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Question
The first excited energy of a He+ ion is the same as the ground state energy of hydrogen. Is it always true that one of the energies of any hydrogen-like ion will be the same as the ground state energy of a hydrogen atom?
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Solution
The energy of hydrogen ion is given by
`E_n = -((13.6 eV)Z^2)/n^2`
For the first excited state (n = 2), the energy of He+ ion (with Z = 2) will be 13.6 eV. This is same as the ground state energy of a hydrogen atom.
Similarly, for all the hydrogen like ions, the energy of the (n - 1)th excited state will be same as the ground state energy of a hydrogen atom if Z = n.
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