The M.I. of a diatomic molecule is I. what is its rotational energy in the nth orbit , (where n `ne` 0) if Bohr's quantization condition is used ?

Options

A. `1/n((h^2)/(8pi^2I))`
B. `n^2((h^2)/(8pi^2I))`
C. `1/n^2 ((h^2)/(8pi^2I))`
D. `n((h^2)/(8piI))`

Answer

B

Explanation

As per Bohr' quantum condition ,
`I omega = (nh)/( 2pi) " " …(1)`
The relational K.E. `=1/2 I oemga^2 = 1/2 (I^2omega^2)/(I)`
`=1/2 ((I omega)^2)/(I)`
`=1/2 . (n^2h^2)/(4pi^2I) " "` From (1)
`=n^2 ((h^2)/(8pi^2I))`