A single electron species in energy level (orbit number ) with energy was provided with excess of en — Atomic Structure Chemistry Question
Question
A single electron species in energy level (orbit number $n$) with energy $X$ was provided with excess of energy so that it jumps to higher energy level with energy $Y$. If it can emit radiations of six different wavelengths on de-excitement between these two energy levels, then the correct relation is
Answer: C
💡 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.
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