CHEM 442 Lecture 22 Problems 22

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CHEM 442 Lecture 22 Problems
22-1. The neon atom has the configuration (1s)2(2s)2(2p)6. Let the operator for the sum of
10
all z-component orbital angular momentum be
å lˆ ( r ) , where r
z
n
n
is the spatial
n=1
coordinates of the nth electron. Let the operator for the sum of all z-component spin
10
angular momentum be
å ŝ (s ) , where s
z
n
n
is the spin coordinates of the nth electron.
n=1
Show that the total z-component orbital and spin angular momenta of the neon atom are
zero. Argue that the total orbital and spin angular momenta of the neon atom are also
zero.
22-2. Identify the levels that may arise from the configurations and their degrees of
degeneracy: (a) (3s)1, (b) (3p)1.
22-3. Identify the levels that may arise from the configurations and their degrees of
degeneracy: (a) (4d)1, (b) (4f)1.
22-4. Suggest the first-order perturbation expression for the energy shift caused by the
spin-orbit coupling. Use the spin-orbit coupling constant A given in units of cm−1.
(
)
1 2 ˆ2 2
22-5. Show that ŝ × lˆ =
ĵ - l - ŝ and evaluate the expression of 22-4.
2
22-6. Using the result of 22-5, evaluate the spin-orbit energy shifts in (a) (3s)1, (b) (3p)1.
22-7. The potassium emission spectra includes two lines at 766.49 nm and 769.90 nm.
Determine the spin-orbit coupling constant A for the 4p orbital of K.
22-8. Find the lithium emission lines corresponding to the (1s ) ( 2 p ) ® (1s ) ( 2s ) from
the NIST Atomic Spectroscopy Database (http://www.nist.gov/pml/data/asd.cfm).
Determine the spin-orbit coupling constant A for the 2p orbital of Li.
2
1
2
1
22-9. What are the differences between fluorescence and phosphorescence? Why is
phosphorescence more common in heavy-element compounds?
22-10. What is an intersystem crossing?
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