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  4. Calculate the highest frequency of the emitted photon in the Paschen series of spectral lines of the hydrogen atom

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Q. Calculate the highest frequency of the emitted photon in the Paschen series of spectral lines of the hydrogen atom

AMUAMU 2012Atoms

Solution:

$\frac{1}{\lambda} = R \left[\frac{1}{\left(n_{1}\right)^{2}} - \frac{1}{\left(n_{2}\right)^{2}}\right] $
For Paschen series
$ \frac{1}{\lambda} = R \left[\frac{1}{\left(3\right)^{2}} - \frac{1}{\left(\infty\right)^{2}}\right]$
$ = R \left[\frac{1}{9} -0\right] = R \frac{1}{9} $
$\frac{1}{\lambda} = \frac{R}{9} $
$\lambda = \frac{9}{R}$
$\lambda = \frac{9}{1.09\times 10^{7}} $
$ = 8.25 \times 10^{-7} $
Frequency $n = \frac{c}{\lambda} $
$= \frac{3\times 10^{8}}{8.25 \times 10^{-7}} $
$ n = 3.7 \times 10^{14} Hz$