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 ....... $Ci$ $(N_A = 6 \times 10^{23} \, mol^{-1})$.

Two radioactive materials $A$ and $B$ have decay constants $5\lambda$ and $\lambda$ respectively. At $t=0$,they have the same number of nuclei. The ratio of the number of nuclei of $A$ to that of $B$ will be $(1/e)^2$ after a time interval of:

Half-lives of two radioactive elements $A$ and $B$ are $20 \ min$ and $40 \ min$,respectively. Initially,the samples have equal number of nuclei. After $80 \ min$,the ratio of decayed number of $A$ and $B$ nuclei will be

Define the decay constant and state its $SI$ unit.

Element $X$ decays into element $Y$ with a half-life of $3$ days. On March $1$st,the mass of $X$ is $10 \, g$. What will be the masses of $X$ and $Y$ after $6$ days?

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?