In rutherford's experiment, the mumber of alpha-particles scattered through an angle of `90^(@)` is 28 per minute. Then,the number of particles scattered through an angle of `60^(@)`per minute by the same nucleus is

Options

A. 28 per minute
B. 112 per minute
C. 125 per minute
D. 7 per minute

Answer

B

Explanation

According to Rutherford's scattering formula, if the `alpha`-particle scattered at angles `theta` is directly proportional to `(1)/(sin^(4)(theta//2))`, then
`N_(theta)=(K)/(sin^(4)(theta//2))`
when `theta=90^(@),N_(theta)=28"min"^(-1)`
`implies 28=(K)/(sin(45^(@)))=4Kimplies K=7`
thus, `N_(theta)=(7)/(sin^(4)(theta//2))`
Hence, the number of `alpha`-particles scattered at an angle of `60^(@)` per minute is `N_(theta)'=(7)/(sin^(4)30^(@))=(7)/((1//2)^(4))`
`=7xx16=112`