xray of wavelength 0.112 nm is scattered from a carbon target calculate at 90 degree with respect to original direction the energy of the scattered electron after collision

To solve this problem, we need to use the Compton scattering formula, which is:

λ' - λ = h/(m*c) * (1 - cosθ)

where: λ' is the wavelength of the scattered x-ray, λ is the initial wavelength of the x-ray, h is Planck's constant (6.626 x 10^-34 Js), m is the rest mass of the electron (9.109 x 10^-31 kg), c is the speed of light (3 x 10^8 m/s), and θ is the scattering angle.

Given: λ = 0.112 nm = 0.112 x 10^-9 m, θ = 90 degrees = π/2 radians.

We can calculate λ':

λ' - λ = h/(m*c) * (1 - cos(π/2)) λ' - 0.112 x 10^-9 = (6.626 x 10^-34)/(9.109 x 10^-31 * 3 x 10^8) * (1 - 0) λ' = 0.112 x 10^-9 + (6.626 x 10^-34)/(9.109 x 10^-31 * 3 x 10^8) λ' = 0.112 x 10^-9 + 2.43 x 10^-12 λ' = 0.11200243 x 10^-9 m

The energy of the scattered x-ray (E') can be calculated using the formula:

E' = h*c/λ'

Substituting the values, we get:

E' = (6.626 x 10^-34 * 3 x 10^8) / 0.11200243 x 10^-9 E' = 1.77 x 10^-15 J

The energy of the incident x-ray (E) can be calculated similarly:

E = h*c/λ E = (6.626 x 10^-34 * 3 x 10^8) / 0.112 x 10^-9 E = 1.77 x 10^-15