At a given instant, say $t = 0,$ two radioactive substances $A$ and $B$ have equal activates. The ratio $\frac{{{R_B}}}{{{R_A}}}$ of their activities. The ratio $\frac{{{R_B}}}{{{R_A}}}$ of their activates after time $t$ itself decays with time $t$ as $e^{-3t}.$ If the half-life of $A$ is $ln2,$ the half-life of $B$ is

Consider an initially pure $M$ gm sample of$_ A{X}$, an isotope that has a half life of $T$ hour, what is it’s initial decay rate ($N_A$ = Avogrado No.)

The activity of a radioactive sample

A sample contains $10^{-2}\, kg$ each of two substances A and $B$ with half lives $4 \,s$ and $8 \,s$ respectively. The ratio of then atomic weights is $1: 2$ The ratio of the amounts of $A$ and $B$ after $16 \,s$ is $\frac{x}{100}$. the value of $x$ is........

Mean life of a radioactive sample is $100$ seconds. Then its half life (in minutes) is

Plutonium decays with a half-life of $24000 \,years$. If the plutonium is stored for $72000 \,years$, then the fraction of plutonium that remains is