In Rutherford scattering experiment, the number of `alpha`-particles scattered at `60^(@)` is `5 xx 10^(6)`. The number of `alpha`-particles scattered at `120^(@)` will be

Options

A. `15 xx 10^6`
B. `3/5 xx 10^6`
C. `5/9 xx 10^6`
D. None of these

Explanation

`N prop (1)/( sin ^4 theta //2 ) , (N_2) /(N_1) = ( sin ^4 ( theta _1 // 2))/( sin ^4 ( theta _2 // 2) )`
`or (N_2)/(5 xx 10 ^6 ) = ( sin ^4 ( 60 ^@ //2 ))/( sin^4 ( 120 ^@ //2 ))`
` or (N_2 )/( 5 xx 10^6 ) = ( sin ^4 30^@ )/( sin ^4 60 ^@)`
` or N_2 = 5 xx 10^6 xx ((1)/(2)) ^4 ((2)/( sqrt(3)))^4 =5/9 xx 10^6 `