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The energy of He$$^+$$ ion in its first state is, (The ground state energy for the Hydrogen atom $$-13.6$$ eV):
The energy of a hydrogen-like ion in state $$n$$ is:
$$E_n = -\frac{13.6 \times Z^2}{n^2} \text{ eV}$$
For He$$^+$$: $$Z = 2$$. The first excited state means $$n = 2$$.
$$E_2 = -\frac{13.6 \times 4}{4} = -13.6 \text{ eV}$$
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