$A$ sample contains $16\, g$ of a radioactive material, the half-life of which is $2\, days$. After $32\, days$, the amount of radioactive material left in the sample is:

$A$ radioactive source has a half-life of $6 \,h$. $A$ freshly prepared sample of the same exhibits radioactivity $32$ times the permissible safe value. The minimum time after which it would be possible to work safely with the source is (in $\,h$)

$A$ parent nucleus $X$ undergoes $\alpha$-decay with a half-life of $75000 \text{ yrs}$. The daughter nucleus $Y$ undergoes $\beta$-decay with a half-life of $9 \text{ months}$. In a particular sample, it is found that the rate of emission of $\beta$-particles is nearly constant (over several months) at $10^{7} / \text{h}$. What will be the number of $\alpha$-particles emitted in an hour?

In a radioactive decay process,the activity is defined as $A = -\frac{dN}{dt}$,where $N(t)$ is the number of radioactive nuclei at time $t$. Two radioactive sources,$S_1$ and $S_2$,have the same activity at time $t = 0$. At a later time,the activities of $S_1$ and $S_2$ are $A_1$ and $A_2$,respectively. When $S_1$ and $S_2$ have just completed their $3^{\text{rd}}$ and $7^{\text{th}}$ half-lives,respectively,the ratio $A_1/A_2$ is:

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

Half-lives of two radioactive substances $A$ and $B$ are,respectively,$20 \ min$ and $40 \ min$. Initially,the samples of $A$ and $B$ have an equal number of nuclei. After $80 \ min$,the ratio of the remaining number of $A$ and $B$ nuclei is