Table of Contents
What Is Wavenumber?
Wavenumber is the number of wave cycles per unit distance, essentially the reciprocal of wavelength. It is the spatial analogue of temporal frequency. In spectroscopy, it is measured in cm&supmin;¹ (reciprocal centimeters, also called kayser). The wavenumber is directly proportional to the energy of the photon, making it particularly useful for analyzing molecular vibrations and electronic transitions.
Infrared spectroscopy typically uses the range 400-4000 cm&supmin;¹, which covers the fundamental vibrational modes of most organic molecules. Each functional group has characteristic absorption wavenumbers, making IR spectroscopy a powerful tool for identifying chemical bonds.
Formula
Where ν̅ is wavenumber and λ is wavelength in the same length unit. For cm&supmin;¹: ν̅ = 10&sup7; / λ(nm). The energy relation is E = hcν̅, making wavenumber proportional to photon energy.
IR Spectroscopy Reference
| Bond | Wavenumber (cm&supmin;¹) | Wavelength (μm) |
|---|---|---|
| O-H stretch | 3200-3600 | 2.78-3.13 |
| N-H stretch | 3300-3500 | 2.86-3.03 |
| C-H stretch | 2850-3000 | 3.33-3.51 |
| C=O stretch | 1650-1750 | 5.71-6.06 |
| C=C stretch | 1600-1680 | 5.95-6.25 |
Frequently Asked Questions
Why use wavenumber instead of wavelength?
Wavenumber is directly proportional to energy (E = hcν̅), making it intuitive for comparing energy differences between spectral features. Wavelength is inversely proportional to energy, which makes mental arithmetic and spectral comparison harder.
How do I convert cm&supmin;¹ to eV?
Multiply by 1.24 × 10&supmin;&sup4;. For example, 1000 cm&supmin;¹ = 0.124 eV. This is useful for comparing infrared absorption with electronic transition energies.
What wavenumber range is the fingerprint region?
The fingerprint region is 600-1500 cm&supmin;¹. Absorption patterns in this region are unique to each molecule and are used like a fingerprint for identification purposes in analytical chemistry.