Atomic StructureHard

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

Options

A.$\frac{X}{Y} = (n - 1)^{2}$
B.$\frac{X}{Y} = 1 + \frac{3}{n}$
C.$\sqrt{\frac{X}{Y}} = 1 + \frac{3}{n}$
D.$\frac{X}{Y} = 1 + \frac{n}{3}$

Solution

$X = \frac{E}{n^{2}}\text{ and }Y = \frac{E}{(n + 3)^{2}}$

$\therefore\sqrt{\frac{X}{Y}} = 1 + \frac{3}{n}$

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