# Zeeman splitting.

• hhhmortal

## 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) ?

q1. Seems correct - remember you can't shift between states with the same l-number.

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.

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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