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MCQEasyJEE 2023Bohr Model & Hydrogen Spectrum

JEE Chemistry 2023 Question with Solution

Given below are two statements:

Statement I: According to Bohr’s model of hydrogen atom, the angular momentum of an electron in a given stationary state is quantised.

Statement II: The concept of electron in Bohr’s orbit violates the Heisenberg uncertainty principle.

In the light of the above statements, choose the most appropriate answer from the options given below:

  • A

    Both Statement I and Statement II are correct

  • B

    Both Statement I and Statement II are incorrect

  • C

    Statement I is correct but Statement II is incorrect

  • D

    Statement I is incorrect but Statement II is correct

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: Two statements about Bohr’s model of hydrogen atom and the Heisenberg uncertainty principle.

Find: Which option correctly identifies the truth of Statement I and Statement II.

Step 1: Analysis of Statement I.

According to Bohr’s atomic model, the angular momentum of an electron revolving in a stationary orbit is quantised and is given by the relation:

mvr=nh2πmvr = \frac{nh}{2\pi}

where n=1,2,3,…n = 1, 2, 3, \ldots

Hence, Statement I is correct.

Step 2: Analysis of Statement II.

Bohr’s model assumes that the electron moves in a fixed circular orbit with a definite position and momentum at the same time. This assumption directly contradicts the Heisenberg uncertainty principle, which states that position and momentum cannot be simultaneously determined with certainty.

Therefore, Statement II is also correct.

Step 3: Conclusion.

Since both Statement I and Statement II are correct, the most appropriate answer is Option A.

Quick Tip: Bohr’s model successfully explained atomic spectra but failed to satisfy quantum mechanical principles like the Heisenberg uncertainty principle.

Common mistakes

  • Assuming Statement II is false because Bohr’s model gives correct spectral results. A model can explain some observations and still conflict with a deeper principle. Check conceptual consistency separately from experimental success.

  • Confusing quantisation of angular momentum with classical circular motion. In Bohr’s model, the allowed orbits are selected by the quantisation condition mvr=nh2πmvr = \frac{nh}{2\pi}, so Statement I is not a classical claim.

  • Thinking that a fixed orbit with known radius does not imply knowledge of position and momentum together. A definite circular orbit assigns both trajectory and motion too sharply, which is why it conflicts with the Heisenberg uncertainty principle.

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