Compton Scattering Calculator
Evaluate how the wavelength of X-rays or gamma rays shifts after a collision with electrons using a transparent quantum-mechanical model.
Inputs
Enter the electron-impact wavelength and the scattering angle. Values are treated as positive nanometers and degrees.
How to Use This Calculator
This calculator is designed for physics students and professionals who want to quantify the Compton wavelength shift when X-rays or gamma rays scatter off electrons.
Provide the incident photon wavelength in nanometers and the scattering angle in degrees, then tap Calculate. The result card updates instantly with the scattered wavelength, the Δλ shift, and the effective angle you supplied.
Methodology
All calculations follow the Compton scattering expression derived from first-principles quantum mechanics. The calculator converts the entered angle to radians, applies the Planck constant over electron rest mass and speed of light, and computes the wavelength change induced by the collision.
The emitted photon’s final wavelength equals the incident wavelength plus Δλ where Δλ = (h / (mₑ·c)) × (1 − cos θ). This formula is independent of the photon energy beyond the angle and initial wavelength.
Glossary
- Initial Wavelength: Photon wavelength before encountering the electron.
- Scattering Angle: Angle between incoming and outgoing photon direction, entered in degrees.
- Scattered Wavelength: Photon wavelength after the collision.
- Δλ: Difference between scattered and initial wavelengths, capturing the Compton shift.
Practical Example
With an initial wavelength of 0.071 nm and a 45° scattering angle, the formula predicts a small but measurable shift. Enter those values to confirm the calculator mirrors the theoretical result.
Frequently Asked Questions
What is Compton scattering?
Compton scattering occurs when X-rays or gamma rays collide with loosely bound electrons, transferring energy and increasing wavelength. It highlights the particle nature of light.
How do I use this calculator?
Input the photon’s initial wavelength and the scattering angle, then click the Calculate button. The card on the right reports the scattered wavelength and the Compton shift.