The half-life of tritium is $ 12.5 $ years. What mass of tritium of initial mass $ 64 \ mg $ will remain undecayed after $ 50 $ years (in $mg$)?

$A$ radioactive sample disintegrates via two independent decay processes having half-lives $T_{1/2}^{(1)}$ and $T_{1/2}^{(2)}$ respectively. The effective half-life $T_{1/2}$ of the nuclei is

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 percentage of ${}^{235}U$ presently on Earth is $0.72\%$ and the rest $(99.28\%)$ may be taken to be ${}^{238}U$. Assume that all uranium on Earth was produced in a supernova explosion long ago with the initial ratio ${}^{235}U / {}^{238}U = 2.0$. How long ago did the supernova event occur? (Take the half-lives of ${}^{235}U$ and ${}^{238}U$ to be $7.1 \times 10^8$ years and $4.5 \times 10^9$ years respectively).

Two radioactive materials $A$ and $B$ having decay constants $7 \lambda$ and $\lambda$ respectively,initially have the same number of nuclei. The time taken for the ratio of the number of nuclei of material $B$ to that of $A$ to be $e$ is:

$A$ solution containing active cobalt ${}_{27}^{60}Co$ having activity of $0.8\,\mu Ci$ and decay constant $\lambda$ is injected into an animal's body. If $1\,cm^3$ of blood is drawn from the animal's body after $10\,hrs$ of injection,the activity found is $300\,decays$ per minute. What is the total volume of blood in the animal's body in litres? (Given: $1\,Ci = 3.7 \times 10^{10}$ decays per second and at $t = 10\,hrs$,$e^{-\lambda t} = 0.84$)