From a newly formed radioactive substance (half-life $2$ hours), the intensity of radiation is $64$ times the permissible safe level. The minimum time after which work can be done safely from this source is .......... $hours$.

The counting rate observed from a radioactive source at $t=0$ second was $1600$ counts per second and at $t=8$ seconds it was $100$ counts per second. The counting rate observed,as counts per second at $t=6$ seconds,will be

The activity of a radioactive sample reduces from $A_0$ to $\frac{A_0}{\sqrt{3}}$ in $1$ hour. What will be the activity after $3$ hours more?

Radioactive material $A$ has decay constant $8 \lambda$ and material $B$ has decay constant $\lambda$. Initially,they have the same number of nuclei. After what time will the ratio of the number of nuclei of material $B$ to that of $A$ be $\frac{1}{e}$?

The half-life of a radioactive sample undergoing $\alpha$-decay is $1.4 \times 10^{17} \; s$. If the number of nuclei in the sample is $2.0 \times 10^{21}$,the activity of the sample is nearly:

The half-life of radium is $1620$ years and its atomic weight is $226 \, g/mol$. What is the number of atoms decaying per second in a $1 \, g$ sample? $[N_A = 6.023 \times 10^{23} \, \text{atoms/mol}]$