$A$ 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 ......... $g$.

The half-life of radioactive $C^{14}$ is $5760 \ years$. In how many years will a $200 \ mg$ sample of $C^{14}$ be reduced to $25 \ mg$?

If $8.0 \ g$ of a radioactive substance has a half-life of $10 \ hrs.$,the half-life of $2.0 \ g$ of the same substance is .......... $hr$.

The unit of the decay constant for radioactive disintegration is:

The radioactivity due to the $^{14}C$ isotope (half-life $6000 \ years$) of a sample of wood from an ancient tomb was found to be nearly half that of fresh wood. The tomb is therefore about ........... years old.

$A$ piece of wood from an archaeological sample has $5.0 \text{ counts min}^{-1} \text{ g}^{-1}$ of $^{14}C$, while a fresh sample of wood has a count of $15.0 \text{ counts min}^{-1} \text{ g}^{-1}$. If the half-life of $^{14}C$ is $5770 \text{ yr}$, the age of the archaeological sample is: