The electrostatic energy of protons uniformly distributed throughout a spherical…

PHYSICS · Single correct · A Level · Physics · Nuclear physics · Nuclear physics

Problem

The electrostatic energy of

Z

protons uniformly distributed throughout a spherical nucleus of radius

R

is given by

E = \frac{3Z(Z-1)e^2}{5 \cdot 4\pi\epsilon_0 R}

The measured masses of the neutron

{}_1^1\text{H}

{}_7^{15}\text{N}

and

{}_8^{15}\text{O}

are

1.008665 \text{ u}

1.007825 \text{ u}

15.000109 \text{ u}

and

15.003065 \text{ u}

, respectively. Given that the radii of both the

{}_7^{15}\text{N}

and

{}_8^{15}\text{O}

nuclei are same,

1 \text{ u} = 931.5 \text{ MeV}/c^2

(

c

is the speed of light) and

e^2/(4\pi\epsilon_0) = 1.44 \text{ MeV fm}

. Assuming that the difference between the binding energies of

{}_7^{15}\text{N}

and

{}_8^{15}\text{O}

is purely due to the electrostatic energy, the radius of either of the nuclei is (

1 \text{ fm} = 10^{-15} \text{ m}

) (1)

2.85 \text{ fm}

(2)

3.03 \text{ fm}

(3)

3.42 \text{ fm}

(4)

3.80 \text{ fm}