Understanding Zeeman Splitting: Predicting Components in Weak Applied Fields

L * (L+1)In summary, The total number of components that appear when the sodium resonance line is split by a weak applied field is four for the 589.6nm line and six for the 589.0nm line. The necessary conditions for a normal Zeeman triplet are an even number of electrons and the formation of a state with S=0 and 2S+1=1. The transition rule for the 589.6nm line is $\Delta m = +1, 0, -1$ and for the 589.0nm line is $\Delta m = +1, 0, -1, 0, -1, +1$. The Lande g factor for effectively mono
  • #1
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Homework Statement



(Q1) Which transition will produce a normal zeeman triplet in a weak applied field?


(Q2) The sodium resonance line is a doublet. What is the total number of components that appear when the line is split by a weak applied field?


The Attempt at a Solution



(Q1) 1D2 --> 1P1 or 2P(3/2) ---> 2S(1/2) ?
 
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  • #2
q1. Seems correct - remember you can't shift between states with the same l-number.
 
  • #3
The visual effect above is awful, sorry.

1. Sufficient and neccesary conditions for normal Zeeman triplet is:

The total number of electrons is even, and the electrons form the state with S=0, 2S+1=1.

2. As to the famous sodium doublet, the 589.6nm line will split into four lines, with frequency difference 2/3 Lorentz unit (LU), 3/4 LU, 2/3 LU, respectively; the 589.0nm line splits into six ones, with identical frequency difference of 2/3 LU. No line exists at the initial location any more.

Comments:

1. Sodium Doublet: 589.6nm: 2P_(3/2) ----->2S_(1/2), 589.0nm: 2P_(1/2) ----->2S_(1/2).

2. Transition Rule: \Delta m = +1, 0, -1.

589.0nm: 2P_(1/2) ----->2S_(1/2), m, mg

---|----------------------------------------------------- 3/2, 2
---|---------|----|-------------------------------------- 1/2, 2/3
---|---------|----|---------|----|---------------------- -1/2, -2/3
---|---------|----|---------|----|----------|----------- -3/2, -2
1 1 1 1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
---|---------|----|---------|----|----------|----------- 1/2, 1
------------------|--------------|----------|----------- -1/2, -1



589.6nm: 2P_(1/2) ----->2S_(1/2), m, mg

---|---------------------------------------------------- 1/2, 2/3
---|---|-----------------|----|------------------------- -1/2, -2/3
1 1 1 1
1 1 1 1
1 1 1 1
---|---|-----------------|----|-------------------------- 1/2, 1
-------|----------------------|-------------------------- -1/2, -1


where $g$ above is Lande g fractor, and for effectively mono-electron atoms, such as 1H, 3Li, 11Na, 19K, 29Cu, 47Ag, 79Au,

3 1 S * (S+1) -- L * (L+1)
g = --- + --- (---------------------------------)
2 2 J * (J+1)
 
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FAQ: Understanding Zeeman Splitting: Predicting Components in Weak Applied Fields

1. What is Zeeman splitting?

Zeeman splitting is a phenomenon observed in atoms and molecules when they are placed in a magnetic field. It causes the spectral lines of the atom to split into multiple components, which can be observed in spectroscopic experiments.

2. Why does Zeeman splitting occur?

Zeeman splitting occurs due to the interaction between the magnetic field and the magnetic moment of the atom. This interaction causes the energy levels of the atom to shift, resulting in the splitting of spectral lines.

3. What factors affect the magnitude of Zeeman splitting?

The magnitude of Zeeman splitting depends on the strength of the magnetic field, the type of atom or molecule, and the orientation of the magnetic field with respect to the direction of observation.

4. How is Zeeman splitting used in scientific research?

Zeeman splitting is used in various fields of research, such as astrophysics, plasma physics, and quantum mechanics, to study the magnetic properties of atoms and molecules. It is also used in spectroscopic experiments to identify and analyze the composition of materials.

5. Can Zeeman splitting be observed in everyday life?

Zeeman splitting is not visible in everyday life as it requires a strong magnetic field and specialized equipment for observation. However, it is present in natural phenomena such as the polar lights and can be seen in laboratory experiments using spectroscopic techniques.

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