The Sodium Doublet

The well known bright doublet which is responsible for the
bright yellow light from a sodium lamp may be used to demonstrate
several of the influences which cause splitting of the emission
lines of atomic spectra. The transition which gives rise to the
doublet is from the 3p to the 3s level, levels which would be the
same in the hydrogen atom. The fact that the 3s (orbital
quantum number = 0) is lower than the 3p (l=1) is a good example
of the dependence
of atomic energy levels on angular momentum. The 3s electron
penetrates the 1s shell more and is less effectively shielded than
the 3p electron, so the 3s level is lower (more tightly bound). The
fact that there is a doublet shows the smaller dependence of the
atomic energy levels on the total
angular momentum . The 3p level is split into states with total
angular momentum j=3/2 and j=1/2 by the magnetic energy of the
electron spin in the presence of the internal magnetic field caused
by the orbital motion. This effect is called the spin-orbit
effect. In the presence of an additional externally applied
magnetic field, these levels are further split by the magnetic
interaction, showing dependence of the energies on the z-component
of the total angular momentum. This splitting gives the Zeeman
effect for sodium.

The magnitude of the spin-orbit interaction has the form mzB = mBSzLz. In the case of
the sodium doublet, the difference in energy for the 3p3/2 and
3p1/2 comes from a change of 1 unit in the spin orientation
with the orbital part presumed to be the same. The change in energy is of
the form

DE = mBgB
= 0.0021 eV

where mB is the Bohr
magneton and g is the electron
spin g-factor with value very close to 2. This gives an estimate of
the internal magnetic field needed to produce the observed splitting:

mBgB = (5.79 x 10-5
eV/T)2B = 0.0021 eV

B = 18 Tesla

This is a very large magnetic field by laboratory standards. Large
magnets with dimensions over a meter, used for NMR and ESR experiments,
have magnetic fields on the order of a Tesla.

More
on sodium spectrum

Sodium
Zeeman effect

Index

Other
spectra

References
Thornton
& Rex
Sec 9.2

Serway,
Moses, Moyer
Sec 8.3

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The Sodium Zeeman Effect

The sodium spectrum is dominated by the bright doublet
known as the Sodium D-lines at 588.9950 and 589.5924 nanometers. From the
energy
level diagram it can be seen that these lines are emitted in a
transition from the 3p to the 3s levels.

The sodium doublet is further spit by the application of an
external magnetic field (
Zeeman effect). Using the vector
model for total
angular momentum, the splitting is seen to produce one level for
each possible value of the z-component of the total angular momentum
J.

The size of the magnetic energy contribution depends upon a geometrical
factor called the Lande'
g-factor. The values for the relevant quantum numbers and the
associated values for the Lande' g-factor are shown in the table below.

Term

J

L

S

gL

3p3/2

3/2

1

1/2

4/3

3p1/2

1/2

1

1/2

2/3

3s1/2

1/2

0

1/2

2

Examination of the size of the Lande g-factor gL for
the three levels will show why the splittings of the different
levels are different in magnitude. The selection
rules explain why the transitions shown are allowed and others
not.

Some
history

Index

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Sodium Zeeman Effect: Early Observations

The splitting of the sodium
doublet in the presence of an external magnetic field was observed by
Pieter Zeeman in 1896, and the effect was subsequently named the Zeeman
effect. It is remarkable that so much detailed spectroscopy was done long
before the Bohr theory, and perhaps even more remarkable that Zeeman's
first study of the sodium
Zeeman splitting was done the year before J. J.Thomson's discovery of
the electron in 1897.

After Thomson's work, Zeeman and Lorentz did further study of the
influence of magnetic fields on the spectral emissions from atoms. By
analysis of the splitting of the sodium doublet, they were able to
demonstrate that the charge to mass ratio of the charge responsible for
the splitting was the same as Thomson's electron. This was the first
direct demonstration that electrons were involved in the production of the
spectral line emissions.

Index

Reference
Leighton
Ch
2

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