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For a hydrogen-like ion of atomic number $Z$, the ground-state energy is:
A$-13.6 Z^2\,\text{eV}$
B$-13.6\,\text{eV}$
C$-13.6 Z\,\text{eV}$
D$-13.6 / Z^2\,\text{eV}$
Answer & Solution
Correct answer: A. $-13.6 Z^2\,\text{eV}$
For a hydrogen-like single-electron ion of charge $+Ze$, $E_n = -13.6\,Z^2/n^2\,\text{eV}$. The ground state has $n = 1$ so $E_1 = -13.6 Z^2\,\text{eV}$. For example $\mathrm{He}^+$ ($Z = 2$) has a ground state energy of $-54.4\,\text{eV}$.
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