Download Homework Assignment for CHEM 5591 Professor JM Weber

Homework Assignment for CHEM 5591
Professor J. M. Weber
Office: JILA A709; Phone 303-492-7841; email: [email protected]
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Problem Set 3
To be returned before class on Wednesday, February 5, 2014. Please hand them to
me in class or slide them under my office door.
1. Atomic Term Symbols:
a.) Write down all possible terms arising from the ground state electron configuration of
Aluminum (you don’t need a microstate table for this problem). Which term describes the
ground state of Al?
(2 credits)
b.) Write down all possible terms arising from the ground state electron configuration of
Titanium (you do need a microstate table for this problem). Order them in sequence of
energy according to Hund’s rules.
(5 credits)
c.) Consider the C(1s)2(2s)2(2p)1(3d)1 excited configuration in carbon. Construct all
possible term symbols corresponding to this configuration.
(4 credits)
2. Atomic States and Spectral Lines:
a.) The energy levels of alkali atoms can be approximated using a quantum defect
equation, even at the low quantum numbers involved. You can assume that the quantum
defect is independent of n. The ionization energy of Li is 5.3913 eV. The spectral line 2s
2p is observed at  = 6710 Å. Assume that you excite Li vapor selectively into the 3p
level. Calculate the quantum defects s and p.
(4 credits)
b.) Qualitatively draw a level diagram for the electron configurations of Li with all
excited states of the valence electron up to n = 3. Determine all possible term symbols for
the excited states.
(3 credits)
c.) Determine the wavelengths of all emission lines you can observe in the experiment
described in (a), neglecting fine structure splittings between different terms with the
same L.
(4 credits)
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Homework Assignment for CHEM 5591
Professor J. M. Weber
Office: JILA A709; Phone 303-492-7841; email: [email protected]
________________________________________________________________________
3. Electric Fields
a.) Calculate the expectation value for the electric field (in V/m) the electron in an H
atom experiences in the ground state. Compare the QM expectation value and the Bohr
model.
(4 credits)
b.) You want to ionize a potassium atom in an electric field, where the valence electron
has been excited to n = 100, ℓ = 99. Estimate the field strength you need to do that (in
V/m, use the Bohr model here). Argue why you can use the Bohr model here.
(3 credits)
c.) One can show that the expectation value for the electron radius of an H orbital with n
and ℓ is
<rnℓ> = ½ a0·[3n2 – ℓ(ℓ+1)]
Derive an expression for the electric field strength you need to field-ionize an H atom in
state |nℓ>, based on the shape of the potential energy function of an H-atom in an external
electric field with strength E0. Compare with the result you obtained in (b) and comment
on the validity of Bohr’s correspondence principle at n = 100.
(4 credits)
d.) Do you think that an experiment would corroborate your result? If not, what would
you expect E0 to be compared to your result in (c), and why (max 3 sentences!)?
(2 credits)
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