Draw the graphs for variation of potential energy and nuclear for… - Vidyadip

Question

Draw the graphs for variation of potential energy and nuclear force between two nucleons as a function of distance between them.

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Answer

Variation of potential energy U with distance $r$ between the two nucleons is shown in adjacent Fig. Potential energy U is minimum at a distance i.e. separation between the two nucleons $r_{0}$. Hence this is the position of equilibrium of two nucleons and $r_{0}$ is called distance of equilibrium.

(a) For $r < r_{0}$, potential energy U increases rapidly with decreasing $r$. This indicates a strong repulsive nuclear force.
(b) For $r > r_{0}$ potential energy decreases to about zero with increasing $r$. This indicates attractive nuclear force. The attraction is maximum at $r_{0}$ and varies inversely not with square of separation but with some higher power of it.
Thus the part DCBA of (U-r) curve represent repulsive nuclear force region and the part CED represent attractive nuclear force region. In this way the nuclear force variation with distance $r$ can be represented as shown in Fig. (b). Nuclear attractive force between two nucleors increases with decrease in distance between them at distance $r_{1}$ it becomes maximum. When distance becomes less then $r_{1}$ attractive force beings to decrease and at distance $r_{0}$ it becomes zero.

The value of $r_{0}$ is 4 fm which indicates that nuclear force is a short range force. When distance between two nucleors becomes less than $r_{0}$, repulsive force begins to its between them and it increases rapidly with decrease in distance.

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