$A$ radioactive isotope has a half-life of $10 \, \text{years}$. What percentage of the original amount of it remains after $20 \, \text{years}$?

The activity of carbon-$14$ in a piece of an ancient wood is only $12.5\%$. If the half-life period of carbon-$14$ is $5760 \, years$,the age of the piece of wood will be $(\log \, 2 = 0.3010)$

What is the half-life period of a nucleus in $days$ if at the end of $4.2$ $days$,$N = 0.798 \ N_0$?

The decay constant of a radioactive sample is $\lambda$. The half-life and mean life of the sample are respectively

The half-life of an isotope is $10 \ hrs$. How much will be left behind after $4 \ hrs$ in a $1 \ gm$ sample? (Assume the molar mass of the isotope is $1 \ g/mol$ for calculation purposes).

The half-life period $t_{1/2}$ of a radioactive element is $N$ years. The period of its complete decay is