The half-lives of two radioactive nuclides $A$ and $B$ are $1 \ min$ and $2 \ min$ respectively. Equal weights of $A$ and $B$ are taken separately and allowed to disintegrate for $4 \ min$. What will be the ratio of weights of $A$ and $B$ disintegrated?

$10 \ g$ of a radioactive substance is reduced to $1.25 \ g$ after $15 \ days$. Its $1 \ kg$ mass will reduce to $500 \ g$ in how many days?

The decay constant of a radioactive sample is $\lambda$. The half-life and mean life of the sample are respectively

$A$ radioactive isotope has a half-life of $10 \ days$. If today $125 \ mg$ is left over,what was its original weight $40 \ days$ earlier?

$A$ piece of wood from an archaeological sample has $5.0 \text{ counts min}^{-1} \text{ g}^{-1}$ of $^{14}C$, while a fresh sample of wood has a count of $15.0 \text{ counts min}^{-1} \text{ g}^{-1}$. If the half-life of $^{14}C$ is $5770 \text{ yr}$, the age of the archaeological sample is:

$A$ radioactive element has a half-life of $20 \ \text{minutes}$. How much time should elapse before the element is reduced to $\frac{1}{8}$th of the original mass? (Answer in $\text{minutes}$)