The ratio of wavelength of spectral lines Hα and Hβ in the Balmer series is x/20. The value of x is _________. Numerical answer type. Work it out, then open the answer.

Answer: 27. Hα ( 3 → 2): (1)/(λα) = 5R/36; Hβ ( 4 → 2): (1)/(λβ) = 3R/16 (λα)/(λβ) = (3/16)/(5/36) = 108/80 = 27/20 Answer: x = 27

The ratio of wavelength of spectral lines Hα and Hβ in the Balmer… | JEE Main 2023 (8 Apr, Shift 2)

Q37JEE Main 2023 · 8 APR · SHIFT 2Medium

Hydrogen Spectrum & Spectral Series

The ratio of wavelength of spectral lines $\text{H}_\alpha$ and $\text{H}_\beta$ in the Balmer series is $\frac{x}{20}$ . The value of $x$ is _________.

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

Show answer and solution

Answer: 27

$H_\alpha$ ( $3 \to 2$ ): $\frac{1}{\lambda_\alpha} = \frac{5R}{36}$ ; $H_\beta$ ( $4 \to 2$ ): $\frac{1}{\lambda_\beta} = \frac{3R}{16}$
$\frac{\lambda_\alpha}{\lambda_\beta} = \frac{3/16}{5/36} = \frac{108}{80} = \frac{27}{20}$
Answer: $x = 27$

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