Initial Parameters:
- Photon initial momentum: P
- Electron rest mass: m
- Electron relativistic momentum: P
- Electron energy: E

Scattering Process:
When the photon collides with the electron, it transfers some of its momentum and energy to the electron. The electron then scatters at an angle θ.

Change in Wavelength:
The change in wavelength of the photon after scattering through an angle θ can be calculated using the Compton Scattering formula:
Δλ = λ' - λ = h / (m * c) * (1 - cosθ)
Where:
- Δλ is the change in wavelength
- λ' is the final wavelength
- λ is the initial wavelength
- h is the Planck constant
- m is the electron rest mass
- c is the speed of light
- θ is the scattering angle

Explanation:
During Compton scattering, the photon transfers some of its energy to the electron, causing it to recoil. This results in a change in the wavelength of the photon after scattering. The change in wavelength is dependent on the scattering angle and the rest mass of the electron.
By applying the Compton Scattering formula, we can calculate the change in wavelength of the photon after scattering through an angle θ. This change in wavelength provides valuable information about the interaction between the photon and the electron during the scattering process.
In conclusion, the change in wavelength of the photon after scattering through an angle θ can be determined using the Compton Scattering formula, which takes into account the initial parameters of the photon and electron.