2.1 Basic Concepts and Formulae
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parallel to the light path), they are split into two, which are circularly polarized in
the opposite directions.
The selection rule is Δm = 0, ±1, where m is the magnetic quantum number.
We thus get a simple triplet or doublet. In the former they are equally spaced.
Anamolous Zeeman effect
For not too strong field, one observes splitting into more than three components,
unequally spaced. The additional magnetic energy is given by
E mag = −
eBmg
2μc
(2.28)
where g is Lande’s g-factor. The undisturbed term again splits up into 2J +1 equidistant terms but the lines will not be equidistant because the g-factor for the upper and
lower levels would be different.
g = 1 +
j( j + 1) + s(s + 1) − l(l + 1)
2 j( j + 1)
(2.29)
Degeneracy of H-atom energy levels
The degeneracy = 2
n−1
l=0
(2l + 1) = 2n
2
(2.30)
where n is the principal quantum number.
Broadening of spectral lines
The observed spectral lines are not perfectly sharp. The broadening is due to
(i) Natural width explained by the uncertainty principle for time and energy.
(ii) Thermal motion of atoms.
(iii) Molecular collisions.
Spectroscopic notation
2S+1 L J ,where S is the total electron spin, L is the orbital angular momentum, and
J the total angular momentum.
Stern–Gerlah experiment
In this experiment a collimated beam of neutral atoms emerging from a hot oven is
sent through an inhomogeneous magnetic field. The beam is split up into 2J + 1
components. The experiment affords the determination of the spin of the atoms.
91
parallel to the light path), they are split into two, which are circularly polarized in
the opposite directions.
The selection rule is Δm = 0, ±1, where m is the magnetic quantum number.
We thus get a simple triplet or doublet. In the former they are equally spaced.
Anamolous Zeeman effect
For not too strong field, one observes splitting into more than three components,
unequally spaced. The additional magnetic energy is given by
E mag = −
eBmg
2μc
(2.28)
where g is Lande’s g-factor. The undisturbed term again splits up into 2J +1 equidistant terms but the lines will not be equidistant because the g-factor for the upper and
lower levels would be different.
g = 1 +
j( j + 1) + s(s + 1) − l(l + 1)
2 j( j + 1)
(2.29)
Degeneracy of H-atom energy levels
The degeneracy = 2
n−1
l=0
(2l + 1) = 2n
2
(2.30)
where n is the principal quantum number.
Broadening of spectral lines
The observed spectral lines are not perfectly sharp. The broadening is due to
(i) Natural width explained by the uncertainty principle for time and energy.
(ii) Thermal motion of atoms.
(iii) Molecular collisions.
Spectroscopic notation
2S+1 L J ,where S is the total electron spin, L is the orbital angular momentum, and
J the total angular momentum.
Stern–Gerlah experiment
In this experiment a collimated beam of neutral atoms emerging from a hot oven is
sent through an inhomogeneous magnetic field. The beam is split up into 2J + 1
components. The experiment affords the determination of the spin of the atoms.