What is the half-life (in years) of a radioactive material if its activity drops to $1/16$th of its initial value in $30$ years (in $.5$)?

The half-life of radium is about $1600$ years. Of $100 \, g$ of radium existing now, $25 \, g$ will remain unchanged after .......... $years$.

The half-life of a radioactive element is $10 \, days$. The time required for the mass of the sample to reduce to $\frac{1}{10}$ of its initial mass is approximately ........ days.

The half-lives of two radioactive materials $A$ and $B$ are $T$ and $2T$ respectively. If the ratio of the initial masses of the materials $A$ and $B$ is $8:1$, then the time after which the ratio of the masses of the materials $A$ and $B$ becomes $4:1$ is

If ${N_0}$ is the original mass of the substance of half-life period ${T_{1/2}} = 5 \text{ years}$,then the amount of substance left after $15 \text{ years}$ is

If $T$ is the half-life of a radioactive substance,then its instantaneous rate of change of activity is proportional to