......................................................................(10.3)
.............................................................................(10.4)
| The spring constant, k is the measure of the bond strength. The stronger the bond, the higher the k , and consequently the higher is the frequency of vibration. This treatment implies that the diatomic molecule is a simple harmonic oscillator. The energy of a quantum harmonic oscillator is given by: |  |
........................................................................(10.5)
where, n = 0, 1, 2, …… and h is the Plancks's constant
Absorption of infrared radiation
A molecular vibration is IR active i.e. it absorbs IR radiation if the vibration results in a change in the dipole moment. A diatomic molecule, that has one mode of vibration, may not absorb an IR radiation if the vibration does not accompany a change in the dipole moment. This is true for all the homonuclear diatomic molecules such as H2, N2, O2, etc. Vibration of carbon monoxide (C=O), on the other hand, causes a change in dipole moment and is therefore IR active. Vibration of a bond involving two atoms that have large electronegativity difference is usually IR active.
An IR active vibration of a particular frequency absorbs the IR radiation of same frequency.
Let us calculate the position of absorption band for carbonyl stretching vibration (frequency = 5.1 × 1013 vibrations/second) in acetone.
