The decay constant for a radioactive nuclide is $1.5 \times 10^{-5} \, s^{-1}$. The molar mass of the substance is $60 \, g \, mol^{-1}$,$(N_A = 6 \times 10^{23})$. The activity of $1.0 \, \mu g$ of the substance is $....... \times 10^{10} \, Bq$.

Two radioactive materials $M_1$ and $M_2$ have decay constants $9 \lambda$ and $\lambda$ respectively. Initially,they have the same number of nuclei. The ratio of the number of nuclei of $M_1$ to that of $M_2$ will be $\frac{1}{e}$ after a time interval of:

The half-life of $^{131}I$ is $8 \, days$. Given a sample of $^{131}I$ at time $t = 0$,we can assert that

The activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at a later time $t_2$. Its decay constant is $\lambda$. Which of the following relations is correct?

$A$ parent nucleus $X$ decays into a daughter nucleus $Y$,which in turn decays into $Z$. The half-lives of $X$ and $Y$ are $40000 \, yr$ and $20 \, yr$,respectively. In a certain sample,it is found that the number of $Y$ nuclei hardly changes with time. If the number of $X$ nuclei in the sample is $4 \times 10^{20}$,the number of $Y$ nuclei present in it is

$A$ sample of a radioactive element has a mass of $10 \, g$ at an instant $t = 0$. The approximate mass of this element in the sample after two mean lives is .......... $g$.