Basic spectrometry: Thermal line broadening

If atoms are contained in a hot gas cloud and are giving rise to emission lines in their spectra, then the profiles are likely to be broadened by thermal Doppler effects.
As a result of the local temperature, the atoms acquire a distribution of kinetic energies referred to as the Maxwell distribution. Within such a radiating cloud some atoms will be receding and others will be approaching the observer such that at the times of the emissions, individual contributions may be red or blue shifted as a result of the Doppler effect. The overall shape of the emission line is, therefore, broadened into a ‘bell-shaped’ profile with the halfwidth dependent on the temperature. A typical kinetic energy of an atom may be obtained by taking the most probable value of the Maxwell distribution this being

where k is Boltzmann’s constant. Hence,

If, for example, a cloud of hydrogen is considered to be at a temperature of 10 000 K, a typical value for the velocity is

giving a value for v ∼ 1 × 10⁴ m s⁻¹. The Doppler shift associated with such a velocity is readily detectable. It is obvious that thermal Doppler broadeningwould be less apparent for the heavier atomic species.