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

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

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

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

The wavelength ranges of Lyman and Balmer series do not overlap

answer is A.

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Detailed Solution

$\begin{array}{l} (A) \frac{1}{λ} = R (\frac{1}{2^{2}} - \frac{1}{n^{2}}) \\ \frac{1}{λ_{2}} = R (\frac{1}{2^{2}} - \frac{1}{3^{2}}) = \frac{5 R}{36} . . . . . . . (1) \\ \frac{1}{λ_{3}} = R (\frac{1}{2^{2}}) = \frac{R}{4} . . . . . . . (2) \\ \frac{(2)}{(1)} = \frac{λ_{2}}{λ_{3}} = \frac{\frac{R}{4}}{\frac{5 R}{36}} = \frac{9}{5} (A) iscorrect \end{array}$

(B) Balmer series belongs to visible
Pasehen series belongs to I.R region.

$(C) \frac{1}{λ} = R (1 - \frac{1}{m^{2}}); \frac{1}{λ_{0}} = R when m \to \infty \Rightarrow λ = \frac{1}{R} \frac{1}{(1 - \frac{1}{m^{2}})} = \frac{λ_{0}}{(1 - \frac{1}{m^{2}})}$