The half-life of a radioactive substance is $12 \text{ minutes}$. The time gap between $28 \%$ decay and $82 \%$ decay of the radioactive substance is

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

$N$ atoms of a radioactive element emit $n$ number of $\alpha$-particles per second. The mean life of the element in seconds is:

There are three lumps of a given radioactive substance. Their activity is in the ratio of $1 : 2 : 3$ now. What will be the ratio of their activities at any further date?

If $75 \%$ of a radioactive sample disintegrates in $16 \text{ days}$, the half-life of the radioactive sample is (in $\text{ days}$)

In a radioactive material,the fraction of active material remaining after time $t$ is $\frac{9}{16}$. The fraction that was remaining after $\frac{t}{2}$ is: