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 …… $sec$

A freshly prepared radioactive source of half life $2$ hours $30$ minutes emits radiation which is $64$ times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be hours.

Curie is a unit of

For a radioactive material, its activity $A$ and rate of change of its activity $R$ are defined as $A=-\frac{d N}{d t}$ and $R=-\frac{d A}{d t}$, where $N(t)$ is the number of nuclei at time $t$. Two radioactive sources $P$ (mean life $\tau$ ) and $Q$ (mean life $2 \tau$ ) have the same activity at $t=0$. Their rates of change of activities at $t=2 \tau$ are $R_p$ and $R_Q$, respectively. If $\frac{R_p}{R_Q}=\frac{n}{e}$, then the value of $n$ is

Half life of a radioactive element is $10\, days$. The time during which quantity remains $1/10$ of initial mass will be ………$days$