The excitation energy of an electron from second orbit to third orbit of a hydrogen-like atom or ion

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The excitation energy of an electron from second orbit to third orbit of a hydrogen-like atom or ion with +Ze nuclear charge is 47.2 eV. If the energy of H-atom in the lowest energy state is –13.6 eV, then the value of Z is

Accepted Answer

$\Delta E = 13.6z^{2}\left( \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} ight)eV$Or, $47.2 = 13.6 	imes z^{2}\left( \frac{1}{2^{2}} - \frac{1}{3^{2}} ight) \Rightarrow z \approx 5$

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