Compton Scattering Calculator
Calculate wavelength shift and energy changes in Compton scattering of X-rays and gamma rays
Calculate Compton Scattering
X-rays: 0.01-10 nm, Gamma rays: <10 pm
Angle between incident and scattered photon (0° to 180°)
Scattering Results
Compton Formula: Δλ = (h/mc) × (1 - cos θ)
Compton Wavelength: λc = 2.426 pm
Maximum Shift: 4.853 pm (at θ = 180°)
Scattering Analysis
Example: Medical X-ray Scattering
Typical Medical X-ray
Energy: 100 keV (medical imaging)
Wavelength: 12.4 pm
Scattering angle: 90°
Expected wavelength shift: 2.43 pm
Result
Δλ = 2.43 pm × (1 - cos(90°)) = 2.43 pm
Energy transfer = 20.2 keV (20.2% of incident energy)
Clinical significance: Reduced image contrast
Compton Scattering Physics
Photon-Electron Collision
High-energy photon transfers momentum to free electron
Energy Conservation
Total energy before equals energy after collision
Momentum Conservation
Vector sum of momenta is conserved
Wavelength Increase
Scattered photon has longer wavelength (less energy)
Important Constants
Applications
Medical imaging (X-ray scatter reduction)
Gamma-ray astronomy and detection
Material analysis and density measurement
Radiation therapy dose calculations
Nuclear physics research
Understanding Compton Scattering
What is Compton Scattering?
Compton scattering is the inelastic scattering of high-energy photons (X-rays and gamma rays) by free or loosely bound electrons. This quantum mechanical phenomenon demonstrates the particle nature of light and was crucial in establishing quantum mechanics.
The Compton Effect
- •Photon loses energy when scattered by electron
- •Wavelength increases proportional to (1 - cos θ)
- •Effect is independent of material properties
- •Most significant for high-energy radiation
Compton Formula
Δλ = (h/mc) × (1 - cos θ)
- Δλ: Wavelength shift (scattered - incident)
- h: Planck constant (6.626 × 10⁻³⁴ J⋅s)
- m: Rest mass of scattering particle
- c: Speed of light (2.998 × 10⁸ m/s)
- θ: Scattering angle (0° to 180°)
Historical Note: Arthur Compton received the 1927 Nobel Prize in Physics for discovering this effect, which provided key evidence for the quantum nature of light.
Physical Significance
Quantum Nature of Light
Compton scattering confirmed that light behaves as particles (photons) with energy E = hf and momentum p = h/λ, supporting Einstein's photon theory.
Conservation Laws
The effect demonstrates conservation of energy and momentum in quantum interactions, treating photons as relativistic particles with zero rest mass.
Medical Applications
Understanding Compton scattering is crucial for X-ray imaging, radiation therapy, and radiation protection in medical physics.