A point source of \(\gamma \)-radiation has a half life of 30 minutes. The initial count rate, recorded by Geiger counter placed 2 m from the source is \(360{ s }^{ -1 }.\) The distance between the counter and the source is altered. After 1.5 hours, the count rate recorded in \(5{ s }^{ -1 }.\) What is the new distance between the counter and the source?

Consider a radioactive nucleus A which decays to a stable nucleus C through the following sequence:
  A \(\longrightarrow \) B \(\longrightarrow \) C
where, B is an intermediate nuclei, which is also radioactive. Considering that there are N₀ atoms of A initially, plot the graph showing the variation of number of atoms of A and B versus time.

At atomic power nuclear reactor can deliver 300 MW. The energy released due to fission of each nucleus of uranium atoms U²³⁸ is 170 MeV. What will be the number of atoms fissioned per hour?

(i) Using Bohr's second postulate of quantisation of orbital angular momentum, show that the circumference of the electron in the nth orbital state in H-atom is n times the de-Broglie wavelength associated with it.
(ii) The electron in H-atom is initially in the third excited state. What is the maximum number of spectral lines which can be emitted when it finally moves to the ground state?

Nuclei with magic number of protons Z = 2,8,20,28,50,52 and magic number of neutrons N = 2,8,20,28,5082 and 126 are found to be very stable.
(i) Verify this by calculating the proton separation energy \({ S }_{ p }\)  for \({ 120 }_{ Sn }(Z=50)\) and \({ 121 }_{ Sn }(Z=51)\) .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 
\({ S }_{ P }=({ M }_{ Z-1,N }+{ M }_{ H }-{ M }_{ Z,N }){ c }^{ 2 }\)
\(given,{ 119 }_{ In }=118.9058 \ u,\)
\( { 120 }_{ Sn }=119.902199 \ u,\)
\({ 121 }_{ Sb }=120.903824 \ u,\)
\( { 1 }_{ H }=1.0078252u\)
(ii) What does the existence of magic number indicate?