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The energy required to remove the electron from the first excited state ($n=2$) of $He^+$ is

A$54.4\,eV$
B$3.4\,eV$
C$27.2\,eV$
D$13.6\,eV$
Answer & Solution
Correct answer: D. $13.6\,eV$
For a hydrogen-like ion, $E_n = -13.6 \cdot Z^2/n^2\,eV$. For $He^+$ ($Z=2, n=2$): $E_2 = -13.6 \cdot 4/4 = -13.6\,eV$. Energy to take the electron from $n=2$ to $n=\infty$ (where $E=0$) is $|E_2| = 13.6\,eV$. Option B ($3.4\,eV$) is the corresponding value for *hydrogen*'s $n=2$ — a classic trap.
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