$A$ sample of radioactive material has mass $m$,decay constant $\lambda$,and molar mass $M$. If the Avogadro constant is $N_A$,what is the initial activity of the sample?

The half-life of $Au^{198}$ is $2.7 \, days$. The activity of $1.50 \, mg$ of $Au^{198}$ if its atomic weight is $198 \, g \, mol^{-1}$ is ....... $Ci$ $(N_A = 6 \times 10^{23} \, mol^{-1})$.

$A$ radioactive substance decays to $1/64$ of its initial value in $15$ hours. Find its half-life in hours.

Three-fourths of the active nuclei decay in a radioactive sample in $3/4 \, s$. The half-life of the sample is:

At some instant,a radioactive sample $S_1$ having an activity $5\,\mu Ci$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10\,\mu Ci$. The half-lives of $S_1$ and $S_2$ are:

An accident in a nuclear laboratory resulted in the deposition of a certain amount of radioactive material with a half-life of $18$ days inside the laboratory. Tests revealed that the radiation level was $64$ times higher than the permissible level required for safe operation. What is the minimum number of days after which the laboratory can be considered safe for use?