MHT CET202521 Apr 2025Evening ShiftPhysicsAtomic PhysicsActual
Using Bohr's quantization condition, the rotational kinetic energy in the third orbit for a diatomic molecule is ( h= Planck's constant, I= moment of inertia of diatomic molecule)
Options
- A9 h^2 8 ^2 I
- B3 ~h ^2 8 ^2 I
- C6 ~h ^2 8 I
- D12 h^2 7 ^2 I
Correct answer
A. 9 h^2 8 ^2 I
Step-by-step solution
Rotational kinetic energy in the third orbit follows from Bohr's quantization of angular momentum: L = n h 2 , where n = 3 for the third orbit, giving L₃ = 3h 2 . Substituting into the rotational kinetic energy formula KE_ rot = L^2 2I yields: KE_ rot = ( 3h 2 )^2 2I = 9h^2 4 ^2 2I = 9h^2 8 ^2 I . This corresponds to option A .