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?

$A$ radioactive element $A$ converts into another stable element $B$. The half-life of $A$ is $1.5 \ hrs$. After time $t$,the ratio of the number of atoms of $A$ to $B$ is found to be $1:8$. Then $t$ in hours is:

$A$ radioactive sample decays by $\beta$-emission. In the first $2 \ s$,$n$ $\beta$-particles are emitted,and in the next $2 \ s$,$0.25n$ $\beta$-particles are emitted. The half-life of the radioactive nuclei is ...... $s$.

Ten percent of a radioactive sample has decayed in $1$ day. After $2$ days,the decayed percentage of nuclei will be ...... $\%$

The half-life period of a radioactive sample is $3.8 \ days$. After how many days will the sample become $\frac{1}{8}$ of the original substance?

The activity of a radioactive material is $6.4 \times 10^{-4} \text{ curie}$. Its half-life is $5 \text{ days}$. The activity will become $5 \times 10^{-6} \text{ curie}$ after how many days?