The half-life period of a radioactive metal is $20 \ days$. What fraction of the metal remains after $80 \ days$?

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.

The half-life of a radioactive isotope is $3 \ hr$. The value of its disintegration constant is: (in $hr^{-1}$)

$A$ 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:

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 $25 \ mg$?

The $C^{14}$ to $C^{12}$ ratio in a wooden article is $13\%$ that of the fresh wood. Calculate the age of the wooden article. Given that the half-life of $C^{14}$ is $5770 \ years$.