Dia-atomic molecule is composed of masses `m_(1)` and `m_(2)` and distance between them is r. By using the principle of quantisation of angular momentem of Bohr its energy of rotation is given by the formula ....... [Where n is integer and `h=(h)/(2pi)` ]

Options

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

Answer

C

Explanation

Reduced mass of this system `m=(m_(1)m_(2))/((m_(1)+m_(2)))`
`:.` Moment of inertia
`I=mr^(2)`
`=(m_(1)m_(2))/((m+m_(2)))r^(2)" ".......(1)`
`:.` Angular momentum in `n^(th)` orbit in Bohr model `L=(nh)/(2pi)=nh" "......(2)`
`:.` Rotational energy `E=(L^(2))/(2I)`
`:.E(n^(2)h^(2)(m_(1)+m_(2)))/(2m_(1)m_(2)r^(2))`