Two radioactive nuclei $P$ and $Q$ in a given sample decay into a stable nucleus $R$. At time $t = 0$, number of $P$ species are $4\, N_0$ and that of $Q$ are $N_0$. Half-life of $P$ (for conversion to $R$) is $1$ minute where as that of $Q$ is $2$ minutes. Initially  there are no nuclei of $R$ present in the sample. When number of nuclei of $P$ and $Q$ are equal, the number of nuclei of $R$ present in the sample would be

A radioactive material has a half life of $10$ days. What fraction of the material would remain after $30$ days

A fresh radioactive sample is given at $t = 0$. Its decay fraction are $\frac{1}{5}$ at $t_1$ instant and $\frac{4}{5}$ at $t_2$ instant. Its mean life is

After $3$ hours, only $0.25 \,mg$ of a pure radioactive material is left. If initial mass was $2 \,mg$ then the half life of the substance is ...... $hr$

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

$99\%$ of a radioactive element will decay between