Explain the processes of nuclear fission and nuclear fusion by using the plot of binding energy per nucleon (BE/A) versus the mass number A. A radioactive isotope has a half-life of 10 years. How long will it take for the activity to reduce to 3.125?

A. The value of binding energy per nucleon gives a measure of the stability of that nucleus; greater is the binding energy per nucleon of a nucleus, more stable is the nucleus. The above graph shown, binding energy per nucleon drawn against mass number A. The saturation effect of nuclear forces is the property responsible for the approximate constancy of binding energy in range 30<A<170. It is clear from the curve that binding energy per nucleon of the fused nuclei is more than that of the light nuclei taking part in nuclear fusion. Hence energy gets released in the process. In a nuclear fission, the sum of the masses of the final products is less than the sum of the masses of the reactant component.
B. N = N₀e⁻λt
But N = N₀/32
N₀/32 = N₀e⁻λt
1/32 = e⁻λt
5 ln2 = λt
but given half life so λ = ln2/10
so t = 50 Years