If one starts with $1 \, \text{curie}$ of a radioactive substance $(T_{1/2} = 12 \, \text{hrs})$, the activity left after a period of $1 \, \text{week}$ will be about:

Write a formula showing the relation between half-life and average life of a radioactive substance.

Carbon-$14$ decays with a half-life of about $5,800$ years. In a sample of bone,the ratio of Carbon-$14$ to Carbon-$12$ is found to be $\frac{1}{4}$ of what it is in free air. This bone may belong to a period about $x$ centuries ago,where $x$ is nearest to:

The half-life period of element $X$ is same as the mean life time of element $Y$. Assume initially $X$ and $Y$ have same number of atoms. Then

The half-life of a radioactive element $A$ is the same as the mean-life of another radioactive element $B.$ Initially, both substances have the same number of atoms, then

The activity of a radioactive sample falls from $700 \; s^{-1}$ to $500 \; s^{-1}$ in $30 \; min$. Its half-life is close to ......... $min$.