1)

The electrostatic energy of Zprotons uniformly distributed throughout a spherical nucleus of radius R is given by E=35Z(Z1)e24πϵ0R.The measured masses of the neutron, 11H,157Nand 158Oare  1.008665u. 1.007825u, 15.000109u and 15.003065 u. respectively. Given that the radii of both the 157N and158O nuclei are same,1 u =931.5MeV/c2 ,c is the speed of light and e2/(4πϵ0)=1.44 meV fm.Assuming that the difference between the binding energies of 157N and 158O  is purely due to the electrostatic energy, the radius of either of the nuclei is (1 fm = 10-15m)


A) 2.85 fm

B) 3.03 fm

C) 3.42 fm

D) 3.80 fm

Answer:

Option C

Explanation:

Electrostatic energy = Binding energy of N - Binding energy of O

=[(7MH+8Mn-MN)]-[(8MH+7Mn-MO)]xc2

=[-MH+Mn+Mo-MN]c2

=[- 1.007825 + 1.008665 + 15.003065- 15.000109]x 931.5 = + 3.5359 MeV

E=35×1.44×8×7R35×1.44×7×6R=3.5359MeV

R=3×1.44×145×3.5359=3.42fm