The half life period of radium is $1600$ years. The fraction of a sample of radium that would remain after $6400$ years is

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 sample has half-life of $5$ years. Probability of decay in $10$ years will be  ……..$\%$

The graph shows the $\log$ of activity $\log R$ of a radioactive material as a function of time $t$ in minutes.The half-life (in minute) for the decay is closest to

The half life of a radioactive substance is $20$ minutes. The approximate time interval $(t_2 – t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it had decayed and time $t_1$ when $\frac{1}{3}$ of it had decayed is ……….$min$