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. `((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

Energy `=L^(2)/(2 I)=((nh)^(2))/(2(mur^(2)))`
where `mu=` reduced mass `=(m_(1)m_(2))/(m_(1)+m_(2))`
so energy `=(n^(2)h^(2)(m_(1)+m_(2)))/(2m_(1)m_(2)r^(2))`