For small nuclei, an equal number of protons and neutrons gives rise to a stable nucleus. However, for larger nuclei, an excess of neutrons is required. Using your knowledge of the relevant physics, discuss why additional neutrons make one of these larger nuclei more stable.
To understand why additional neutrons make larger nuclei more stable, we need to delve into the concept of nuclear binding energy and the strong nuclear force.
In the nucleus, protons have a positive charge, and like charges repel each other. The electrostatic repulsion between protons tries to overcome the strong nuclear force that holds the nucleus together. On the other hand, the strong nuclear force attracts nucleons (protons and neutrons) to each other, overcoming the electrostatic repulsion. However, the strong nuclear force is a very short-range force, acting only within a small distance. Thus, it is effective only for the nearest neighbors.
When the number of protons and neutrons is small, the strong nuclear force can effectively hold the nucleus together. This is because the strong nuclear force has a stronger effect than the electrostatic repulsion between protons. An equal number of protons and neutrons can stabilize the nucleus due to the balance between attractive and repulsive forces.
However, as the number of protons increases, the electrostatic repulsion between them becomes stronger. The strong nuclear force between protons is less effective at large distances compared to the short-range repulsive electrostatic force. To counterbalance this increased repulsion, additional neutrons are needed to increase the strong nuclear force in the nucleus.
The presence of more neutrons increases the total number of attractive strong nuclear forces within the nucleus. These extra neutrons act as "buffers" between the protons, reducing the electrostatic repulsion and stabilizing the nucleus. By adding more neutrons, the forces holding the nucleus together can compensate for the electrostatic repulsion and make the larger nucleus more stable.
In summary, larger nuclei require an excess of neutrons to overcome the increased electrostatic repulsion between protons. These additional neutrons enhance the overall strength of the strong nuclear force, helping to stabilize the nucleus.