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Q. In a sample of $H$ atoms, electrons make transition from fifth state to ground state producing all possible wavelengths, then the value of the fifth highest energy line (in $eV$ ) is

Structure of Atom

Solution:

In the hydrogen spectrum, Balmer series lines have second highest energy.
$\Rightarrow 5^{\text {th }}$ highest energy line belongs to $5 \rightarrow 2$ transition. $\Rightarrow \Delta E=2.86\, eV$
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Clearly $5^{\text {th }}$ highest line is $5 \rightarrow 2$
$\Rightarrow \Delta E=3.4-0.54=2.86\, eV$.