JEE Main · 2026 · 28 Jan 2026 · Shift 1 · Atomic Structure

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)

Answer: (A)

Solution

Balmer lines end on

n = 2

, so

\overset{ν}{ˉ} = R (\frac{1}{2 ^{2}} - \frac{1}{n ^{2}})

with

n = 3, 4, 5, \dots

For

n = 3

\overset{ν}{ˉ} = R (\frac{1}{4} - \frac{1}{9}) = \frac{5 R}{36}

; for

n = 4

R (\frac{1}{4} - \frac{1}{16}) = \frac{3 R}{16}

; and for

n = 5

R (\frac{1}{4} - \frac{1}{25}) = \frac{21 R}{100}

. The set of Balmer wave numbers is therefore

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

JEE Main · 2026 · 28 Jan 2026 · Shift 1 · Single correct option