If the decay or disintegration constant of a radioactive substance is $\beta $, then its half life and mean life are respectively 

$(log_e \,2 =ln\, 2)$

The energy spectrum of $\beta$-particles [number $N(E)$ as a function of $\beta$-energy $E$] emitted from a radioactive source is

Consider a radioactive nucleus $A$ which decays to a stable nucleus $C$ through the following sequence : $A \to B \to C$ Here $B$ is an intermediate nuclei which is also radioactive. Considering that there are $N_0$, atoms of $A$ initially, plot the graph showing the variation of number of atoms of $A$ and $B$ versus time. 

The half life period of radioactive element ${x}$ is same as the mean life time of another radioactive element $y.$ Initially they have the same number of atoms. Then:

A small quantity of solution containing $Na^{24}$ radio nuclide of activity $1$ microcurie is injected into the blood of a person. A sample of the blood of volume $1\, cm^3$ taken after $5$ hours shows an activity of $296$ disintegration per minute. What will be the total volume of the blood in the body of the person. Assume that the radioactive solution mixes uniformly in the blood of the person ……… $liter$

(Take $1$ curie $= 3.7 × 10^{10}$ disintegration per second and ${e^{ – \lambda t}} = 0.7927;$ where $\lambda$= disintegration constant)