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Chapter 8: 78E (page 344)

In its ground state, carbon's 2pelectrons interact to produce jT=0. Given Hund's rule. what does this say about the total orbital angular momentum of these electrons?

Short Answer

Expert verified

Total orbital angular momentum isL=2h.

Step by step solution

01

Total spin of two electrons

The total spin of the two electronsSTis

ST=ST(ST+1)h ….(1)

02

total spin quantum number

The quantum number jT is zero jT=0.

The spin quantum number of each electron is s1=s2=12.

By using Hund's rule, we conclude that the total spin quantum number st is given by

ST=s1+s2=12+12ST=1

03

total spin of electrons

By using Eq. (I), we find the total spin of the electrons sT as

ST=sTsT+1h=1.1+1hST=2h

04

The total orbital angular momentum LT

Now, since jT=0, we conclude that the total orbital angular momentum LT must be equal to the total spin ST

LT=ST=2h

Hence the total orbital angular momentum is LT=2h.

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The Zeeman effect occurs in sodium just as in hydrogen-sodium's lone 3svalence electron behaves much as hydrogen's 1.5. Suppose sodium atoms are immersed in a0.1Tmagnetic field.

(a) Into how many levels is the3P1/2level split?

(b) Determine the energy spacing between these states.

(c) Into how many lines is the3P1/2to3s1/2spectral line split by the field?

(d) Describe quantitatively the spacing of these lines.

(e) The sodium doublet (589.0nmand589.6nm)is two spectral lines.3P3/2→3s1/2and3P1/2→3s1/2. which are split according to the two differentpossible spin-orbit energies in the 3Pstate (see Exercise 60). Determine the splitting of the sodium doublet (the energy difference between the two photons). How does it compare with the line splitting of part (d), and why?
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