The electrotatic energy of `Z` protons uniformly distributed throughout a spherical nucleus of ratio `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)^(15)O are 1.008665 u, 1.007825 u , 15.000109 u and 15.003065 u, ` repectively Given that the ratio of both the _(7)^(12) N and _(8)^(15) O nu8cles are same , 1 u = = 931.5 Me Vc^(2) ` (c is the speed of light ) and `e^(2)//(4 p-i e^_(0)) = 1.44 MeV` fm Assuming that the difference between the binding e4nergies of `_(7_^(15) N and _(8)^(15) O ` is puraly due to the electric energy , The radius of the nucleas of the nuclei is

Options

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

Answer

C

Explanation

Binding energy of introgon atom
`= [8 xx 1.00665 + xx 7 xx 1.007825 - 15.000109] xx 931`
binding energy of orygen atom
`[ 7 xx 1.008665 + 8 xx 1.0077825 - 15.003065] xx 931`
`:.` differencce `= 0.007960 xx 931 MeV` …(i)
`Also `E_(0) = (3)/(5) xx (8 xx 7)/(R) xx (e^(2))/(4 pi e_(0)) = (3)/(5) xx (56)/(R) xx 1.44 MeV`
`E_(0) = (3)/(5) xx (7 xx 6)/(R) xx (e^(2))/(4 pi e_(0)) = (3)/(5) xx (42)/(R) xx 1.44 MeV`
`E_(0) - E_(N) = (3)/(5) xx (14)/(R) xx 1.44 MeV` ....(ii)
from (i) and(ii)
` (3)/(5) xx (14)/(R) xx 1.44 = 0.0037960 xx 931`
`:. R = 3.42 fm`