# Mention the change in wave length of the photon after it collides with free electron?? Is the rule of particle can be applied here?

Mention the change in wave length of the photon after it collides with free electron?? Is the rule of particle can be applied here?
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You are probably familiar with the relation
$c=\lambda f$
where c is the speed of light, $\lambda$ the wavelength and f the frequency of a photon.
The general formula for Compton scattering is normally given as
${\lambda }^{\prime }={\lambda }_{C}\left(1-\mathrm{cos}\alpha \right)+\lambda$
where ${\lambda }^{\prime }$ is the wavelength of the scattered photon, $\lambda$ the initial wavelength, ${\lambda }_{C}$ the Compton wavelength ${\lambda }_{C}=\frac{h}{{m}_{e}c}$ and $\alpha$ is the angle at which the photon scatters.
From this formula, we can see that the wavelength of a photon increases when it scatters at an electron. To visualize, the photon gives some of its energy to the electron. The energy of a photon is given as
$E=hf$
or $E=\frac{hc}{\lambda }$ so if the wavelength increases, the energy of the photon decreases. To illustrate further, if you shoot blue light at a stationary electron, you end up with scattered red light.
For the case of electromagetic radiation (light!), you can convert between frequency and wavelength using $c=\lambda f$. Those formulas combined allow you to find the frequency and wavelength of a scattered photon.