The relation between the mean life time $\tau$ and the half-life time $T_{1/2}$ of a radioactive substance is:

$A$ radioactive sample has ${N_0}$ active atoms at $t = 0$. If the rate of disintegration at any time is $R$ and the number of atoms is $N$,then the ratio $R/N$ varies with time as:

For a radioactive material,its activity $A$ and rate of change of its activity $R$ are defined as $A = -\frac{dN}{dt}$ and $R = -\frac{dA}{dt}$,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

The half-life of a radioactive sample is $20 \ days$. This means that:

$A$ radioactive substance decays by $10\%$ in $5$ days. What percentage of the original substance will remain after $20$ days (in $\%$)?

The specific activity of radium is close to: