An element $X$ of a half-life of $1.4 \times 10^9$ years decays to form another stable element $Y$. A sample is taken from a rock that contains both $X$ and $Y$ in the ratio $1: 7$. If at the time of formation of the rock $Y$ was not present in the sample, then the age of the rock in years is

Energy levels $A, B$ and $C$ of a certain atom corresponding to increasing values of energy i.e $E_A < E_B < E_C$. If $\lambda_1, \lambda_2$ and $\lambda_3$ are the wavelengths of a photon corresponding to the transitions shown then.

The principle quantum number $n$ corresponding to the exited state of $\mathrm{He}^{+}$ion. If on transition to the ground state two photons in succession with wavelength $1026 \mathop {\rm{A}}\limits^{\rm{o}}$ and $304 \mathop {\rm{A}}\limits^{\rm{o}}$ are emitted $\left(R=1.097 \times 10^{-7} \mathrm{~m}^{-1}\right)$