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?

Answer 1

Answer:

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Answer 2

The energies of any hydrogen-like ion will be the same as the ground state energy of a hydrogen atom

Explanation:

• The energy of the hydrogen ions is given by the

         $E_{n}=-\frac{(13.6 \mathrm{eV}) Z^{2}}{n^{2}}$

• The energy of He+ ion (with Z = 2) will be -13,6 eV for the first excited state (n = 2). That is the same as the energy of a ground-state hydrogen atom.

• Furthermore, the energy of the (n-1)th excited state will be the same for all hydrogen-like ions as the Ground-state hydrogen energy atom, if Z = n.