$87.5\%$ decomposition of a radioactive substance completes in $3$ hours. What is the half-life of that substance?

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 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 $(\log \, 2 = 0.3010)$

The half-life period of radioactive decay of ${}^{14}C$ is $5730 \ years$. An archaeological artifact contains $80\%$ of ${}^{14}C$ as compared to a living tree. Calculate the age of the sample in $years$.

$A$ freshly prepared radioactive source of half-life $2 \ hours$ emits radiations of intensity which is $64$ times the permissible safe level. The minimum time after which it would be possible to work safely with this source is ......... $hours$.

$A$ certain nuclide has a half-life period of $30 \ min$. If a sample containing $600$ atoms is allowed to decay for $90 \ min$,how many atoms will remain (in $atoms$)?