Physics to help some student

Question

a. Find the change in wavelength of 80-pm x-rays that are scattered 120 degrees by a target.

b. Find the angle between the directions of the recoil electron and the incident photon.

c. Find the energy of the recoil electron.

Answer 1

Given Data:

• The wavelength of the incident X-rays is λ = 80 pm = 80 x 10^-12 m.
• The angle of scattering is θ = 120°

a. The wavelength shift in Compton scattering is given as,

Here, λ′ is the wavelength of the scattered photon, h is the plank constant, m_e is the mass of electron, and c is the seed of light.

 

is the Compton wavelength.

Substitute given values in the above equation.

∆λ = (2.43 pm)(1−cos120^∘)

Δλ=(2.43 pm)(1−(−0.5))

Δλ=3.645 pm

Thus, the change in the wavelength of the photon is Δλ=3.645 pm.

b. In Compton scattering, the angle between the direction of incident photon and recoil electron is given as,

Here, θ is the scattering angle of the photon and λ is the wavelength of the incident photon.

Substitute known values in the above equation.

Thus, the angle between the direction of the incident photon and recoil electron is ϕ=29.28^∘

c. From energy conservation, the kinetic energy of the recoil electron is the difference in the energies of the incident and scattered photon.

K = E − E′

Here,

hc=1240 keV⋅pm

λ′=Δλ + λ=3.645 pm + 80 pm = 83.645 pm

Substitute these values in the above equation.

Thus, the energy of the recoil electron is K = 0.68 ke V