From a newly formed radioactive substance (Half life $2$ hours), the intensity of radiation is $64$ times the permissible safe level. The minimum time after which work can be done safely from this source is ……….$hours$

A radioactive nuclei with decay constant $0.5/s$ is being produced at a constant rate of $100\, nuclei/s$. If at $t\, = 0$ there were no nuclei, the time when there are $50\, nuclei$ is

The activity of a radioactive sample is $1.6\, curie$ and its half-life is $2.5 \,days$. Its activity after $10\, days$ will be ………. $curie$

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. 

A piece of wood from a recently cut tree shows $20\,decays$ per minute. A wooden piece of same size placed in a museum ( obtained from a tree cut many years back) shows $2\,decays$ per minute. If half life of $C^{14}$ is $5730\, years$, then age of the wooden piece placed in the museum is approximately ……….. $years$