The disintegration rate of a certain radioactive sample at any instant is $4250$ disintegrations per minute.$10$ minutes later, the rate becomes $2250$ disintegrations per minute. The approximate decay cons $.........\min^{-1}$

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

Starting with a sample of pure $^{66}Cu,\,\frac{7}{8}$ of it decays into $Zn$ in $15\, min$. The corresponding half-life is .......... $min$

Consider a radioactive nucleus $A$ which decays to a stable nucleus $C$ through the following sequence : $A \to B \to C$ Here $B$ is an intermediate nuclei which is also radioactive. Considering that there are $N_0$, atoms of $A$ initially, plot the graph showing the variation of number of atoms of $A$ and $B$ versus time. 

A heavy nucleus $Q$ of half-life $20$ minutes undergoes alpha-decay with probability of $60 \%$ and beta-decay with probability of $40 \%$. Initially, the number of Q nuclei is $1000$ . The number of alphadecays of $Q$ in the first one hour is

Radioactive element decays to form a stable nuclide, then the rate of decay of reactant is