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

Options

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

Answer

A

Explanation

`m_(1)r_(1)=m_(2)r_(2)andr_(1)+r_(2)=r`
`because r_(1)=(m_(2)r)/(m_(1)+m_(2))" "...(1)`
and `r_(2)=(m_(1)r)/(m_(1)+m_(2))" "...(2)`

`E=(1)/(2)Iomega^(2)=(1)/(2)(m_(1)r_(1)^(2)+m_(2)r_(2)^(2))omega^(2)" "...(3)`
`because mvr=(nh)/(2pi)=omegaIimpliesomega=(nh)/(2piI)" "...(4)`
(put equations (1), (2) and (4) in (3))
we get
`E=((m_(1)+m_(2))n^(2)h^(2))/(2m_(1)m_(2)r^(2))`