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Rotational spectroscopy
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===Units=== The units used for rotational constants depend on the type of measurement. With infrared spectra in the [[wavenumber]] scale (<math>\tilde \nu</math>), the unit is usually the [[inverse centimeter]], written as cm<sup>β1</sup>, which is literally the number of waves in one centimeter, or the reciprocal of the wavelength in centimeters (<math>\tilde\nu = 1 / \lambda</math>). On the other hand, for microwave spectra in the frequency scale (<math>\nu</math>), the unit is usually the [[gigahertz]]. The relationship between these two units is derived from the expression :<math> \nu \cdot \lambda = c,</math> where Ξ½ is a [[frequency]], Ξ» is a [[wavelength]] and ''c'' is the [[velocity of light]]. It follows that :<math> \tilde \nu / \text{cm}^{-1} = \frac{1}{\lambda / \text{cm}} = \frac{\nu / \text{s}^{-1}}{c / \left(\text{cm} \cdot \mathrm{s}^{-1}\right)} = \frac{\nu / \text{s}^{-1}}{2.99792458 \times 10^{10}}. </math> As 1 GHz = 10<sup>9</sup> Hz, the numerical conversion can be expressed as :<math>\tilde\nu / \text{cm}^{-1} \approx \frac{\nu / \text{GHz}}{30}.</math>
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