Zeeman Effect: Counting Frequencies and Explaining Zero Frequency

In summary, for a system with two levels corresponding to rotational quantum number J=2 and J=1, each with sublevels corresponding to J=2: m_J=-2, -1, 0, 1, 2 and J=1: m_J=-1, 0, 1, transitions can be induced by tuning the external field to correspond to \Delta m_J=-1, 0, 1. This results in 9 different transitions, but only 5 distinct frequencies will be observed due to the selection rule. For the transition \Delta m_J=0, the frequency will not be zero as the Zeeman term is just a correction to the energy. The number of distinct frequencies observed may be
  • #1
KFC
488
4
Suppose for a system with two levels with corresponding rotational quantum number J=2 and J=1, each of these have sublevels corresponding to [tex]J=2: m_J=-2, -1, 0, 1, 2[/tex] and [tex]J=1: m_J=-1, 0, 1[/tex], tune the external field such that we have transitions corresponds to [tex]\Delta m_J=-1, 0, 1[/tex]. So how many different frequencies will be observed? And for the transition [tex]\Delta m_J=0[/tex], does it mean the corresponding observed frequency is ZERO? How come?
 
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  • #2
hi,
for your 1st question: 9.
2nd question: i guess freq. won't be zero..
 
  • #3
Thanks. For the second question, I think I make a mistake, I forget that the Zeeman term is just the correction of the energy, so the frequency will not be zero.

But for the first question, someone said though there are 9 different transitions but only 5 frequencies are distinct, why?
 
  • #4
I don't know sorry..But it may be something to do with relaxations between sub-states..
May i know where you got to know that 5 freq. are distinct..some book?
 
  • #5
KFC said:
Suppose for a system with two levels with corresponding rotational quantum number J=2 and J=1, each of these have sublevels corresponding to [tex]J=2: m_J=-2, -1, 0, 1, 2[/tex] and [tex]J=1: m_J=-1, 0, 1[/tex], tune the external field such that we have transitions corresponds to [tex]\Delta m_J=-1, 0, 1[/tex]. So how many different frequencies will be observed?

The Zeeman effect has about three patterns as follows. (the external magnetic field is the z direction.)

1 [tex]J_{Z}[/tex] is an integer, which means the electron number is even. The normal Zeeman effect is seen (in the case of the sum of the spin is zero.(equal triplet pattern due to the selection rule ([tex]\Delta J = +1,0,-1[/tex]).))

2 [tex]J_{Z}[/tex] is not an integer(1/2, 3/2, 5/2...). When the magnetic field is strong, the Paschen-Back effect is seen. ([tex]S_{Z}[/tex] is 1/2, so the z component of the spin magnetic moment is the Bohr magneton(due to 2 x 1/2 =1)).

3 When the magnetic field is weak, the anomalous Zeeman effect is seen. Strange to say, in this case [tex]S_{Z}[/tex] is not exactly 1/2 and it's changing continuously. Because this includes three rotations as follows,
-------------------------
Rotation (spin + orbital)

Precession(1) ---- The combined magnetic moment [tex]\vec{\mu}=2\vec{S}+\vec{L}[/tex] precesses about [tex]\vec{J}=\vec{S}+\vec{L}[/tex](not [tex]\vec{J_{Z}}[/tex]).
(But I think this precession is very strange. Why does this precession occur? Because the [tex]\vec{J}[/tex] is an angular mometum, not the magnetic moment. So this direction has no relation to the direction of the force such as the magnetic field([tex]\vec{Z}[/tex] or the magnetic moment[tex]\vec{\mu}, 2\vec{S}, or \vec{L}{[/tex].)

Precession(2) ----- The [tex]\vec{J}[/tex] component of the [tex]\vec{\mu}[/tex] precesses about Z axis.
See this Google book (in page 238).
------------------------

I think your case is 1. So it's the normal Zeeman triplet=3 patten. OK?
 
Last edited:

Related to Zeeman Effect: Counting Frequencies and Explaining Zero Frequency

1. What is the Zeeman Effect?

The Zeeman Effect is a phenomenon in which the spectral lines of an atom are split into multiple lines when placed in a magnetic field. This splitting is caused by the interaction between the magnetic field and the spin of the electrons in the atom, resulting in different energy levels for the electrons.

2. How is the Zeeman Effect observed and measured?

The Zeeman Effect can be observed through spectroscopy, which involves passing light through a sample of the atom and measuring the resulting spectrum. The splitting of the spectral lines can then be measured and analyzed to determine the effect of the magnetic field.

3. What is meant by "counting frequencies" in the context of the Zeeman Effect?

In the Zeeman Effect, counting frequencies refers to measuring the difference in energy between the split spectral lines. Each line represents a different frequency, and by counting the number of lines and their spacing, scientists can calculate the strength of the magnetic field and the fine structure constant of the atom.

4. Why is the concept of zero frequency important in explaining the Zeeman Effect?

The concept of zero frequency is important because it represents the original, unsplit spectral line of the atom. This line is used as a reference point to measure the splitting and calculate the frequencies of the split lines. The presence of a zero frequency also confirms the presence of a magnetic field, as without it, the spectral lines would not be split.

5. What are the applications of the Zeeman Effect?

The Zeeman Effect has various applications in different fields, such as astronomy, where it is used to study the magnetic fields of stars and galaxies. It is also used in atomic and molecular spectroscopy, as well as in the development of new technologies such as magnetic resonance imaging (MRI). Additionally, the Zeeman Effect has been used to test the validity of quantum mechanics and to study the behavior of atoms in extreme conditions, such as in high magnetic fields.

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