The electrostatic energy of `Z` protons uniformly distributed throughout a spherical nucleus of radius `R` is given by
`E = (3 Z(Z- 1)e^(2))/5( 4 pi e _(0)R)`
The measured masses of the neutron `_(1)^(1) H, _(7)^(15) N and , _(8)^(16)O are 1.008665 u, 1.007825 u , 15.000109 u and 15.003065 u, ` respectively Given that the ratio of both the `_(7)^(12) N` and `_(8)^(15) O` nucleus are same , 1 u = = 931.5 Me V`c^(2) ` (c is the speed of light ) and `e^(2)//(4 pi e_(0)) = 1.44 MeV` fm Assuming that the difference between the binding energies of `_7^(15) N and `_(8)^(15) O ` is purely due to the electric energy , The radius of the nucleus of the nuclei is

Options

A. `2.85 fm`
B. `3.03 fm`
C. `3.42 fm`
D. `3.80 fm`

Answer

C

Explanation

Ealectrostatic energy `= BE_(N) - BE_(0)`
`= [[7M_(H) + 8M_(n) - M_(N)] - [8M_(H) + 7M_(n) - M_(o)]] xx C^(2)`
`=[-M_(H) + M_(n) + M_(o) - M_(N)]C^(2)`
`= [-1.007825 + 1.008665 + 15.003065 - 15.000109] xx 931.5`
`+ 3.5359 MeV`
`Delta E = (3)/(5) xx (1.44 xx 8 xx 7)/(R) - (3)/(5) xx (1.44 xx 7 xx 6)/(R) = 3.5359`
`R = (3 xx 1.44 xx 14)/(5 xx 3.5359) = 3.42 fm`