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, electron revolves around the nucleus 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:

Planck’s constant \( h \) and angular momentum \( L \) have the same dimensional formula. Also, in Bohr’s model, angular momentum is quantized in integer multiples of \( h/2\pi \).

Answer 1

The Correct Option is C

1. Statement I: The dimensions of Planck’s constant and angular momentum are the same. Planck’s constant \( h \) has the dimension of \( [ML^2 T^{-1}] \), where: 
- \( M \) is mass, 
- \( L \) is length, 
- \( T \) is time. 
Angular momentum \( L \) also has the dimension of \( [ML^2 T^{-1}] \), since it is given by the product of mass, length, and velocity. 
Hence, Statement I is correct. 
2. Statement II: In Bohr’s model, electron revolves around the nucleus in those orbits for which angular momentum is an integral multiple of Planck’s constant. According to Bohr’s model, the angular momentum \( L \) of an electron is quantized and is an integral multiple of Planck’s constant \( h \), i.e. \[ L = \frac{nh}{2\pi} \] where \( n \) is a positive integer. 
Hence, Statement II is also correct. 
Since both statements are correct, the correct answer is (3).