Question

2. In a Compton scattering experiment, an x-ray photon scatters through an angle of 21.4° from a free electron that is initially at rest. The electron recoils with a speed of 1,880 km/s.

(a) Calculate the wavelength of the incident photon.

(b) Calculate the angle through which the electron scatters.

Answer 1

let L1 is the wavelengtgh of of incident phtoton and L2 is the wavelength of the scattred photon.

a) use L2 - L1 = h/(m*c)*(1 - cos(theta))

L2 - L1 = 6.626*10^-34/(9.1*10^-31*3*10^8)*(1 - cos(21.4))

L2 - L1 = 1.6733*10^-13   ---------(1)

and

E - E' = kE_electron

h*c/L - h*c/L' = (1/2)*m*v^2

6.626*10^-34*3*10^8/L1 - 6.626*10^-34*3*10^8/L2 = (1/2)*9.1*10^-31*(1880*10^3)^2 ----(2)

on solving equation 1 and 2

we get

L1 = 1.4373*10^-10 m
L2 = 1.4390*10^-10 m

E1 = h*c/L1

= 6.626*10^-34*3*10^8/(1.4373*10^-10)

= 1.383*10^-15 J (or) 8644 eV <<<<<<<<<<<<<<<-----------------------------Answer

b) let theta is the angle made by electron motion.

Py_electron = Py_photon

m*v*sin(theta) = (h*c/L2)*sin(21.4)

sin(theta) = (h/L2)*sin(21.4)/(m*v)

= (6.626*10^-34/(1.4390*10^-10))*(sin(21.4)/(9.1*10^-31*1880*10^3))

= 0.982

theta = sin^-1(0.982)

= 79.1 degrees <<<<<<<<<<<<<<<-----------------------------Answer