Vibrational Frequency of a Diatomic Molecule

Vibrational Frequency of a Diatomic Molecule

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 m1 and m2 oscillate against each other like a harmonic oscillator.
Vibrational Frequency  Diatomic Molecule
Let re be the equilibrium distance between two atoms and becomes r when stretched. Atoms shift by −x1 to x2 in two opposite directions so that the displacement-
x = r − re = −x1 + x2 = x2 − x1
The restoring force on each atom is proportional to displacement, x.
Restoring force constant = −k.x
where k is force constant.
If x1 and x2 be the distances of the center of the molecule from the centers of A and B atoms respectively. Then-
Vibrational Frequency  Diatomic Molecule
Therefore, the vibrational frequency (๐œˆ) of a diatomic molecule is related to the force constant (k) and reduced mass (ยต).

The fundamental vibrational frequency of HCl is 2890 cm−1. Calculate its force constant.

We know that-
fundamental vibrational frequency of HCl is 2890 cm-1. Calculate its force constant