The half-life of $_{6}^{14}C$ having a decay constant of $2.25 \times 10^{-4} \text{ year}^{-1}$ is .......... years.

$A$ radioactive substance has a constant activity of $2000$ disintegrations/minute. The material is separated into two fractions,one of which has an initial activity of $1000$ disintegrations per minute while the other fraction decays with $t_{1/2} = 24 \ h$. The total activity in both samples after $48 \ h$ of separation is

$10 \ g$ 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?

If $8.0 \ g$ of a radioactive isotope has a half-life of $10 \ hrs$. The half-life of $2.0 \ g$ of the same substance is ...... $hrs$.

The $T_{1/2}$ of $C^{14}$ isotope is $5770$ years. The time after which $72\%$ of the isotope is left is .......... years.

To determine the half-life of a radioactive element,a student plots a graph of $\ln|dN(t)/dt|$ versus $t$. Here $dN(t)/dt$ is the rate of radioactive decay at time $t$. If the number of radioactive nuclei of this element decreases by a factor of $p$ after $4.16 \ \text{years}$,the value of $p$ is