Cm⁻¹

Definition

cm⁻¹ is a unit of wavenumber, which is the reciprocal of the wavelength of electromagnetic radiation. It is commonly used to express the frequency of infrared and Raman spectroscopy, providing information about the vibrational modes of molecules.

5 Must Know Facts For Your Next Test

1. The wavenumber is directly proportional to the frequency of the electromagnetic radiation and inversely proportional to the wavelength.
2. In infrared spectroscopy, the wavenumber range typically used is 4000 cm⁻¹ to 400 cm⁻¹, covering the mid-infrared region.
3. Characteristic absorption bands for various functional groups, such as C-H, C=O, and N-H, can be observed in the infrared spectrum and are reported in cm⁻¹.
4. The position of the absorption bands in the infrared spectrum, measured in cm⁻¹, can be used to identify the presence and type of functional groups in a molecule.
5. Raman spectroscopy also utilizes the concept of wavenumber, as the shift in the frequency of the scattered light (Raman shift) is reported in cm⁻¹.

Review Questions

• Explain the relationship between wavenumber, wavelength, and frequency in the context of infrared and Raman spectroscopy.
  • The wavenumber, $\text{cm}^{-1}$, is the reciprocal of the wavelength, $\lambda$, of the electromagnetic radiation used in infrared and Raman spectroscopy. The relationship can be expressed as $\text{wavenumber} = 1/\lambda$. This means that as the wavelength decreases, the wavenumber increases, and vice versa. The frequency, $\nu$, of the radiation is also related to the wavenumber through the equation $\nu = c \text{wavenumber}$, where $c$ is the speed of light. Therefore, the wavenumber provides a direct measure of the frequency of the vibrational modes observed in these spectroscopic techniques.
• Describe how the wavenumber, measured in $\text{cm}^{-1}$, is used to identify functional groups in infrared spectroscopy.
  • In infrared spectroscopy, the position of the absorption bands in the spectrum, reported in $\text{cm}^{-1}$, is characteristic of the vibrational modes of specific functional groups within a molecule. For example, the C-H stretch typically appears around 2900-3000 $\text{cm}^{-1}$, the C=O stretch is observed around 1700 $\text{cm}^{-1}$, and the N-H bend is seen around 1600 $\text{cm}^{-1}$. By analyzing the wavenumber positions of the absorption bands in the infrared spectrum, researchers can identify the presence and type of functional groups in an unknown sample, providing valuable information about the molecular structure.
• Discuss the importance of the wavenumber range used in infrared and Raman spectroscopy, and explain how it relates to the information obtained about the molecular structure.
  • The wavenumber range used in infrared and Raman spectroscopy is crucial for the identification of functional groups and the elucidation of molecular structure. The mid-infrared region, typically from 4000 $\text{cm}^{-1}$ to 400 $\text{cm}^{-1}$, is particularly important as it contains the characteristic absorption bands for many common functional groups. By analyzing the positions and intensities of these bands, reported in $\text{cm}^{-1}$, researchers can determine the presence, type, and relative abundance of various functional groups within a molecule. This information is then used to infer the overall molecular structure and connectivity, which is essential for the identification and characterization of unknown compounds in organic chemistry.

Related terms

Wavenumber: The number of waves per unit distance, measured in inverse length units such as cm⁻¹.

Infrared Spectroscopy: A technique that measures the absorption of infrared radiation by a sample, providing information about the molecular structure and functional groups present.

Raman Spectroscopy: A technique that measures the inelastic scattering of light by a sample, also providing information about the molecular structure and vibrational modes.