A diatomic molecule is made of two masses `m_(1) and m_(2)` which are separated by a distance `r` . If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization it energy will be ( n is an integer )

Options

A. `((m_(1)+m_(2))^(2)n^(2)h^(2))/(2m_(1)^(2)m_(2)^(2)r^(2))`
B. `(2n^(2)h^(2))/((m_(1)+m_(2))r^(2))`
C. `(n^(2)h^(2))/(2(m_(1)+m_(2))r^(2))`
D. `((m_(1)+m_(2))n^(2)h^(2))/(2m_(1)m_(2)r^(2))`

Answer

D

Explanation

Moment of inertia `I=(m_(1)+m_(2))/(m_(1)+m_(2)) r^(2)`
`L=I omega =(nh)/(2pi)`
Rotational K.E.`=(L^(2))/(2I)=(n^(2)(h^(2)//4pi^(2)))/(2((m_(1)m_(2))/(m_(1)+m_(2))))r^(2)`
`=(n^(2)h^(2)(m_(1)+m_(2)))/(2m_(1)m_(2)r^(2)),(h=(h)/(2pi))`