Modern Physics 5 Question 6

6. The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by

E=35Z(Z1)e24πε0R

The measured masses of the neutron, 11H,715N and 815O are 1.008665u,1.007825u,15.000109u and 15.003065u, respectively. Given that the radii of both the 715N and 815O nuclei are same, 1u=931.5MeV/c2 ( c is the speed of light) and e2/(4πε0)=1.44MeVfm. Assuming that the difference between the binding energies of 715N and 815O is purely due to the electrostatic energy, the radius of either of the nuclei is ( 1fm=1015m)

(2016 Adv.)

(a) 2.85fm

(b) 3.03fm

(c) 3.42fm

(d) 3.80fm

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Answer:

Correct Answer: 6. (a)

Solution:

  1. Electrostatic energy

= Binding energy of N Binding energy of O

=[[7MH+8MnMN][8MH+7MnMO]]×C2

=[MH+Mn+MOMN]C2

=[1.007825+1.008665+15.00306515.000109]×93.15

=+3.5359MeV

ΔE=35×1.44×8×7R=3.5359R=3×1.44×145×3.5359=3.42fm



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