Tru Physics

Compton Scattering

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Compton scattering is a fundamental process in quantum mechanics that describes how photons and electrons interact with each other. Discovered by Arthur Holly Compton in 1923, Compton scattering provided strong evidence for the particle nature of light and was a crucial component in understanding the behavior of radiation.

Compton scattering is depicted as the incoming photon (left) strikes an electron which is the scattered at some angle phi while the photon is scattered at an angle theta.
Compton scattering diagram with incident photon (left) striking an electron (center) which is stationary in its center of mass frame. The outgoing photon is depicted on the right. A higher quality image can be viewed and downloaded here.

Compton scattering occurs when a photon collides with an electron and transfers some of its energy to the electron, causing it to recoil. As a result, the photon’s wavelength increases, and its energy decreases, which is known as the Compton effect. This process is an example of inelastic scattering, as the photon loses energy and changes direction.

Formula:

\lambda_f-\lambda_i=\Delta \lambda=\dfrac{h}{m_ec}(1-\cos{\theta})

The Compton scattering formula is used to calculate the change in wavelength and angle of a photon after it undergoes scattering. The formula considers the electron’s mass, the speed of light, and the scattering angle, among other variables. Compton scattering has practical applications in fields such as medical imaging, where X-ray photons are used to produce images of the body.

Knowing that E_{\gamma }=hc/ \lambda and that E_{ \gamma ' }=hc/ \lambda ', the above equation can be rewritten as:

E_{\gamma ' }=\dfrac{E_\gamma }{1+(E_\gamma /m_ec^2)(1-\cos \theta )}

We can also derive the relation between the electron and photon scattering angles and write this relation as:

\cot \phi = (1+\frac{hf}{m_ec^2}) \tan (\theta /2)

with the angles \phi and \theta defined as given in the figure above.

Calculators:

Wavelength Shift (Δλ)

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