Question

Draw a plot showing the variation of potential energy of a pair of nucleons as a function of their separation (r). Using this plot, show that the nuclear force is (i) attractive for r > r₀, and (ii) repulsive for r < r₀.

Answer 1

The graph of potential energy (U) vs separation (r) between two nucleons has the following features:

• At large distances, the U ≈ 0 nuclear force is negligible.
• As nucleons come closer, potential energy becomes negative, indicating an attractive force.
• The potential energy reaches a minimum at a distance r = r₀ (equilibrium separation).
• For distances less than r₀, the potential energy rises sharply to positive values, indicating a repulsive force.

Force is related to potential energy by:

F = `-(dU)/(dr)`

(i) For r > r₀: In this region, as the distance between nucleons decreases, the potential energy decreases (becomes more negative).

`(dU)/(dr) < 0`

F > 0

Force is attractive. Nucleons are pulled together.

(ii) For r < r₀: In this region, as the distance decreases further, the potential energy increases sharply.

`(dU)/(dr) > 0`

F < 0

Force is repulsive. Prevents the collapse of the nucleus.