The half-life of a radioactive substance is $5$ years. What is the probability of decay of this element in $10$ years?

The half-life of $Ra^{226}$ is $1620$ years. Calculate the number of atoms that decay in one second in $1 \ g$ of radium (Avogadro number $= 6.023 \times 10^{23}$).

Let $N_{\beta}$ be the number of $\beta$ particles emitted by $1 \, g$ of $^{24}Na$ radioactive nuclei (half-life $= 15 \, hrs$) in $7.5 \, hrs$. $N_{\beta}$ is close to (Avogadro number $= 6.023 \times 10^{23} \, mol^{-1}$)

At $t = 0$,the counting rate from a radioactive source is $1600 \text{ counts/s}$,and at $t = 8 \text{ s}$,it is $100 \text{ counts/s}$. The counting rate at $t = 6 \text{ s}$ will be:

An element $X$ with a half-life of $1.4 \times 10^9$ years decays to form another stable element $Y$. $A$ sample is taken from a rock that contains both $X$ and $Y$ in the ratio $1:7$. If at the time of formation of the rock,$Y$ was not present in the sample,then the age of the rock in years is

$99\%$ of the nuclei of a radioactive element decay between which of the following times?