The ratio of wavelength values of series limit lines 2 (n=α) of Balmer series and Paschen series are

The ratio of wavelength values of series limit lines 2 ($\mathrm{n}=\mathrm{\alpha }$) of Balmer series and Paschen series are

1. A

4:9

2. B

9: 4

3. C

2:3

4. D

3: 2

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Solution:

For limiting line in Balmer series,

For limiting line Paschen series

Wavelength of limiting line in Balmer series,

$\frac{1}{{\mathrm{\lambda }}_{\mathbf{B}}}=\mathrm{R}\left[\frac{1}{{\mathrm{n}}_{1}^{2}}-\frac{1}{{\mathrm{n}}_{2}^{2}}\right]$

Wavelength of limiting line in Paschen series,

$\frac{1}{{\mathrm{\lambda }}_{\mathrm{P}}}=\mathrm{R}\left[\frac{1}{{\left(3\right)}^{2}}-\frac{1}{{\left(\infty \right)}^{2}}\right]=\mathrm{R}\left[\frac{1}{9}-0\right]$

The ratio of wavelengths values of limiting lines for Balmer and Paschen series is given in the below.

$\frac{{\mathrm{\lambda }}_{\mathrm{B}}}{{\mathrm{\lambda }}_{\mathrm{P}}}=\frac{\left(\frac{4}{\mathrm{R}}\right)}{\left(\frac{9}{\mathrm{R}}\right)}⇒\frac{{\mathrm{\lambda }}_{\mathrm{B}}}{{\mathrm{\lambda }}_{\mathrm{P}}}=\frac{4}{9}$