JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Atomic Structure

The hydrogen spectrum consists of several spectral lines in Lyman series

(L_{1}, L_{2}, L_{3} \dots .; L_{1}

has lowest energy among Lyman series). Similarly it consists of several spectral lines in Balmer series (

B_{1}, B_{2}

B_{3} \dots\dots; B_{1}

has lowest energy among Balmer lines). The energy of

L_{1}

is x times the energy of

B_{1}

. The value of

x

is ______

\times 1 0^{- 1}

(Nearest inteter)

Answer: 54

Solution

The lowest-energy Lyman line

L_{1}

is the

n = 2 \to 1

transition and the lowest-energy Balmer line

B_{1}

is the

n = 3 \to 2

transition. Their energies are

E (L_{1}) = 13.6 (1 - \frac{1}{4}) = 13.6 \times \frac{3}{4}

and

E (B_{1}) = 13.6 (\frac{1}{4} - \frac{1}{9}) = 13.6 \times \frac{5}{36}

. The ratio is

\frac{3/4}{5/36} = \frac{27}{5} = 5.4

. Expressed as

x \times 1 0^{- 1}

, the value of

x

54

JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Integer answer