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  4. Which the following series fall in the visible range of electromagnetic spectrum of a hydrogen atom?

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Q. Which the following series fall in the visible range of electromagnetic spectrum of a hydrogen atom?

NTA AbhyasNTA Abhyas 2020Atoms

Solution:

$\frac{1}{\lambda }=R\left[\frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}}\right]$
Balmer Series; $n_{f}=2;n_{i}=3,4,5,......$
$\frac{1}{\lambda }=1.097\times 10^{7} \, m=\left[\frac{1}{4} - \frac{1}{9}\right]$
$\Rightarrow \frac{1}{\lambda }=1.097\times 10^{7} \, m=\left[\frac{5}{36}\right]$
$\Rightarrow \lambda =\frac{36}{5}\times \frac{1 0^{- 7}}{1.097} \, m$
$\Rightarrow \lambda =6.56\times 10^{- 7} \, m$
$\Rightarrow \lambda =656\times 10^{- 9} \, m$
This wavelength falls in visible range.