In physics and

chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...

, motional narrowing is a phenomenon where a certain

resonant frequency Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...

has a smaller

linewidth A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to iden ...

than might be expected, due to motion in an inhomogeneous system.''Solid state: nuclear methods''
by J. N. Mundy, section 6.2.1.1, page 441. The discovery of motional narrowing has been attributed to

Nicolaas Bloembergen Nicolaas Bloembergen (March 11, 1920 – September 5, 2017) was a Dutch-American physicist and Nobel laureate, recognized for his work in developing driving principles behind nonlinear optics for laser spectroscopy. During his career, he was a p ...

during his thesis work in the 1940s

Example: NMR spectroscopy

A common example is NMR. In this process, the

nuclear spin In atomic physics, the spin quantum number is a quantum number (designated ) which describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. The phrase was originally used to describe th ...

of an atom starts rotating, with the frequency of rotation proportional to the external magnetic field that the atom experiences. However, in an inhomogeneous medium, the magnetic field often varies from point to point (depending, for example, on the magnetic susceptibility of nearby atoms), so the frequency of nuclear spin rotation is different in different places. Therefore, when detecting the resonant rotation frequency, there is a

(i.e., finite range of different frequencies) due to the variation in that resonant frequency from point to point. (This is called "

inhomogeneous broadening Homogeneous broadening is a type of emission spectrum broadening in which all atoms radiating from a specific level under consideration radiate with equal opportunity. If an optical emitter (e.g. an atom) shows homogeneous broadening, its spectra ...

".) However, if the atoms are diffusing around the system, they will experience a higher magnetic field than average sometimes, and a lower magnetic field than average other times. Therefore, (in accordance with the central limit theorem), the ''time-averaged'' magnetic field experienced by an atom has less variation than the ''instantaneous'' magnetic field does. As a consequence, when detecting the resonant rotation frequency, the linewidth is smaller (narrower) than it would be if the atoms were stationary. This is the motional narrowing effect.

Example: Vibrational spectroscopy

A similar phenomenon occurs in many other systems. Another example is vibrational modes in a liquid. Each molecule of the liquid has vibrational modes, and the vibrational frequency is influenced by the positions of nearby molecules. However, if the nearby molecules reorient and move around fast enough, the vibration will essentially occur at an averaged frequency, and therefore have a smaller linewidth. For example, simulations suggest that the OH stretch vibration linewidth in liquid water is 30% smaller than it would be without this motional narrowing effect."The Effects of Dissolved Halide Anions on Hydrogen Bonding in Liquid Water", J. D. Smith et al.,

References

{{Reflist Nuclear magnetic resonance Spectroscopy

Example: NMR spectroscopy

Example: Vibrational spectroscopy

See also

References