The graph which represents the correct variation of logarithm of activity $(log\, A)$ versus time, in figure is

The half-life period of a radio-active element $X$ is same as the mean life time of another radio-active element $Y$ Initially they have the same number of atoms. Then

A radio isotope has a half life of $75\, years$. The fraction of the atoms of this material that would decay in $150\, years$ will be...........$\%$

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

A ${\pi ^0}$ at rest decays into $2\gamma $ rays ${\pi ^0} \to \gamma + \gamma $. Then which of the following can happen

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