$A$ radioactive isotope having a half-life of $3 \ days$ was received after $12 \ days$. It was found that there were $3 \ g$ of the isotope in the container. The initial weight of the isotope when packed was ......... $g$.

$A$ freshly prepared radioactive element has a half-life of $2 \ hr$. It emits radiation whose intensity is $64$ times the permissible safe level. The minimum time after which it would be possible to work with this sample is .......... $hr$.

If the half-life of an isotope $X$ is $10 \ yr$,its decay constant is (in $yr^{-1}$)

$A$ radioactive substance is required to have an activity of $0.01 \mu Ci$ in the human body after $24 \ hours$. The half-life of the radioactive substance is $6 \ hours$. What is the maximum initial activity that can be administered (in $\mu Ci$)?

If the half-life of a certain radioactive nucleus is $1000 \ s,$ the disintegration constant is

$8 \, g$ of the radioactive isotope,cesium$-137$ were collected on February $1$ and kept in a sealed tube. On July $1$,it was found that only $0.25 \, g$ of it remained. So the half-life period of the isotope is ....... $days$.