Two radioactive materials $X_1$ and $X_2$ have decay constant $5\lambda$ and $\lambda$ respectively intially they have the saame number of nuclei, then the ratio of the number of nuclei of $X_1$ to that $X_2$ will be $\frac{1}{e}$ after a time

At time $t=0$ some radioactive gas is injected into a sealed vessel. At time $T$ some more of the gas is injected into the vessel. Which one of the following graphs best represents the logarithm of the activity $A$ of the gas with time $t$ ?

$1 \,mg$ gold undergoes decay with $2.7$ days half-life period, amount left after $8.1$ days is ......... $mg$

What percentage of original radioactive atoms is left after five half lives..........$\%$

A $1000 \;MW$ fission reactor consumes half of its fuel in $5.00\; y$. How much $_{92}^{235} U$ (in $kg$) did it contain initially? Assume that the reactor operates $80 \%$ of the time, that all the energy generated arises from the fission of $_{92}^{235} U$ and that this nuclide is consumed only by the fission process.

The decay constant of the end product of a radioactive series is