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  4. The longest wavelength line in the Lyman series of the hydrogen spectrum is

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Q. The longest wavelength line in the Lyman series of the hydrogen spectrum is

BHUBHU 2009

Solution:

$\frac{1}{\lambda} R_{H}\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right]$
For longest wavelength in Lyman series,
$n_{1}=1, n_{2}=2 $
$\frac{1}{\lambda}=1.09678 \times 10^{7}\left[\frac{1}{(1)^{2}}-\frac{1}{(2)^{2}}\right] $
$\frac{1}{\lambda}=\frac{1.09678 \times 10^{7} \times 3}{4} $
$\therefore \lambda=1.2156 \times 10^{-7} \,m $
$=1215.6\,\mathring{A}$