Answer: [tex]4.86(10)^{-12}m[/tex]
Explanation:
The Compton Shift [tex]\Delta \lambda[/tex] in wavelength when photons are scattered is given by the following equation:
[tex]\Delta \lambda=\lambda' - \lambda_{o}=\lambda_{c}(1-cos\theta)[/tex] (1)
Where:
[tex]\lambda'=500 nm=500(10)^{-9} m[/tex] is the wavelength of the scattered photon
[tex]\lambda_{o}[/tex] is the wavelength of the incident photon
[tex]\lambda_{c}=2.43(10)^{-12} m[/tex] is a constant whose value is given by [tex]\frac{h}{m_{e}.c}[/tex], being [tex]h=4.136(10)^{-15}eV.s[/tex] the Planck constant, [tex]m_{e}[/tex] the mass of the electron and [tex]c=3(10)^{8}m/s[/tex] the speed of light in vacuum.
[tex]\theta=180\°[/tex] the angle between incident phhoton and the scatered photon.
[tex]\Delta \lambda=2.43(10)^{-12} m (1-cos(180\°))[/tex] (2)
[tex]\Delta \lambda=4.86(10)^{-12}m[/tex] (3) This is the shift in wavelength
