If $n_t$ number of radioatoms are present at time $t$,the following expression will be a constant:

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

The radium and uranium atoms in a sample of uranium mineral are in the ratio of $1 : 2.8 \times 10^6$. If the half-life period of radium is $1620$ years,the half-life period of uranium will be:

The half-life of a radioactive element is $10 \ hours$. How much will be left after $4 \ hours$ in a $1 \ g$-atom sample?

The half-life of $_{92}U^{238}$ is $4.5 \times 10^9$ years. After how many years,the amount of $_{92}U^{238}$ will be reduced to half of its present amount?

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).