After $280$ days, the activity of a radioactive sample is $6000\, dps$. The activity reduces to $3000\, dps$ after another $140\, days$. The initial activity of the sample in dps is

A sample of a radioactive nucleus $A$ disintegrates to another radioactive nucleus $B$, which in turn disintegrates to some other stable nucleus $C.$ Plot of a graph showing the variation of number of atoms of nucleus $B$ vesus time is :

(Assume that at ${t}=0$, there are no ${B}$ atoms in the sample)

Radioactive material $'A'$ has decay constant $8 \lambda$ and material $'B'$ has decay constant $ ' \lambda '$. Initially they have same number of nuclei . After what time, the ratio of number of nuclei of material $'B'$ to that $'A'$ will be $\frac{1}{e}$ ?

The graph represents the decay of a newly prepared sample of radioactive nuclide $X$ to a stable nuclide $Y$ . The half-life of $X$ is $\tau $ .  The growth curve for $Y$ intersects the decay curve for $X$ after time $T$ . What is the time $T$ ?

What fraction of a radioactive material will get disintegrated in a period of two half-lives

The radioactivity of a certain radioactive elements drops to $\frac{1}{64}$ of its initial value in $30$ seconds. Its half life is ............. seconds