Two protons in a nucleus experience both the repulsive electrostatic force and the…

PHYSICS · Multi-part · CBSE · Physics · Nuclei · Nuclei

Problem

Two protons in a nucleus experience both the repulsive electrostatic force and the attractive nuclear force. (a) Calculate the magnitude of the electrostatic force between two protons separated by

r = 1.0\,\text{fm}

and by

r = 3.0\,\text{fm}

. Use

k = 9\times10^{9}\,\text{N m}^2\text{C}^{-2}

and

e = 1.6\times10^{-19}\,\text{C}

. (b) The magnitude of the attractive nuclear force between two nucleons is approximately

2.5\times10^{4}\,\text{N}

r = 1.0\,\text{fm}

and negligible at

r = 3.0\,\text{fm}

. Compute the ratio

|F_{\text{nuclear}}|/|F_{\text{Coulomb}}|

at both separations. (c) Using the results of parts (a) and (b), analyse how the short-range character of the nuclear force allows a nucleus containing many protons to remain bound despite electrostatic repulsion. Explain how this analysis is connected to the saturation property of the nuclear force.

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