Forward Scatter (0 deg)

No shift at 0 degrees.

  • delta_lambda = 2.426*(1-1) = 0
  • Photon passes through unchanged
✓ Zero shift at forward scattering

Real-World Applications

☢️
X-ray Spectroscopy
Compton scattering affects X-ray spectra in medical imaging and materials analysis.
🏥
Radiation Therapy
Compton effect dominates X-ray interaction in tissue for therapeutic X-ray energies (0.1-10 MeV).
🔬
Astrophysics
Inverse Compton scattering (electrons hit photons) in jets boosts radio photons to X-ray energies.
⚛️
Particle Physics
Proved photon particle nature and momentum, foundational for quantum electrodynamics.

Common Mistakes to Avoid

⚠️
Wavelength shift is independent of incident wavelength

delta_lambda depends only on theta, not lambda. This was the key experimental confirmation of photon particle nature.

⚠️
Compton wavelength is NOT the photon wavelength

lambda_C = h/(m_e*c) = 2.426 pm is the electron Compton wavelength, not the incident photon wavelength.

⚠️
Effect only significant for short wavelengths

At X-ray wavelengths (0.01-1 nm), the 2.426 pm shift is measurable. For visible light (500 nm), 0.0005% shift is undetectable.

Frequently Asked Questions

What did Compton scattering prove? ▾
It proved photons carry momentum p = h/lambda, behaving as particles in collisions. Classical wave theory predicted no wavelength shift.
What is the Compton wavelength? ▾
lambda_C = h/(m_e*c) = 2.426e-12 m = 2.426 pm. It sets the scale of quantum effects for the electron.
Why does the wavelength always increase? ▾
Photon transfers energy to the electron. Lower energy photon = longer wavelength. Energy is always transferred FROM photon TO electron.
What is inverse Compton scattering? ▾
High-energy electrons collide with low-energy photons, boosting photon energy. Important in astrophysical jets and cosmic background radiation.
How was Compton scattering discovered? ▾
Arthur Compton in 1923 scattered X-rays from graphite and measured the shifted wavelength. The shift matched his particle-collision formula exactly. Nobel Prize 1927.

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Formula Explorer connections

Interpretation: This relationship connects quantized energy, wavelength, probability, nuclear mass or radioactive change. Assumption: Use the correct particle, quantum state, nuclide and energy units. Idealized potentials, nonrelativistic motion or single decay channels may be assumed.

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