Wavenumbertowavelength converter


Wavelength calculator

The calculator can be used to get an idea where absorption bands occur in the infrared spectrum and it demonstrates the effect of atom mass and bond force constant on the band position. However, the exact position of an infrared absorption band depends on a variety of
parameters, like intramolecular and intermolecular chemical effects.
The frequency of molecular vibrations is calculated from the equations given below by substituting the masses of two atoms for
m_{1} and m_{2}; the quantity k becomes the force constant for the chemical bond, which is a measure of its
stiffness (but not necessarily its strength!). Generally, k has been found to lie in the range
3*10^{5} to 8*10^{5} dynes/cm for most single bonds, with
5*10^{5} serving as a reasonable average value (used in calculations). Double and triple bonds have
kvalues of about 2 and 3 times the value for a
single bond, respectively (double bond, 1*10^{6} dynes/cm; triple bond,
1.5*10^{6} dynes/cm). With these values, the equation can be used to estimate the wavenumber of fundamental absorption peak (due to the transition from ground to first excited state) for a variety of bond types.


and 

where: sigma, wavenumber (cm^{1}); c, speed of light (cm/s);
k, bond force constant (dynes/cm); µ, reduced mass; m_{1}, mass for atom
1 (g/atom); m_{2}, mass for atom 2 (g/atom). 

Note that this formula only holds for a harmonic oscillator and is a simple theoretical approximation. From qualitative considerations, however, it is apparent that this description of a molecular vibration is imperfect. In fact a more
quantum mechanically treatment is necessary for anharmonic oscillators. Furthermore, vibrational spectra are complicated by the fact that two different vibrations in a molecule can interact to give absorption peaks with frequencies that are approximately the sums or differences of their fundamental frequencies.
For another detailed
description, including an example of HCl, please click here.

