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, its energy will be given by (n is an integer)

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))`