Derive an expression for the Doppler intensity profile (thermal broadening) of a spectral line emitted near the central frequency ν₀, assuming that the emitting atoms have a Maxwellian velocity distribution. Ignore all other factors that contribute to the shape of the line.

(1) The change in frequency due to the Doppler effect associated with the relative (nonrelativistic) motion of the emitting atoms, with respect to the direction of observation (e.g., x direction), is given by

where in this expression c denotes the speed of light in vacuum. 

(2) The observed intensity in the frequency range between ν and ν + dν, that is, I(ν) dν, is proportional to the number of emitting atoms per unit volume, which have velocities along the direction of observation (x direction) between v_x and v_x + dv_x.

Transcribed Image Text:

V-VO-Vo Vx C