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Structure of Atom · JEE Preparation Chemistry

The energy of an electron in the second Bohr orbit of the hydrogen atom is -3.4 text{ eV}. What is the energy of the electron in the third Bohr orbit?

Practice question from Structure of Atom (JEE Preparation Chemistry), with the correct answer and a step-by-step solution.

medium · MCQ · Q-E72270

The energy of an electron in the second Bohr orbit of the hydrogen atom is −3.4 eV-3.4 \text{ eV}. What is the energy of the electron in the third Bohr orbit?

  1. A.-1.51 eVCorrect answer
  2. B.-0.85 eV
  3. C.-2.27 eV
  4. D.-3.40 eV

Solution

The energy of an electron in the nn-th Bohr orbit is given by En=−13.6×Z2n2 eVE_n = -13.6 \times \frac{Z^2}{n^2} \text{ eV}. For hydrogen, Z=1Z = 1. Thus, E3=−13.6×1232=−13.69=−1.51 eVE_3 = -13.6 \times \frac{1^2}{3^2} = \frac{-13.6}{9} = -1.51 \text{ eV}.

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