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

Two radioactive samples $A$ and $B$ have half lives $T_1$ and $T_2\left(T_1 > T_2\right)$ respectively At $t=0$, the activity of $B$ was twice the activity of $A$. Their activity will become equal after a time

At time $t=0$, a container has $N_{0}$ radioactive atoms with a decay constant $\lambda$. In addition, $c$ numbers of atoms of the same type are being added to the container per unit time. How many atoms of this type are there at $t=T$ ?

The half-life of $^{215}At$ is $100\mu s$. The time taken for the radioactivity of a sample of $^{215}At$ to decay to $\frac{{1}}{{16}} \,th$ of its initial value is .........$\mu s$

The graph between the instantaneous concentration $(N)$ of a radioactive element and time $(t)$ is

Two radioactive substances $A$ and $B$ have decay constants $5\lambda $ and $\lambda $ respectively. At $t = 0$, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $(\frac {1}{e})^2$ will be