The plot of the number $(N)$ of undecayed atoms versus activity $(A)$ of a radioactive substance is

The half-life period of a radioactive element $x$ is the same as the mean life time of another radioactive element $y$. Initially,they have the same number of atoms. Then:

$A$ freshly prepared radioactive sample of half-life $1$ hour emits radiations that are $128$ times as intense as the permissible safe limit. The minimum time after which this sample can be safely used is ......... $hours$.

The half-life of a radioactive substance is $40 \, years$. How long will it take to reduce to one-fourth of its original amount, and what is the value of the decay constant?

For a certain radioactive process,the graph between $\ln R$ and $t \, (\text{sec})$ is obtained as shown in the figure. Then the value of the half-life for the unknown radioactive material is approximately $.... \, \text{sec}$.

Consider a radioactive material of half-life $1.0 \, \text{minute}$. If one of the nuclei decays now,the next one will decay