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The total energy of an electron in the $n$-th orbit of a hydrogen atom is given by $E_n = -13.6/n^2\,\text{eV}$. The energy of the electron in the first excited state ($n = 2$) is:
A$-6.8\,\text{eV}$
B$-3.4\,\text{eV}$
C$-13.6\,\text{eV}$
D$-1.51\,\text{eV}$
Answer & Solution
Correct answer: B. $-3.4\,\text{eV}$
The first excited state corresponds to $n = 2$, so $E_2 = -13.6 / 2^2 = -13.6/4 = -3.4\,\text{eV}$. The ground state $n = 1$ has energy $-13.6\,\text{eV}$; the second excited state $n = 3$ has $-1.51\,\text{eV}$.
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