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 :

Statement I is correct but Statement II is incorrect

Both Statement I and Statement II are correct

Both Statement I and Statement II are incorrect

Statement I is incorrect but Statement II is correct

Atoms and Nuclei PYQ — JEE Main 2025 · 4 Apr · Shift 2 · Q70 with Solution

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Correct answer: B

Planck's constant $h$ has dimensions of action.

From $E = h\nu$ we get $[h] = \frac{[E]}{[\nu]} = \frac{ML^2T^{-2}}{T^{-1}} = ML^2T^{-1}$

Now dimensions of angular momentum are: $L = mvr$ So, $[L] = M \cdot LT^{-1} \cdot L = ML^2T^{-1}$

Hence, dimensions of Planck's constant and angular momentum are the same.

So, Statement (I) is correct.

In Bohr's model, allowed orbits satisfy: $mvr = n\frac{h}{2\pi} = n\hbar$ where $n = 1,2,3,\dots$

Thus angular momentum is an integral multiple of $\dfrac{h}{2\pi}$ , not an integral multiple of $h$ .

So, Statement (II) is incorrect.

Therefore, the correct option is: $\boxed{\text{B}}$

Stored correct answer: B

My derived answer: B

They match.