The wavelength of spectral line obtained in the spectrum of $\mathrm{Li}^{2+}$ ion, when the transition takes place between two levels whose sum is 4 and difference is 2, is

(D) $1.14 \times 10^{-6} \mathrm{~cm}$

(A) $2.28 \times 10^{-7} \mathrm{~cm}$

(B) $2.28 \times 10^{-6} \mathrm{~cm}$

(C) $1.14 \times 10^{-7} \mathrm{~cm}$

JEE Main · 2026 · 24 Jan 2026 · Shift 2 · Atomic Structure

The wavelength of spectral line obtained in the spectrum of

Li^{2 +}

ion, when the transition takes place between two levels whose sum is 4 and difference is 2, is

Answer: (D)

From

n_{1} + n_{2} = 4

and

n_{2} - n_{1} = 2

, the transition is between

n_{1} = 1

and

n_{2} = 3

. For a hydrogen-like ion

\frac{1}{λ} = R_{H} Z^{2} (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}})

. For

L i^{2 +}

Z = 3

, so

\frac{1}{λ} = R_{H} \cdot 9 (1 - \frac{1}{9}) = 8 R_{H}

. With

R_{H} = 1.1 \times 1 0^{5} cm^{- 1}

λ = \frac{1}{8 \times 1.1 \times 1 0 ^{5}} = 1.14 \times 1 0^{- 6} cm

JEE Main · 2026 · 24 Jan 2026 · Shift 2 · Single correct option