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. 12.5 per minute
D. 7 per minute

Answer

B

Explanation

According to Rutherford's scattering formula,if the `alpha`-particle scattered at angle `theta` is directly proportional to
`1/(sin^(4)(theta//2))`
Then,`N_(0)=K/(sin^(4)(theta//2))`
`theta=90^(@),Ntheta=28 min^(-1)`
Rightarrow `28=K/(sin(45^(@)))=4KRightarrowK=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_(0)=7/(sin^(4)30^(@))=7/((1//2)^(@))`
` =7times16=112`