In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is:

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In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is:

A $\frac{5}{27}$
B $\frac{4}{9}$
C $\frac{9}{4}$
D $\frac{27}{5}$

Solution & Step-by-step Explanation

1. Longest wavelength in Lyman series (λ_{L}): Transition from n = 2 to n = 1 . \frac{1}{λ _{L}} = R (\frac{1}{1 ^{2}} - \frac{1}{2 ^{2}}) = \frac{3 R}{4} \Rightarrow λ_{L} = \frac{4}{3 R} 2. Longest wavelength in Balmer series (λ_{B}): Transition from n = 3 to n = 2 . \frac{1}{λ _{B}} = R (\frac{1}{2 ^{2}} - \frac{1}{3 ^{2}}) = \frac{5 R}{36} \Rightarrow λ_{B} = \frac{36}{5 R} 3. Ratio: \frac{λ _{L}}{λ _{B}} = \frac{4/3 R}{36/5 R} = \frac{4}{3} \times \frac{5}{36} = \frac{5}{27} .

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In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is:

\frac{5}{27}

\frac{4}{9}

\frac{9}{4}

\frac{27}{5}

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