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

The ratio of $\frac{{}^{14}C}{{}^{12}C}$ in a piece of wood is $\frac{1}{8}$ part that of the atmosphere. If the half-life of ${}^{14}C$ is $5730 \text{ years}$,the age of the wood sample is $.....$ years.

$A$ radioactive isotope has a $t_{1/2}$ of $10 \ days$. If today $125 \ g$ of it is left,what was its weight $40 \ days$ earlier?

The disintegration constant for a radioactive substance is $0.58 \, hr^{-1}$. Its half-life period is $........ \, hr$.

The half-life of a radioactive isotope is $3 \ hours$. If the initial mass of the isotope is $256 \ g$,how much mass in $g$ will remain after $18 \ hours$ (in $.0$)?

The half-life of a radioactive element depends upon