$1 \, mg$ of gold undergoes decay with a $2.7 \, \text{days}$ half-life period. The amount left after $8.1 \, \text{days}$ is ......... $mg$.

In a radioactive substance at $t = 0$,the number of atoms is $8 \times 10^4$. Its half-life period is $3 \ years$. The number of atoms $1 \times 10^4$ will remain after an interval of ........... $years$.

The half-life period of a radioactive element $x$ is the same as the mean life time of another radioactive element $y$. Initially,they have the same number of atoms. Then:

The half-life of a radioactive nuclide is $100 \, hours$. The fraction of original activity that will remain after $150 \, hours$ would be:

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

The half-life of a radioactive element $X$ is equal to the mean life of another radioactive element $Y$. Initially, the number of atoms for both is the same. Then: