. The electrostatic energy of z protons uniformly distributed throughout a spherical nucleus


The electrostatic energy of z protons uniformly distributed throughout a spherical nucleus of radius R is Given by E = 3/5 Z(Z – 1) e2/4πε0R

The measured masses of the neutron, 11H, 157N and 158O are 1.008665 u, 1.007825 u, 15.000109

u and 15.003065 u, respectively. Given that the radii of both the 157N and 158O nuclei are same,

1 u = 931.5 MeV/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

(1fm = 10-15 m)

A. 2.85

B. 3.03

C. 3.42

D. 3.80

Best Answer

Correct Option is: (C)

(BE)15 7N = 7mp + 8mn – m15 7N

(BE)15 8O = 8mp + 7mn – m15 8O

⇒ ∆(BE) = (mn + mp) + (m15 8O – m15 7N)

= 0.00084 + 0.002956

= 0.003796 u

⇒ 3/5 × 14 × 1.44 MeV fm/0.003796 × 931.5 MeV =R

⇒ R = 3.42fm

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