The __ is inversely proportional to the wavelength and reported in reciprocal centimeters (cm−1).
The correct answer and explanation is:
The wavenumber is inversely proportional to the wavelength and reported in reciprocal centimeters (cm−1).
Explanation:
The term that fits the description is wavenumber. Wavenumber, often denoted by the symbol ν̃ (pronounced “nu tilde”), is defined as the reciprocal of the wavelength (λ). Mathematically, this is expressed as:
ν̃ = 1 / λ
This definition directly shows the inverse relationship: as the wavelength increases, the wavenumber decreases, and vice versa.
The unit reciprocal centimeters (cm⁻¹) arises naturally from this definition when the wavelength is measured in centimeters. If λ is in cm, then 1/λ is in cm⁻¹. Physically, wavenumber in cm⁻¹ represents the number of wavelengths that fit into one centimeter.
Wavenumber is closely related to frequency (ν), which is also inversely proportional to wavelength (via the speed of light, c: ν = c / λ). The relationship between wavenumber and frequency is ν = c * ν̃.
Wavenumber is a particularly useful concept in spectroscopy, such as infrared (IR) and Raman spectroscopy. One key advantage is that wavenumber is directly proportional to the energy (E) of a photon: E = hν = hcν̃, where h is Planck’s constant and c is the speed of light. Because of this linear relationship with energy, using wavenumber as the x-axis in a spectrum provides a scale that is directly representative of the energy transitions occurring within the sample, which makes interpreting spectroscopic data simpler than using wavelength alone. The cm⁻¹ unit is widely adopted in these fields because the wavelengths corresponding to molecular vibrations often result in convenient wavenumber values in the range of hundreds or thousands of cm⁻¹.