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JEE Main 2025 (2 Apr, Shift 1) · Energy of the Electron & Energy Levels

Energy of the Electron & Energy Levels question from JEE Main 2025 (2 Apr, Shift 1)

Q11JEE Main 2025 · 2 APR · SHIFT 1Medium

Energy of the Electron & Energy Levels

Considering Bohr's atomic model for hydrogen atom:

(A) the energy of H atom in ground state is same as energy of He+\text{He}^{+} ion in its first excited state. (B) the energy of H atom in ground state is same as that for Li++\text{Li}^{++} ion in its second excited state. (C) the energy of H atom in its ground state is same as that of He+\text{He}^{+} ion for its ground state. (D) the energy of He+\text{He}^{+} ion in its first excited state is same as that for Li++\text{Li}^{++} ion in its ground state. Choose the correct answer from the options given below:

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Answer: (a)

  1. E=−13.6 Z2n2E = -13.6\,\frac{Z^2}{n^2} eV; H ground state =−13.6= -13.6 eV.
  2. (A) He+^+, n=2n = 2: −13.6×44=−13.6-13.6 \times \frac{4}{4} = -13.6 eV. True.
  3. (B) Li++^{++}, second excited n=3n = 3: −13.6×99=−13.6-13.6 \times \frac{9}{9} = -13.6 eV. True.
  4. (C) He+^+ ground: −54.4-54.4 eV. False. (D) Li++^{++} ground: −122.4-122.4 eV ≠−13.6\ne -13.6 eV. False.
  5. So the answer is (a) (A), (B) only.
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