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Chemistry-

General

Easy

Question

When an electron makes a transition from $left parenthesis n plus 1 right parenthesis$ state to $n$ state, the frequency of emitted radiations is related to $n$ according to $left parenthesis n much greater-than 1 right parenthesis$

$v \propto n^{- 3}$
$v \propto n^{2}$
$v \propto n^{3}$
$v \propto n^{\frac{2}{3}}$

The correct answer is: $v proportional to n to the power of negative 3 end exponent$

$v equals fraction numerator c over denominator lambda end fraction equals R c Z to the power of 2 end exponent open parentheses fraction numerator 1 over denominator n to the power of 2 end exponent end fraction minus fraction numerator 1 over denominator open parentheses n plus 1 close parentheses to the power of 2 end exponent end fraction close parentheses equals R c Z to the power of 2 end exponent open parentheses fraction numerator 1 plus 2 n over denominator n to the power of 2 end exponent open parentheses n plus 1 close parentheses to the power of 2 end exponent end fraction close parentheses$
$almost equal to R c Z to the power of 2 end exponent fraction numerator left parenthesis 2 n right parenthesis over denominator n to the power of 4 end exponent end fraction proportional to n to the power of negative 3 end exponent$

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