A radioactive sample decays by $\beta$  -emission. In first two seconds $‘n’$  $\beta$ -particles are emitted and in next $2\ seconds$ , $‘0.25n’$ $\beta$ -particles are emitted. The half life of radioactive nuclei is ...... $sec$

If the mass of a radioactive sample is doubled, the activity of the sample and the disintegration constant of the sample are respectively

Draw a graph showing the variation of decay rate with number of active nuclei. 

Mean life of a radioactive sample is $100$ seconds. Then its half life (in minutes) is

Deuteron is a bound state of a neutron and a proton with a binding energy $B = 2.2\, MeV$. A $\gamma $ -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 $\gamma $ -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. 

There are $10^{10}$ radioactive nuclei in a given radioactive element, Its half-life time is $1\, minute.$ How many nuclei will remain after $30\, seconds?$

$(\sqrt{2}=1.414)$