$10 \ g$ of a radioactive element is disintegrated to $1 \ g$ in $2.303 \ \text{minutes}$. What is the half-life (in minutes) of that radioactive element?

$A$ radioactive sample has a half-life of $1500 \ years$. $A$ sealed tube containing $1 \ g$ of the sample will contain after $3000 \ years$:

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

In the case of a radioisotope,the value of $T_{1/2}$ and $\lambda$ are identical in magnitude. The value 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 $25 \ mg$?

$A$ freshly prepared radioactive element has a half-life of $2 \ hr$. It emits radiation whose intensity is $64$ times the permissible safe level. The minimum time after which it would be possible to work with this sample is .......... $hr$.