A single electron species in energy level (orbit number ) with energy was provided with excess of en — Atomic Structure Chemistry Question

💡 Solution & Explanation

Six different lines implies the difference in orbit numbers $\Delta n = 3$ since $\frac{\Delta n(\Delta n + 1)}{2} = 6$. New orbit is $n+3$. Magnitudes of energy are $X \propto \frac{1}{n^2}$ and $Y \propto \frac{1}{(n+3)^2}$. Ratio $\frac{X}{Y} = \frac{(n+3)^2}{n^2}$. Taking the square root gives $\sqrt{\frac{X}{Y}} = \frac{n+3}{n} = 1 + \frac{3}{n}$. Therefore, correct answer is C.