Show that the instantaneous rate of change of activity of a radioactive substance is inversely proportional to the square of its half life.

A positronium atom is a bound state of an electron \(\left( { e }^{ - } \right) \) and its antiparticle, the positron \(\left( { e }^{ + } \right) \) revolving round their centre of mass. In which part of the em spectrum does the system radiate when it de-excites from its first excited state to the ground state?

A population inversion for two energy levels is often described by assigning a negative Kelvin temperature to the system. What negative temperature would describe a system in which population of the upper energy level exceeds that of the lower by 10% and the energy difference between the two levels is 2.2 eV?

A radioactive sample decays with an average life of 20 milli sec. A capacitor of capacitance \(100\mu F\) is charged to some potential and then the plates are connected through a resistance R. What should be the value of R so that the ratio of the charge on the capacitor to the activity of the radioactive sample remains constant in time?

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?