Which of the following statement(s) is (are) correct about the spectrum of a hydrogen atom?

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There is an overlap between the wavelength ranges of the Balmer and paschen series

The wavelengths of the Lyman series are given by $(1 + 1 / m^{2}) λ_{0}$ where $λ_{0}$ is the shortest wavelength of Lyman series and m is an integer

The wavelength rages of Lyman and Balmer series do not overlap

The ratio of the longest wavelength to the shortest wavelength in the Balmer series is 9/5

answer is A, D.

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Detailed Solution

For Balmer series: $\frac{1}{λ} = R [\frac{1}{2^{2}} - \frac{1}{n^{2}}]$

n= 3,4,5

$\frac{1}{λ_{\max}} = R [\frac{1}{4} - \frac{1}{9}]$
$\frac{1}{λ_{\max}} = R [\frac{1}{4}]$
$\frac{λ_{\max}}{λ_{\max}} = \frac{9}{5}$
For Layman Series $\frac{1}{λ} = R (1 - \frac{1}{n^{2}})$
$n = 2, 3, 4, ....$
$\frac{1}{λ_{\min}} = R \Rightarrow λ = λ_{0} n^{2} / (n^{2} - 1)$