The first three spectral lines of H-atom in the Balmer series are given λ 1, λ 2, λ 3 considering the Bohr atomic model, the wave lengths of first and third spectral lines ((λ₁)/(λ₃)) are related by a factor of approximately 'x' × 10 - 1. The value of x, to the nearest integer, is _________. Numerical answer type. Work it out, then open the answer.

Answer: 15. First Balmer line ( 3 → 2): (1)/(λ₁) = R(1/4-1/9) = 5R/36 Third Balmer line ( 5 → 2): (1)/(λ₃) = R(1/4-1/25) = (21R)/(100) (λ₁)/(λ₃) = (21/100)/(5/36) = (756)/(500) = 1.512 ≈ 15× 10⁻¹ Answer: x = 15

The first three spectral lines of H-atom in the Balmer series are… | JEE Main 2021 (16 Mar, Shift 1)

Q45JEE Main 2021 · 16 MAR · SHIFT 1Medium

Hydrogen Spectrum & Spectral Series

The first three spectral lines of H-atom in the Balmer series are

given $\lambda$ 1, $\lambda$ 2, $\lambda$ 3 considering the Bohr atomic model, the wave lengths of first and third spectral lines $\left(\frac{\lambda_1}{\lambda_3}\right)$ are related by a factor of approximately 'x' $\times$ 10 $-$ 1.

The value of x, to the nearest integer, is _________.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 15

First Balmer line ( $3 \to 2$ ): $\frac{1}{\lambda_1} = R\left(\frac{1}{4}-\frac{1}{9}\right) = \frac{5R}{36}$
Third Balmer line ( $5 \to 2$ ): $\frac{1}{\lambda_3} = R\left(\frac{1}{4}-\frac{1}{25}\right) = \frac{21R}{100}$
$\frac{\lambda_1}{\lambda_3} = \frac{21/100}{5/36} = \frac{756}{500} = 1.512 \approx 15\times 10^{-1}$
Answer: $x = 15$

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