dopplerbreddningen

Dopplerbreddningen, also known as Doppler broadening, is a phenomenon in spectroscopy where the spectral lines of a given transition are broadened due to the Doppler effect. This effect arises from the thermal motion of atoms or molecules, causing a distribution of velocities within a sample. As a result, the emitted or absorbed light is shifted in frequency according to the velocity of the emitting or absorbing particle. This leads to a broadening of the spectral lines, with the width of the line being proportional to the square root of the temperature of the sample.

Doppler broadening is particularly significant in astrophysics, where it is used to determine the radial velocities of stars and galaxies. It is also important in the study of plasmas, where the high temperatures can cause significant Doppler broadening. In laboratory settings, Doppler broadening can be used to study the thermal motion of atoms and molecules, providing insights into their kinetic properties.

The Doppler broadening formula is given by the equation:

Δλ = λ0 (v/c)

where Δλ is the broadening of the spectral line, λ0 is the wavelength of the transition in the rest frame, v is the velocity of the particle, and c is the speed of light. The full width at half maximum (FWHM) of the Doppler-broadened line is given by:

FWHM = 2 λ0 sqrt(2 ln(2) kT / m c^2)

where k is the Boltzmann constant, T is the temperature, and m is the mass of the particle. This formula shows that the broadening is proportional to the square root of the temperature, as mentioned earlier.