In atomic physics, Doppler broadening is broadening of spectral lines due to the Doppler effect caused by a distribution of velocities of atoms or molecules. Different velocities of the emitting (or absorbing) particles result in different Doppler shifts, the cumulative effect of which is the emission (absorption) line broadening. This resulting line profile is known as a Doppler profile.

A particular case is the thermal Doppler broadening due to the thermal motion of the particles. Then, the broadening depends only on the frequency of the spectral line, the mass of the emitting particles, and their temperature, and therefore can be used for inferring the temperature of an emitting (or absorbing) body being spectroscopically investigated.

When a particle moves (e.g., due to the thermal motion) towards the observer, the emitted radiation is shifted to a higher frequency. Likewise, when the emitter moves away, the frequency is lowered. In the non-relativistic limit, the Doppler shift is

where ${\displaystyle f}$ is the observed frequency, ${\displaystyle f_{0}}$ is the frequency in the rest frame, ${\displaystyle v}$ is the velocity of the emitter towards the observer, and ${\displaystyle c}$ is the speed of light.

Since there is a distribution of speeds both toward and away from the observer in any volume element of the radiating body, the net effect will be to broaden the observed line. If ${\displaystyle P_{v}(v)\,dv}$ is the fraction of particles with velocity component ${\displaystyle v}$ to ${\displaystyle v+dv}$ along a line of sight, then the corresponding distribution of the frequencies is

where ${\displaystyle v_{f}=c\left({\frac {f}{f_{0}}}-1\right)}$ is the velocity towards the observer corresponding to the shift of the rest frequency ${\displaystyle f_{0}}$ to ${\displaystyle f}$. Therefore,

${\displaystyle P_{f}(f)\,df={\frac {c}{f_{0}}}P_{v}\left[c\left({\frac {f}{f_{0}}}-1\right)\right]\,df.}$

We can also express the broadening in terms of the wavelength ${\displaystyle \lambda }$. Since ${\displaystyle v/c\ll 1}$, ${\displaystyle \left|f/f_{0}-1\right|\ll 1}$, and so ${\displaystyle {\frac {\lambda -\lambda _{0}}{\lambda _{0}}}\approx -{\frac {f-f_{0}}{f_{0}}}}$. Therefore,