Discussion
In hydrogen spectral series, the wave numbers of the first Lyman line and the first Balmer line are in the ratio
Answer: C
The ratio is 27 : 5.
Wave number \(\bar{\nu} = R\left(\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}\right)\). The first Lyman line is 2 → 1, and the first Balmer line is 3 → 2.
\[ \begin{aligned} \text{Lyman} &: 1 - \tfrac{1}{4} = \tfrac{3}{4} \\ \text{Balmer} &: \tfrac{1}{4} - \tfrac{1}{9} = \tfrac{5}{36} \\ \tfrac{3}{4} : \tfrac{5}{36} &= 27 : 5 \end{aligned} \]
5 : 27 is the ratio of the wavelengths, since wavelength is the reciprocal of wave number.
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