The half-life of ${}^{198} {Au}$ is $3 \, \text{days}$. If the atomic weight of ${}^{198} {Au}$ is $198 \, \text{g/mol}$, then the activity of $2 \, \text{mg}$ of ${}^{198} {Au}$ is ..... $\times 10^{12} \, \text{disintegration/second}$.

Two radioactive materials $R_1$ and $R_2$ have decay constants $6 \lambda$ and $\lambda$, respectively. The half-life of $R_2$ is $1.4 \times 10^{17} \,s$. Initially, they contain the same number of nuclei. The time at which the ratio of the remaining nuclei of $R_2$ to that of $R_1$ will be $e$ is (Let $\ln 2 = 0.7$):

In the figure,$X$ represents time and $Y$ represents the activity of a radioactive sample. The activity of the sample varies with time according to which curve?

The decay constant of a radioactive element is $0.01 \ s^{-1}$. Its half-life period is ....... $s$.

The age of a tree is determined using the radio-isotope of:

The graph shows the $\log$ of activity $\log R$ of a radioactive material as a function of time $t$ in minutes. The half-life (in minutes) for the decay is closest to