Physics Q41 – JEE-MAIN 2025

Given below are two statements : Statement (I) : The dimensions of Planck's constant and angular momentum are same. Statement (II) : In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant. In the light of the above statements, choose the most appropriate answer from the options given below :

Clue 1 of 3: Fundamental Constants and Quantization

Recall the definitions and significance of Planck's constant and angular momentum, and the postulates of Bohr's atomic model.

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Ninja Strategy•Direct Recall and Dimensional Analysis

Recall Bohr's quantization rule and perform a quick dimensional analysis for Planck's constant and angular momentum.

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Step 1: Analyze Statement I (Dimensional Analysis)✦ Active

The dimensions of Planck's constant ( $h$ ) can be derived from the energy-frequency relation $E = h ν$ . Thus, $h = E / ν$ . The dimensions of energy are $[M L^{2} T^{- 2}]$ and frequency are $[T^{- 1}]$ . Therefore, the dimensions of $h$ are $[M L^{2} T^{- 1}]$ . The dimensions of angular momentum ( $L$ ) can be derived from $L = m v r$ . The dimensions of mass are $[M]$ , velocity are $[L T^{- 1}]$ , and radius are $[L]$ . Therefore, the dimensions of $L$ are $[M] [L T^{- 1}] [L] = [M L^{2} T^{- 1}]$ . Since the dimensions are the same, Statement I is correct.

Step 2: Analyze Statement II (Bohr's Quantization Condition)○ Expand

According to Bohr's second postulate, the angular momentum of an electron in a stationary orbit is quantized. It must be an integral multiple of $\frac{h}{2 π}$ , not just $h$ . The correct condition is $L = n \frac{h}{2 π}$ , where $n$ is an integer ( $n = 1, 2, 3, . . .$ ). Therefore, Statement II, which claims angular momentum is an integral multiple of Planck's constant ( $n h$ ), is incorrect.

Step 3: Conclude based on both statements○ Expand

Statement I is correct, and Statement II is incorrect. This matches option 3.

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Physics Question 41 – JEE-MAIN 2025

Clue 1 of 3: Fundamental Constants and Quantization

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