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  4. The shortest wavelength present in the Paschen series of spectral lines is

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Q. The shortest wavelength present in the Paschen series of spectral lines is

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Solution:

The wavelength for Paschen series,
$\frac{1}{\lambda} = R \left[\frac{1}{3^{2}} -\frac{1}{n^{2}}\right] $
For shortest wavelength $n = \infty$
$\therefore \frac{1}{\lambda} = R \left[\frac{1}{9} -\frac{1}{\infty^{2}}\right] = \frac{R}{9} $
$\Rightarrow \lambda = \frac{9}{R}$
$ = \frac{9}{ 1.097\times10^{7}} $
$= 8.20 \times10^{-7} m $
$ = 820 \,nm $