Starting with a sample of pure $^{66}Cu,\,\frac{7}{8}$ of it decays into $Zn$ in $15\, min$. The corresponding half-life is ………. $min$

The activity of a radioactive sample falls from $700 \;\mathrm{s}^{-1}$ to $500\; \mathrm{s}^{-1}$ in $30\;min$. Its half life is close to………$min$

The half lives of a radioactive substance are $T$ and $2T$. years for $\alpha  – $ emission and $\beta – $ emission respectively. The total de cay constnnt for simultaneous decay of $\alpha$ and $\beta$ adioactive substance is ___

A radioactive sample is $\alpha$-emitter with half life $138.6$ days is observed by a student to have $2000$ disintegration/sec. The number of radioactive nuclei for given activity are

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.