Give the equation form of exponential law. 

The half-life of a radioactive substance is $20\, min$. The approximate time interval $\left(t_{2}-t_{1}\right)$ between the time $t_{2},$ when $\frac{2}{3}$ of it has decayed and time $t_{1},$ when $\frac{1}{3}$ of it had decayed is (in $min$)

The ratio activity of an element becomes $\frac{{1}}{{64}} th$ of its original value in $60\, sec$. Then the half life period is ............$sec$

In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one mean life .......... $\%$

At a given instant, say $t = 0,$ two radioactive substances $A$ and $B$ have equal activates. The ratio $\frac{{{R_B}}}{{{R_A}}}$ of their activities. The ratio $\frac{{{R_B}}}{{{R_A}}}$ of their activates after time $t$ itself decays with time $t$ as $e^{-3t}.$ If the half-life of $A$ is $ln2,$ the half-life of $B$ is

What is the half-life (in years) period of a radioactive material if its activity drops to $1 / 16^{\text {th }}$ of its initial value of $30$ years?