# In a hydrogen atom, the electron makes the transition from $(n+1)^{th}$level to the $n^{th}$ level. If  the frequency of radiation emitted is proportional to Option: 1 Option: 2 Option: 3 Option: 4

An energy gap, $\Delta E= hv$

Here, h is Planck's constant
therefore,
Frequency= $\nu$

$\nu=\frac{\Delta E}{h}=k\left[\frac{1}{(n)^{2}}-\frac{1}{(n+1)^{2}}\right]\Rightarrow \nu=\frac{k (2n+1)}{n^{2}(n+1)^{2}}\\ \ since \ \ n >>> 1 \\So \ (n+1)^2\approx n^2\\ \\\Rightarrow \nu \propto \frac{1}{n^{3}}$

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