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Chapter 8: 76E (page 344)
A hydrogen atom is subjected to a magnetic field Bstrong enough to completely overwhelm the spin-orbit coupling. Into how many levels would the 2p level split, and what would be the spacing between them?
5 levels,
And energy difference is
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Using to eliminate L - S. as wellas , obtain equation (8- 32 )from the equation that precedes it.
To determine the value of Z at which the relativistic effects might affect energies and whether it applies to all orbiting electrons or to some more than others, also guess if it is acceptable to combine quantum mechanical results.
The Slater determinant is introduced in Exercise 42. Show that if states and of the infinite well are occupied. with the particle in state being spin up and the one in being spin down. then the Slater determinant yields the antisymmetric multiparticle state: .
As is done for helium in Table 8.3, determine for a carbon atom the various states allowed according to LS coupling. The coupling is between carbon's two 2p electrons (its filled 2s subshell not participating), one or which always remains in the 2p state. Consider cases in which the other is as high as the 3d level. (Note: Well both electrons are in the 2p, the exclusion principle restricts the number of states. The only allowed states are those in whichand are both even or both odd).
Question: Early on, the lanthanides were found to be quite uncooperative when attempts were made to chemically separate them from one another. One reason can be seen in Figure 8.16. Explain.
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