Chemistry - Why is wavenumber used in IR spectroscopy rather than wavelength?

Solution 1:

Not only in IR spectroscopy. Wavenumber is unit of energy and therefore you can directly deduce the difference of energy between states.

In addition, humans like to think in acceptably small numbers (0.01 - 10,000). Wavenumber allows this for IR and conveniently supplements the eV unit in small energy separations range. Admittedly, the conversion factor of 8,065.73 won't win beauty contest.

Solution 2:

The choice to use wavenumbers for infrared spectroscopy (rather than wavelengths, frequencies, or energies) was probably done to provide a range that has both the appearance of width (so that the difference between two peaks is more meaningful) and spans a set of reasonable values that do not contain very large or very small numbers (which are hard to conceptualize). The goal is to be able to easily compare values.

See the following comparison of units/values for the typical range of IR spectroscopy for organic compounds and some "example" values for the absorptions of common bond types:

absorption     cm⁻¹   m        µm     Hz        THz   J          kJ/mol     meV
high end       500    2.00E-5   20     1.5E+13   15    9.94E-21   5.98       62
C-O            1100   9.09E-6   9.09   3.3E+13   33    2.19E-20   13.2       136
C=C            1660   6.02E-6   6.02   5.0E+13   50    3.30E-20   19.9       206
C=O            1720   5.81E-6   5.81   5.2E+13   52    3.42E-20   20.6       213
C-H            3000   3.33E-6   3.33   9.0E+13   90    5.96E-20   35.9       372
O-H            3500   2.86E-6   2.86   1.05E+14  105   6.96E-20   41.9       434
low end        4000   2.50E-6   2.50   1.20E+14  120   7.95E-20   47.9       496

Let's compare especially the peaks for $\ce{C=C}$ and $\ce{C=O}$. These peaks are easily resolvable by all modern FTIR spectrometers, and there is room for peaks to be resolved between them. Only the values in wavenumbers give this sense of resolution intuitively. Modern spectrometers can resolve data to $1.0\ \text{cm}^{-1}$ or better. A resolution of $1.0\ \text{cm}^{-1}$ is equivalent to resolutions of $0.040\ \mu\text{m}$, $0.030\text{ THz}$, $12\text{ kJ/mol}$, and $0.12\text{ meV}$. Which of these resolutions is most intuitive to understand?