What is the half-life (in $\text{min}$) of a radioactive substance if $75\%$ of a given amount of the substance disintegrates in $30 \, \text{min}$?

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?

The ratio of $\frac{{}^{14}C}{{}^{12}C}$ in a piece of wood is $\frac{1}{8}$ part that of the atmosphere. If the half-life of ${}^{14}C$ is $5730 \text{ years}$,the age of the wood sample is $.....$ years.

$A$ certain nuclide has a half-life period of $30 \ min$. If a sample containing $600$ atoms is allowed to decay for $90 \ min$,how many atoms will remain (in $atoms$)?

The half-life of the radioactive isotope tritium $(_1^3H)$ is $12.3 \ years$. If the initial amount of tritium is $32 \ mg$,how many milligrams will remain after $49.2 \ years$ (in $mg$)?

The half-life of radium-$226$ is $1620$ years. The time taken to convert $10 \ g$ of radium to $1.25 \ g$ is ......... years.