Astronomy Principles and Practice Fourth Edition.pdf

236 The radiation laws
Figure 15.14. The classical Zeeman effect in an emission spectrum illustrating the positions of the observed lines
and the polarizational qualities of their light when the atoms are radiating in a magnetic field.
should be observed: one line should be at the normal position and be linearly polarized with a direction
of vibration parallel to the field; the other lines should be placed either side of the normal position
and both be linearly polarized with vibration perpendicular to the field. The splitting of the lines and
the polarization properties of their light were later verified by Zeeman. Figure 15.14 illustrates the
important features of the classical Zeeman effect.
According to Lorentz’s theory, the split lines should appear at distances from the position of the
line without the field given in terms of a frequency shift by
ν =±
eH
4πm e c
where H is the strength of the magnetic field. Thus, the degree of splitting depends on the strength of
the field. By remembering that ν = c/λ, it is easy to show that dν/dλ =−c/λ 2 and, therefore, that
λ =−λ 2 /c. Hence, in terms of the wavelength shift, the Zeeman splitting can be expressed as
and when H is expressed in tesla (T)
λ =± eHλ2
4πm e c 2
λ =±4·67 × 10 −17 λ 2 H (Å). (15.32)
The Zeeman effect may also be demonstrated in absorption lines and from measurements taken
from spectra it has been found possible to determine the magnitude of magnetic fields of the Sun and
some special stars. In practice, the splitting of spectral lines by magnetic fields is more complex than
that predicted by the Lorentz theory.
Problems—Chapter 15
1. The following is a table of stars together with their listed magnitudes. Commencing with the brightest star,
place them in order of decreasing brightness.
Star no Magnitude
1 +3·1
2 +2·6
3 −0·1
4 +1·1
5 −0·9
6 +3·3