Ratio of longest wavelength corresponding to Lyman and Balmer series in hydrogen spectrum is

5/27

3/23

7/29

9/31

Solution

5/27

Wavelength space for space Lyman space series straight lambda subscript straight L space equals space fraction numerator 1 over denominator straight R open parentheses 1 minus begin display style 1 fourth end style close parentheses end fraction space equals space fraction numerator 4 over denominator 3 straight R end fraction and space wavlength space space for space Balmer space series straight lambda subscript straight B space equals space fraction numerator 1 over denominator straight R open parentheses begin display style 1 fourth end style minus begin display style 1 over 9 end style close parentheses end fraction space equals space fraction numerator 1 over denominator straight R open parentheses begin display style 5 over 36 end style close parentheses end fraction space equals space fraction numerator 36 over denominator 5 straight R end fraction space straight lambda subscript straight L over straight lambda subscript straight B space equals space fraction numerator 4 over denominator 3 straight R end fraction straight x fraction numerator 5 straight R over denominator 36 end fraction space equals space 5 divided by 27 space

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