Using Bohr's quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule? ( I= moment of inertia of diatomic molecule and h= Planck's constant)

Step-by-step solution

Rotational energy quantization for a diatomic molecule The angular momentum L is quantized by Bohr's condition: L = J h 2 , where J is the rotational quantum number. For the second orbit, J = 2 , yielding L = 2 h 2 = h . Rotational energy E_R relates to angular momentum through E_R = 1 2 I ^2 with L = I , giving = L I . Substitution results in E_R = 1 2 I ( L I )^2 = L^2 2I . Inserting the quantized L value, E_R = ( h )^2 2I = h^2 2I ^2 . This matches option B: h^2 2I ^2 . The correct answer is B .