After two hours, one-sixteenth of the starting amount of a certain radioactive isotope remained undecayed. The half-life of the isotope is:

The half-life of $Au^{198}$ is $2.7 \, days$. The activity of $1.50 \, mg$ of $Au^{198}$ if its atomic weight is $198 \, g \, mol^{-1}$ is ....... $Ci$ $(N_A = 6 \times 10^{23} \, mol^{-1})$.

The half-life of a radioactive substance is $12 \text{ minutes}$. The time gap between $28 \%$ decay and $82 \%$ decay of the radioactive substance is

$A$ source contains two phosphorus radionuclides $_{15}^{32} P \left(T_{1/2} = 14.3 \ d\right)$ and $_{15}^{33} P \left(T_{1/2} = 25.3 \ d\right)$. Initially,$10\%$ of the decays come from $_{15}^{33} P$. How long must one wait until $90\%$ of the decays come from $_{15}^{33} P$?

$A$ radioactive substance emits $100$ beta particles in the first $2 \,s$ and $50$ beta particles in the next $2 \,s$. The mean life of the sample is

Activity of a radioactive sample is $R_1$ at a time $t_1$ and $R_2$ at a time $t_2$. Its half-life period is $T$. The number of atoms that have disintegrated in the time interval $(t_2 - t_1)$ is equal to $\frac{n(R_1 - R_2)T}{\ln 4}$. Then '$n$' is equal to