Y n T T

It can be shown that the corresponding line profile is

2n (v - vo)2 + y2/4 ' where v0 is the frequency at the centre of the line and I0 the total intensity of the line. At the centre of the line the intensity per frequency unit is 2

Thus the width Y is the width of the line profile at a depth where the intensity is half of the maximum. This is called the full width at half maximum (FWHM).

Doppler Broadening. Atoms of a gas are moving the faster the higher the temperature of the gas. Thus spectral lines arising from individual atoms are shifted by the Doppler effect. The observed line consists of a collection of lines with different Doppler shifts, and the shape of the line depends on the number of atoms with different velocities.

Each Doppler shifted line has its characteristic natural width. The resulting line profile is obtained by giving each Doppler shifted line a weight proportional to the number of atoms given by the velocity distribution and integrating over all velocities. This gives rise to the Voigt profile (Fig. 5.5), which already describes most spectral lines quite well. The shapes of different profiles don't

Doppler Line Profile

Fig. 5.5. Each spectral line has its characteristic natural width (solid line). Motions of particles broaden the line further due to the Doppler effect, resulting in the Voigt profile (dashed line). Both profiles have the same area

Fig. 5.5. Each spectral line has its characteristic natural width (solid line). Motions of particles broaden the line further due to the Doppler effect, resulting in the Voigt profile (dashed line). Both profiles have the same area

Equivalent Width
the maximum. The equivalent width W is defined so that the line and the shaded rectangle have the same area in the pic-tare. The two measures are not generally the same, although they usually are close to each other

seem very different; the most obvious consequence of the broadening is that the maximum depth decreases.

One way to describe the width of a line is to give its full width at half maximum (Fig. 5.6). Due to Doppler broadening this is usually greater than the natural width. The equivalent width is another measure of a line strength. It is the area of a rectangular line that has the same area as the line profile and that emits no light at all. The equivalent width can be used to describe the energy corresponding to a line independently of the shape of the line profile.

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