Number of nuclei of a radioactive substance at time $t = 0$ are $1000$ and $900$ at time $t = 2$ $s$. Then number of nuclei at time $t = 4$ $s$ will be

A freshly prepared radioactive source of half life $2$ hours $30$ minutes emits radiation which is $64$ times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be hours.

State the relation between average life and decay constant. 

The half lives of a radioactive substance are $T$ and $2T$. years for $\alpha  - $ emission and $\beta - $ emission respectively. The total de cay constnnt for simultaneous decay of $\alpha$ and $\beta$ adioactive substance is ___

The half life of a radioactive substance is $20$ minutes. In $........\,minutes$ time,the activity of substance drops to $\left(\frac{1}{16}\right)^{ th }$ of its initial value.

The graph between number of decayed atoms $N'$ of a radioactive element and time $t$ is