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 :

Solution

Physics sir · 4 steps

Statement II forgets the 2π: Bohr quantised L in steps of h/2π, not in steps of h.

1. Check Statement I. From E = hν, h = E/ν has units J s = kg m² s⁻¹, that is [ML²T⁻¹]. Angular momentum L = mvr has units kg × m s⁻¹ × m, which is also [ML²T⁻¹]. So Statement I is correct.
2. Bohr's actual condition. Bohr's postulate says an electron can stay only in orbits where its angular momentum is a whole-number multiple of h/2π.

   mvr = nh/2π, n = 1, 2, 3, …

3. Check Statement II. Statement II says integral multiple of h. That would make the smallest allowed angular momentum h instead of h/2π, which is 2π times too large. So Statement II is incorrect.
4. So. Statement I is correct and Statement II is incorrect, which is option (b).

The idea to keep. In Bohr's model, L comes in steps of h/2π, never h. When a statement quotes a quantisation rule, check every factor of 2π.

Answer from the NTA final answer key. Solution by PrepWiser.