The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by $$E=\frac{3}{5} \frac{Z(Z-1) e^2}{4 \pi \varepsilon_0 R}$$ The measured masses of the neutron, H 1 1 ,   O 8 15 are 1.008665 u, 1.007825 u, 15.000109 u and 15.003065 u…

Question

The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by $$E=\frac{3}{5} \frac{Z(Z-1) e^2}{4 \pi \varepsilon_0 R}$$ The measured masses of the neutron, H 1 1 , &#160; O 8 15 are 1.008665 u, 1.007825 u, 15.000109 u and 15.003065 u respectively. Given that the radii of both the N 7 15 &#160; a n d &#160; O 8 15 nuclei are same, 1u = 931.5 Me V/ c 2 (c is the speed of light) and e 2 4 &#960; &#1013; 0 = 1.44 &#160; M e V &#160; f m . Assuming that the difference between the binding energies of N 7 15 &#160; a n d &#160; O 8 15 is purely due to the electrostatic energy, the radius of either of the nuclei is 1 &#160; f m = 10 - 15 m

Aicharya · Accepted Answer

Electrostatic energy = B E N - B E O = 7 M H + 8 M n - M N - 8 M H + 7 M n - M O &#215; C 2 = - M H + M n + M O - M N C 2 = - 1.007825 + 1.008665 + 15.003065 - 15.000109 &#215; 931.5 = + 3.5359 &#160; M e V &#8710; E = 3 5 &#215; 1.44 &#215; 8 &#215; 7 R - 3 5 &#215; 1.44 &#215; 7 &#215; 6 R = 3.5359 R = 3 &#215; 1.44 &#215; 14 5 &#215; 3.5359 = 3.42 &#160; f m

The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is…

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