In infrared (IR) spectroscopy, the wave number is a unit of measurement commonly used to describe the frequency of molecular vibrations. The wave number (ν) is defined as the reciprocal of the wavelength (λ) of light, expressed in units of reciprocal centimeters (cm^-1). Mathematically, it is given by:
ν = 1/λ
The wave number is proportional to the frequency (ν̃) of the molecular vibrations. The relationship between the wave number and the frequency is given by:
ν̃ = cν
Where c is the speed of light. This equation relates the frequency of a molecular vibration to its corresponding wave number.
In IR spectroscopy, molecules absorb infrared light at specific frequencies that correspond to their vibrational energy levels. The absorption frequencies are typically reported in wave numbers (cm^-1) on an IR spectrum.
The fundamental frequency of a molecular vibration refers to the lowest energy vibration that a molecule can undergo. It corresponds to the most intense absorption peak in the IR spectrum, often referred to as the "fundamental band."
The wave number of the fundamental vibration is directly related to the energy of the vibration. Higher wave numbers indicate higher energy vibrations. Different functional groups and molecular bonds have characteristic wave numbers associated with their vibrations, which allows chemists to identify and analyze the molecular structure of a compound using IR spectroscopy.
Therefore, in IR spectroscopy, the wave number is a useful measure to describe the fundamental frequency of molecular vibrations and provides information about the molecular composition and structure of a substance.