The half-life period of a radioactive sample is $3.8 \ days$. After how many days will the sample become $\frac{1}{8}$ of the original substance?

Radioactive material $A$ has decay constant $8 \lambda$ and material $B$ has decay constant $\lambda$. Initially,they have the same number of nuclei. After what time will the ratio of the number of nuclei of material $B$ to that of $A$ be $\frac{1}{e}$?

Half-life of radium is $1620$ years. How many radium nuclei decay in $5$ hours in $5 \, g$ of radium? (Atomic weight of radium $= 223$)

The average life $T$ and the decay constant $\lambda$ of a radioactive nucleus are related as

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

$A$ radioactive sample disintegrates via two independent decay processes having half-lives $T_{1/2}^{(1)}$ and $T_{1/2}^{(2)}$ respectively. The effective half-life $T_{1/2}$ of the nuclei is