The difference between the frequencies of the first and second Lyman lines of hydrogen atom is ( $R=$ Rydberg constant and $c=$ speed of light in vacuum)

If the half-life of a radioactive element is 12.5 hours, then the time taken to disintegrate 256 g of the substance into 1 g is (in hours)

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.