Two radioactive materials $A$ and $B$ have decay constants $10\,\lambda $ and $\lambda $, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of a to that of $B$ will be $1/e$ after a time

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

Draw a graph showing the variation of decay rate with number of active nuclei. 

The half life of a radioactive isotope $'X'$ is $20$ years, It decays to another element $'Y'$ which is stable. The two elements $'X'$ and $'Y'$ were found to be in  the ratio $1:7$ in a simple of a given rock . The age of the rock is estimated to be…………$years$

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