The activity R of an unknown radioactive nuclide is measured at hourly intervals. The results found are tabulated as follows:

(i) Plot the graph of R versus t and calculate half-life from the graph.

(ii) Plot the graph of versus t and obtain the value of half-life from the graph.

Deuteron is a bound state of a neutron and a proton with a binding energy. A -ray of energy E is aimed at a deuteron nucleus to try to break it into a (neutron + proton) such that the n and p move in the direction of the incident -ray. If E = B, show that this cannot happen. Hence calculate how much bigger than B must E be for such a process to happen.

The deuteron is bound by nuclear forces just as H-atom is made up of p and e bound by electrostatic forces. If we consider the force between neutron and proton in deuteron as given in the form of a Coulomb potential but with an effective charge e’:

Estimate the value of (e’/e) given that the binding energy of a deuteron is 2.2 MeV.

Before the neutrino hypothesis, the beta decay process was thought to be the transition,

If this was true, show that if the neutron was at rest, the proton and electron would emerge with fixed energies and calculate them. Experimentally, the electron energy was found to have a large range.

Nuclei with magic no. of proton Z = 2, 8, 20, 28, 50, 52 and magic no. of neutrons N = 2, 8, 20, 28, 50, 82 and 126 are found to be very stable.

(i) Verify this by calculating the proton separation energy

S_p for ¹²⁰Sn (Z = 50) and ¹²¹Sb = (Z = 51).

The proton separation energy for a nuclide is the minimum energy required to separate the least tightly bound proton from a nucleus of that nuclide. It is given by

Sp = (M_{Z–1, N} + M_H – M_Z,N) c².

Given ¹¹⁹In = 118.9058u, ¹²⁰Sn = 119.902199u,

¹²¹Sb = 120.903824u, ¹H = 1.0078252u.

(ii) What does the existence of magic number indicate?