$37$ Rutherford equals

The half life of a radioactive isotope $X$ is $50$ years. It decays to another element $Y$ which is stable. The two elements $X$ and $Y$ were found to be in the ratio of $1 : 15$ in a sample of a given rock. The age of the rock was estimated to be..........$years$

Radioacitive nuclei $A$ and $B$ disintegrate into $C$ with half lives $T$ and $2T$. At $t = 0$, pumber of nuclei of each $A$ and $B$ is $x$. The number of nuclei of $C$ when rate of disintegration of $A$ and $B$ are equal is

Two radioactive materials $X_1$ and $X_2$ have decay constant $5\lambda$ and $\lambda$ respectively intially they have the saame number of nuclei, then the ratio of the number of nuclei of $X_1$ to that $X_2$ will be $\frac{1}{e}$ after a time

Deuteron is a bound state of a neutron and a proton with a binding energy $B = 2.2\, MeV$. A $\gamma $ -ray of energy $E$ is aimed at a deuteron nucleus to try to break it into a (neutron + proton) such that the $n$ and $p$ move in the direction of the incident $\gamma $ -ray. If $E = B$, show that this cannot happen. Hence calculate how much bigger than $B$ must $E$ be for such a process to happen. 

At $t = 0$, number of active nuclei in a sample is $N_0$. How much no. of nuclei will decay in time between its first mean life and second half life?