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  4. If first excitation potential of a hydrogen-like atom is V electron volt, then the ionization energy of this atom will be

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Q. If first excitation potential of a hydrogen-like atom is $V$ electron volt, then the ionization energy of this atom will be

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Solution:

First excitation energy $=\textit{Rhc}\left(\frac{1}{1^{2}} - \frac{1}{2^{2}}\right)=\textit{Rhc}\frac{3}{4}$
$\therefore \frac{3}{4}\textit{Rhc}=\textit{V}\text{ eV}$
$\therefore \textit{Rhc}=\frac{4 \textit{V}}{3}\text{eV}$