The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series.
( $\mathrm{R}=$ Rydberg constant)

Question

The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series. ( R= Rydberg constant)

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Correct answer: D. 5 R 36 , 3 R 16 , 21 R 100

For the Balmer series, transitions end at n=2.
Using the Rydberg formula

\bar{\nu} = R\left(\frac{1}{2^2} - \frac{1}{n^2}\right) = R\left(\frac{1}{4} - \frac{1}{n^2}\right)

, we calculate wavenumbers for transitions from different upper levels:
From n=3:

\bar{\nu} = R\left(\frac{1}{4} - \frac{1}{9}\right) = \frac{5R}{36}

From n=4:

\bar{\nu} = R\left(\frac{1}{4} - \frac{1}{16}\right) = \frac{3R}{16}

From n=5:

\bar{\nu} = R\left(\frac{1}{4} - \frac{1}{25}\right) = \frac{21R}{100}

Option (4) contains exactly these three wavenumbers corresponding to the Balmer series transitions.

The wave numbers of three spectral lines of H atom are considered....

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