If a radioactive substance reduces to $\frac{1}{16}$ of its original mass in $40$ days,what is its half-life in days?

Half-life of a radioactive substance $A$ is two times the half-life of another radioactive substance $B$. Initially,the number of nuclei of $A$ and $B$ are $N_A$ and $N_B$ respectively. After three half-lives of $A$,the number of nuclei of both are equal. Then $\frac{N_A}{N_B}$ is

The half-life of a radioactive sample,where the initial activity of the material was $8 \text{ counts}$ and after $3 \text{ hours}$ it becomes $1 \text{ count}$,is ............... $hours$.

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

The activity of a sample reduces from $A_0$ to $A_0 / \sqrt{3}$ in one hour. The activity after $3$ hours more will be

$A$ radioactive sample has a half-life of $5$ years. The percentage of the fraction decayed in $10$ years will be (in $\%$)