The half life of a radioactive substance is $20$ minutes. The approximate time interval $(t_2 – t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it had decayed and time $t_1$ when $\frac{1}{3}$ of it had decayed is ……….$min$

If the decay or disintegration constant of a radioactive substance is $\beta $, then its half life and mean life are respectively 

$(log_e \,2 =ln\, 2)$

Half-lives of two radioactive elements $A$ and $B$ are $20$ minutes and $40$ minutes, respectively. Initially, the samples have equal number of nuclei. After $80$ minutes, the ratio of decayed number of $A$ and $B$ nuclei will be

In a radioactive decay chain reaction, ${ }_{90}^{230} Th$ nucleus decays into ${ }_{84}^{214} Po$ nucleus. The ratio of the number of $\alpha$ to number of $\beta^{-}$particles emitted in this process is. . . . . 

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At $t = 0$ it was $1600$ counts per second and $t = 8\, seconds$ it was $100$ counts per second. The count rate observed, as counts per second, at $t = 6\, seconds$ is close to