Binding energy per nucleon is the amount of energy required to break apart a nucleus into its individual nucleons (protons and neutrons). It is a measure of the stability of a nucleus and is typically expressed in units of MeV per nucleon.
The binding energy per nucleon is calculated by taking the total binding energy of a nucleus and dividing it by the number of nucleons in the nucleus. The binding energy can be calculated using the famous equation E=mc2, where E is the energy, m is the mass defect (difference between the mass of the nucleus and the sum of the masses of its individual nucleons), and c is the speed of light.
These elements were chosen because they have varying numbers of nucleons and can help illustrate the trend of binding energy per nucleon as the number of nucleons increases. 2H (deuterium) has 2 nucleons, 24Mg has 24 nucleons, 32S has 32 nucleons, and 238U has 238 nucleons.
The trend is that the binding energy per nucleon increases as the number of nucleons increases, up to a certain point. This is due to the fact that larger nuclei have a stronger nuclear force holding the nucleons together, resulting in a more stable nucleus with a higher binding energy per nucleon. However, for very large nuclei, the repulsive forces between protons start to dominate, leading to a decrease in binding energy per nucleon.
Calculating binding energy per nucleon allows us to understand the stability and properties of different nuclei. It is also important in nuclear reactions, such as fusion and fission, as the difference in binding energy between reactants and products determines the amount of energy released or required in the reaction. Additionally, binding energy per nucleon is a key factor in determining the stability and abundance of elements in the universe.