## Vibrational levels of a diatomic molecule in terms of force constant and masses of atoms

Let us consider a diatomic molecule in which atoms having masses m_{1}and m

_{2}oscillate against each other like a harmonic oscillator.

Let r

_{e}be the equilibrium distance between two atoms and becomes r when stretched. Atoms shift by −x

_{1}to x

_{2}in two opposite directions so that the displacement-

x = r − r

_{e}= −x

_{1}+ x

_{2}= x

_{2}− x

_{1}

The restoring force on each atom is proportional to displacement, x.

Restoring force constant = −k.x

where k is force constant.

If x

_{1}and x

_{2}be the distances of the center of the molecule from the centers of A and B atoms respectively. Then-

Therefore, the vibrational frequency (๐) of a diatomic molecule is related to the force constant (k) and reduced mass (ยต).