Question

A 0.475 nm photon collides with a stationary electron. After the collision, the electron moves forward and the photon recoils backward. Find the momentum and the kinetic energy of the electron.

Answer 1

From Comptons Effect

since the photon recoils back \theta =180,
where

is the initial wavelength,

is the wavelength after scattering,

h is the Planck constant,

m_e is the electron rest mass,

c is the speed of light, and

is the scattering angle

From the energy equation

The energy of the photon is

J

J

From conservation of energy the K.E of recoiling electron is J
K.E=3.78*10^-16J

b)K.E=mv²

3.78*10^-16=9.3*10^-31*v²
v²⁼3.78*10^-16/9.3*10-31
v=2.01*10⁷m/s
so momentom is m*v=1.87*10^-23kgm/s