In Rutherford's scattering experiment , 60 particles were scattered per min for `theta_1 = 90^@`. How many particles will be scattered per min for `theta_2 = 60^@` ?

Options

A. 60
B. 120
C. 180
D. 240

Answer

D

Explanation

`theta_1=90^@ " and " N_1 = 56, theta_2 = 60^@`
In Rutherford's scattering experiment , the number of scattered particles
`N prop (1)/(sin^4 (theta/2))`
`therefore N_2/N_1 = [(sin(theta_1/2))/(sin(theta_2/2))]^4 = [(sin45^@)/(sin30^@)]^4`
`=[(1/sqrt2)/(1/2)]^4 = [2/sqrt2]^4 = [sqrt2]^4 = 4`
`therefore N_2 = 4N_1 = 4xx60=240`