Question

By classical, hard sphere assumption, what smallest value of $A$ would make one nucleon surrounded. Relate your answer with figure 11.14.

Short answer

The smallest number of nucleons to surround a nucleon is $6$.

Step-by-step solution

Given data

There will be three nucleons on each layer above and below the nucleon.

Concept of  α particle

Alpha particles are composite particles consisting of two protons and two neutrons tightly bound together.

Calculation for the smallest value of  A

The smallest number of nucleons to surround a nucleon is$6$.

That is when a sphere is surrounded by one sphere above, one below, one left, one right, one in front, and one on the back.

In addition to it there will be three nucleons on each layer above and below the nucleon.

So the minimum number of nucleons surrounded by each nucleon is $12$hence the minimum number of nucleons in the nucleus is $13$.

Since adding more nucleons could make the center nucleon surrounded by more nucleons and thus increase me binding energy.

So a nucleus with $13$nucleons increases the binding energy enormously up to the point $(A=13$) is reached as shown in figure $11.14$ and after this point the binding energy increases slowly with increase in atomic number unto $(A=56)$