Question

Find the longest wavelength in Paschen series $(GivenR=1.097\times {10}^7{m}^{-1})$

Answer 1

In Paschen’s series corresponds to the transitions between the states with principal quantum number $n_1=3and{n}_2=4,5,\mathrm{6......}\infty$

For finding the longest wavelength in Paschen’s series the relation is as follows

$\frac{1}{\lambda }=R[\frac{1}{n_1}-\frac{1}{n_2}]$

Using all the values we get :

$\frac{1}{\lambda }=1.097\times {10}^7[\frac{1}{{\left(3\right)}^2}-\frac{1}{{\infty }^2}]$

$\frac{1}{\lambda }=\frac{1.097\times {10}^7}{9}$

$\frac{1}{\lambda }=0.1218\times {10}^7$

$\lambda =8.2041\times {10}^{-7}m$

$\lambda =8204\dot{A}$