Question

Two protons are kept at a separation of 10nm. let $F_n$ and $F_e$ be the nuclear force and electromagnetic force between them,
(A) ${{F}_{e}}={{F}_{n}}$
(B) ${{F}_{e}}\gg {{F}_{n}}$
(C) ${{F}_{e}}\ll {{F}_{n}}$
(D) ${{F}_{e}}and{{F}_{n}}$ differs slightly

Answer 1

The electromagnetic forces are the forces between charged particles. They operate over distances which are not very large. On the other hand, the forces that bind the neutrons and protons together in a nucleus are called strong nuclear forces. Nuclear forces have a short range. They operate within the nucleus only i.e., up to distance of order of ${{10}^{-14}}\text{m}$ .

Complete step by step solution:
The electromagnetic forces are the forces between charged particles. The forces between unlike charges are attractive and forces between like charges are repulsive. Since, two protons have the same charges so they give a repulsive force. These forces are governed by Coulomb’s law. $F=k\dfrac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}$ ; $k=9\times {{10}^{9}}N{{m}^{2}}/{{c}^{2}}$ is a constant ${{q}_{1}}$ and ${{q}_{2}}$ are point, charges separated by distance r. The electromagnetic forces are ${{10}^{36}}$ stronger than gravitational force. They operate over distances which are not very large.
Strong nuclear force acts between two protons or two neutrons or a proton and neutron but only if they are very close together. When two neutrons (protons) are within 1 Fermi $\left( {{10}^{-15}} \right)$ of each other, the strong nuclear attractive force is about 10 times stronger than repulsive force between two protons at this separation. Nuclear forces are very short range i.e. their strength decreases very rapidly with increasing separation.
We have given, two protons at distance = $10nm=10\times {{10}^{-9}}m={{10}^{-8}}m$
Hence, the nuclear force is lesser than the electromagnetic force.
Option B is correct.

Note:
Electromagnetic forces obey inverse square law, while the nuclear forces don’t.
Electromagnetic forces are central forces, while nuclear forces are non-central.
Electromagnetic forces are conservative forces while nuclear forces are non-conservative.