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The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balme…

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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)

[JEE Main 2026, 28 Jan (Shift 1)]

a

\(\frac{3\text{R}}{4},\frac{3\text{R}}{16},\frac{7\text{R}}{144}\)

b

\(\frac{5\text{R}}{36},\frac{8\text{R}}{9},\frac{15\text{R}}{16}\)

c

\(\frac{7\text{R}}{144},\frac{3\text{R}}{16},\frac{16\text{R}}{255}\)

d

\(\frac{5\text{R}}{36},\frac{3\text{R}}{16},\frac{21\text{R}}{100}\)

✓ Correct answer: d)

\(\frac{5\text{R}}{36},\frac{3\text{R}}{16},\frac{21\text{R}}{100}\)

Explanation

Balmer series line \(\Rightarrow \overset{¯}{\nu }={R}_{H}{z}^{2}\left[\frac{1}{{2}^{2}}−\frac{1}{{n}^{2}}\right]\)

If n = 3 \(\Rightarrow \overset{¯}{\nu }=R{(1)}^{2}\left[\frac{1}{{2}^{2}}−\frac{1}{{3}^{2}}\right]=\frac{5R}{36}\)

If n = 4 \(\Rightarrow \overset{¯}{\nu }=\frac{3R}{16}\)

If n = 5 \(\Rightarrow \overset{¯}{\nu }=\frac{21R}{100}\)

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