Thermal Doppler broadening gives spectral lines what standard line-shape profile?

Thermal Doppler broadening gives spectral lines a Gaussian profile. The shape arises because atoms or molecules in a hot gas have a Maxwellian distribution of velocities along the observer’s line of sight.

Atoms moving toward the observer emit light shifted slightly toward higher frequencies, while atoms moving away emit light shifted lower. Adding the contributions from all those differently moving particles spreads an originally narrow spectral line into a symmetric bell-shaped curve.

The width contains physical information. At fixed temperature, lighter particles move faster and produce broader Doppler lines; at fixed particle mass, hotter gas produces broader lines. In the nonrelativistic approximation, the frequency standard deviation scales as the rest frequency times √(kT/mc²).

Gaussian is the answer for purely thermal Doppler broadening, but real spectra often combine several mechanisms. Natural or pressure broadening has Lorentzian characteristics, and the convolution of Gaussian Doppler broadening with Lorentzian pressure broadening produces a Voigt profile.