Answer –
Using the Rydberg’s formula, given the relation –
![\[\frac{hc}{\lambda }=21.76\times {{10}^{-19}}[\frac{1}{{{n}_{1}}^{2}}-\frac{1}{{{n}_{2}}^{2}}]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-96ec2a05ae09e373225138959d9cd4b6_l3.png "Rendered by QuickLaTeX.com")
Where
h is the Planck’s constant, given = 6.6 × 10-34
c is the speed of the light, given = 3 × 108 m/s
and n1 and n2 are integers.
We know that in the Paschen series of the spectral lines, the shortest wavelength corresponds for the following values –
n1 = 3 and n2 = ∞, from above formula we get –
![\[\frac{hc}{\lambda }=21.76\times {{10}^{-19}}[\frac{1}{{{3}^{2}}}-\frac{1}{{{\infty }^{2}}}]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f5c8f3b970b098f09e56a80aa7b712e4_l3.png "Rendered by QuickLaTeX.com")
![\[\lambda =\frac{9}{8\times 1.097\times {{10}^{7}}}=102.55nm\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-56a4cb3fdcc5fa530c85e4de40bc4ee4_l3.png "Rendered by QuickLaTeX.com")
![\[\lambda =\frac{6.6\times {{10}^{-34}}\times 3\times {{10}^{8}}\times 9}{21.76\times {{10}^{-19}}}\text{= }8.189~\times \text{ }{{10}^{7}}~m\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-10bf42bfdb99969db6bca3ace26b1e46_l3.png "Rendered by QuickLaTeX.com")
![\[\therefore \lambda =818.9nm\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1621d3be41a46688d42517917916105e_l3.png "Rendered by QuickLaTeX.com")
