Question

Given below are two statements:
Statement (I): The dimensions of Planck's constant and angular momentum are same.
Statement (II): In Bohr's model, electrons revolve around the nucleus only in those orbits for which angular momentum is an integral multiple of Planck's constant.
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. Statement I is incorrect but Statement II is correct
• C. Statement I is correct but Statement II is incorrect
• D. Both Statement I and Statement II are incorrect

Hint:

Always remember Bohr’s quantization rule: \[ mvr = n\frac{h}{2\pi} \] Angular momentum is quantized in units of \( \frac{h}{2\pi} \), not \(h\).

Answer 1

The Correct Option is C

Concept:

Planck’s constant has the dimensions of action.
Angular momentum also has the dimensions of action.
In Bohr’s atomic model, angular momentum is quantized.
Step 1: Verification of Statement (I). Dimensions of Planck’s constant: \[ [h] = \text{energy} \times \text{time} = ML^2T^{-1} \] Dimensions of angular momentum: \[ [L] = mvr = ML^2T^{-1} \] Since both have identical dimensions, Statement (I) is correct.
Step 2: Verification of Statement (II). According to Bohr’s quantization condition: \[ L = mvr = n\frac{h}{2\pi} \] Thus, angular momentum is an integral multiple of \( \frac{h}{2\pi} \), not \(h\). Hence, Statement (II) is incorrect.
Step 3: Final conclusion. \[ \text{Statement (I) is correct and Statement (II) is incorrect.} \]