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If n >>1, then the dependence of frequency of photon emitted as a result of transition of an electron n^th orbit to (n–1)^th orbit, on n will be

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$v \propto \frac{1}{n}$

$v \propto \frac{1}{n^{2}}$

$v \propto \frac{1}{n^{3}}$

$v \propto \frac{1}{n^{4}}$

answer is C.

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Detailed Solution

$∆ E = 13.6 \times Z^{2} (\frac{1}{{(n - 1)}^{2}} - \frac{1}{n^{2}})$

$\Rightarrow ν \propto (\frac{1}{n - 1^{2}} - \frac{1}{n^{2}})$

$\Rightarrow ν \propto (\frac{n^{2} - n^{2} - 1 + 2 n}{(n (n - 1))^{2}})$

$\Rightarrow ν \propto \frac{1}{n^{3}}$

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