The radioactive sources $A$ and $B$ have half-lives of $2 \ hr$ and $4 \ hr$ respectively,and initially contain the same number of radioactive atoms. At the end of $2 \ hr$,their rates of disintegration are in the ratio:

Two radioactive materials $A$ and $B$ have decay constants $5\lambda$ and $\lambda$ respectively. At $t=0$,they have the same number of nuclei. The ratio of the number of nuclei of $A$ to that of $B$ will be $(1/e)^2$ after a time interval of:

$A$ radioactive element emits $\alpha$ and $\beta$ particles. Its mean lives for $\alpha$ and $\beta$ decay are $1620$ years and $405$ years,respectively. After how many years will the activity be reduced to $1/4$ of its initial value?

$A$ radioactive substance decays to $\left(\frac{1}{16}\right)^{th}$ of its initial activity in $80\, days$. The half-life of the radioactive substance expressed in days is ... .

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

$A$ piece of wood from a recently cut tree shows $20$ decays per minute. $A$ wooden piece of the same size placed in a museum (obtained from a tree cut many years back) shows $2$ decays per minute. If the half-life of $C^{14}$ is $5730$ years,then the age of the wooden piece placed in the museum is approximately ........... years.