Compton Scattering Calculator

Compton Scattering Calculator | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Science & Education
Input types: number, select
Output type: text
Sample coverage: 4
API ready: Yes

Overview

The Compton Scattering Calculator computes the quantum wavelength shift, scattered photon energy, and recoil electron kinematics when high-energy photons collide with stationary electrons. By evaluating the fundamental equation Δλ = (h/m_e·c)(1 − cos θ), it provides instant conversions across picometers, Ångströms, and nanometers alongside full relativistic energy transfers.

When to use

Analyzing X-ray or gamma-ray scattering off electrons in modern physics coursework and laboratory experiments.
Determining photon energy loss and recoil electron trajectories at specific detector angles between 0° and 180°.
Evaluating backscattering limits and edge cases for radiation shielding or detector calibration.

How it works

1Enter the incident photon wavelength and select the measurement unit (pm, Å, or nm).
2Specify the photon scattering angle θ in degrees (ranging from 0° forward transmission to 180° backscattering).
3Calculate the shifted wavelength, scattered photon energy in keV/eV, electron recoil kinetic energy, and recoil angle.

Use cases

Verifying quantum scattering equations in modern physics and quantum mechanics problem sets.
Predicting detector photon energy peaks in X-ray spectroscopy and Compton camera setups.
Modeling secondary radiation spectra and electron recoil angles for medical physics dosimetry.

Examples

1. 90° Molybdenum K-alpha X-Ray Scattering

Physics Student

Background

A student is replicating Arthur Compton's 1923 benchmark experiment using molybdenum K-alpha X-rays scattered by graphite at a right angle.

Problem

Calculate the wavelength shift, scattered energy, and kinetic energy imparted to the recoil electron at 90°.

How to use

Enter 71 with unit 'pm' and set the scattering angle to 90 degrees.

Incident λ: 71 pm, Unit: pm, Angle: 90°

Outcome

Wavelength shifts by 2.426 pm to 73.426 pm, reducing photon energy from 17.46 keV to 16.89 keV with 577.0 eV transferred to the electron.

2. 180° Backscatter Maximum Shift

Radiation Safety Specialist

Background

A safety specialist needs to calculate maximum energy loss from 100 pm X-rays undergoing direct backscatter in a target material.

Problem

Find the maximum possible wavelength shift and resulting photon energy when θ = 180°.

How to use

Set incident wavelength to 100 pm and input an angle of 180 degrees.

FAQ

What is the electron Compton wavelength?

The electron Compton wavelength λ_C = h/(m_e·c) is approximately 2.42631 pm (0.02426 Å).

What happens at a scattering angle of 0°?

At θ = 0°, cos θ = 1, resulting in zero wavelength shift and no kinetic energy transferred to the electron.

What produces the maximum Compton shift?

Maximum shift occurs at θ = 180° (backscattering), where Δλ = 2λ_C ≈ 4.85262 pm.

Does the wavelength shift depend on incident photon energy?

No, the wavelength shift Δλ depends only on the scattering angle θ and fundamental physical constants.

How is the recoil electron kinetic energy determined?

Recoil kinetic energy is calculated by subtracting the scattered photon energy from the incident photon energy (T = E − E').

Incident λ: 100 pm, Unit: pm, Angle: 180°

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Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. 90° Molybdenum K-alpha X-Ray Scattering

2. 180° Backscatter Maximum Shift

FAQ

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