An element has a half-life of $1600 \ years$. The fraction of the mass left after $6400 \ years$ will be:

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-life of a radioactive disintegration $(A \to B)$ having a rate constant of $231 \ sec^{-1}$ is:

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 half-life of an isotope is $10 \ hrs$. How much will be left behind after $4 \ hrs$ in a $1 \ gm$ sample? (Assume the molar mass of the isotope is $1 \ g/mol$ for calculation purposes).

What is the half-life of a radioactive substance if $87.5\%$ of any given amount of the substance disintegrates in $40 \, min$?