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The energy of the electron in third excited state of the hydrogen atom is

  • A.-0.54 eV
  • B.-1.51 eV
  • C.-13.6 eV
  • D.-3.4 eV
  • E.-0.85 eV

Answer: E

The energy is -0.85 eV.

The ground state is \(n = 1\), so the first, second and third excited states are \(n = 2, 3, 4\). The energy levels of hydrogen are \(E_n = -\frac{13.6}{n^{2}}\) eV.

\[ E_4 = -\frac{13.6}{16} = -0.85 \text{ eV} \]

-1.51 eV is the n = 3 level, the second excited state, which is the trap of taking 'third excited' as n = 3. -3.4 eV is n = 2 and -13.6 eV the ground state.

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