The radioactivity of a sample is $R_1$ at time $T_1$ and $R_2$ at time $T_2.$ If the half-life of the specimen is $T,$ the number of atoms that have disintegrated in time $(T_2 - T_1)$ is proportional to

In the radioactive decay of an element,it is found that the count rate reduces from $1024$ to $128$ in $3$ minutes. Its half-life will be ...... minutes.

The nuclide $^{131}I$ is radioactive,with a half-life of $8.04$ days. At noon on January $1$,the activity of a certain sample is $600 \, Bq$. The activity at noon on January $24$ will be

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 the radioisotope tritium $(_1^3H)$ is $12.3$ years. If the initial amount of tritium is $32 \ mg$, how much amount (in $mg$) will remain after $49.2$ years?

In a mean life of a radioactive sample,