The half-life of a radioactive sample is $T$. The fraction of the initial mass of the sample that decays in an interval $T / 2$ is

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

The graph shows the $\log$ of activity $\log R$ of a radioactive material as a function of time $t$ in minutes. The half-life (in minutes) for the decay is closest to

The half-life of a radioactive substance is $20$ minutes. The difference between the points of time when it is $33\%$ disintegrated and $67\%$ disintegrated is approximately ......... $min$.

If the half-life of a substance is $3.8\, days$ and its initial quantity is $10.38\, gm$,then the quantity of the substance remaining after $19\, days$ will be ........$gm$.

$A$ radioactive nucleus $A$ has a single decay mode with half-life $\tau_A$. Another radioactive nucleus $B$ has two decay modes $1$ and $2$. If decay mode $2$ were absent,the half-life of $B$ would have been $\tau_A / 2$. If decay mode $1$ were absent,the half-life of $B$ would have been $3 \tau_A$. If the actual half-life of $B$ is $\tau_B$,then the ratio $\tau_B / \tau_A$ is