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The energy of a hydrogen atom in the ground state is −13.6 eV. The energy of a $He^+$ ion in the first excited state will be
A
−6.8 eV
B
−13.6 eV
C
−27.2 eV
D
−54.4 eV
Detailed Solution
For a hydrogen-like ion: $E_n = -13.6\frac{Z^2}{n^2}$ eV
For $He^+$, Z = 2; the first excited state is n = 2.
$E_2 = -13.6\times\frac{2^2}{2^2} = -13.6\times\frac{4}{4}$
$E_2 = -13.6$ eV
For $He^+$, Z = 2; the first excited state is n = 2.
$E_2 = -13.6\times\frac{2^2}{2^2} = -13.6\times\frac{4}{4}$
$E_2 = -13.6$ eV