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In a hydrogen like atom electron makes transition from an energy level with quantum number $n$ to another with quantum number $(n-1)$. If $n>>1$, the frequency of radiation emitted is proportional to
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$\frac{1}{n^3}$
In a hydrogen like atom, when an electron makes an transition from an energy level with $n$ to $n-1$, the frequency of emitted radiation is
$v=R c Z^2\left[\frac{1}{(n-1)^2}-\frac{1}{n^2}\right]=\frac{R c Z^2(2 n-1)}{n^2(n-1)^2}$
As $n>>1$
$\therefore \quad \mathrm{v}=\frac{R c Z^2 2 n}{n^4}=\frac{2 R c Z^2}{n^3}$ or $\quad v \propto \frac{1}{n^3}$
$v=R c Z^2\left[\frac{1}{(n-1)^2}-\frac{1}{n^2}\right]=\frac{R c Z^2(2 n-1)}{n^2(n-1)^2}$
As $n>>1$
$\therefore \quad \mathrm{v}=\frac{R c Z^2 2 n}{n^4}=\frac{2 R c Z^2}{n^3}$ or $\quad v \propto \frac{1}{n^3}$
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