Download C475A Homework 7. Due Monday Nov. 15 at 5pm in Prof. Ginger`s

C475A
Homework 7. Due Monday Nov. 15 at 5pm in Prof. Ginger’s mailbox.
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CIRCLE YOUR ANSWERS AND KEY INTERMEDIATE RESULTS
STAPLE YOUR PAPERS TOGETHER
INCLUDE ALL COMPUTER PRINTOUTS
McQuarrie Exercises
8-14 A plug’n’chug and estimate of NMR frequency. Make a similar calculation to
estimate the field strength of the 900Mhz wide-bore NMR that was installed at PNNL in
2002 (http://www.pnl.gov/news/2002/02-08.htm) (now that’s a big magnet)
8-15 Normalization of a wave function including spin.
8-20 Total Sz for an n-electron system. Li-like determinant.
8-30 Terms. You may state the np4 result and argue (vs. ‘prove’) it is the same
8-31 Sets of quantum numbers corresponding to atomic terms.
8-37 Ground state of magnesium
Additional Problems
Spin
1) a) Write out all of the allowed wave-functions for the first excited state of the He atom
including electron spin. Which functions correspond to triplet states and which to singlet
states.
b) List 5 particles that are Fermions. List 5 that are Bosons. (Google is fair game if you
don’t happen to know this many particles off the top of your head!). What do you notice
as far as a trend goes for the ‘fundamental’ particles.
Term symbol practice
1) Derive (do not just state) the possible term symbols for the 1s22s22p3 configuration of
a nitrogen atom.
Qualitative Understanding of the Material
2) a) Explain why the Hartree-Fock SCF method doesn’t obtain the exact ground state
energy even though it incorporates an interelectron repulsion term into the Hamiltonian.
b) Explain why the energy of an orbital depend on l for electrons in atoms other than
hydrogen? Annotate your discussion with a plot of the radial wave functions for 3s, 3p
and 3d.
c) Explain why, all other things being equal, parallel (unpaired) spins generally produce
states of lower energy that states with antiparallel (paired) (Hund’s rule)
3) Draw a diagram (similar to the one we drew in lecture for excited Helium), for carbon
showing the progressive splitting and relative positions of the electron configuration,
atomic terms, atomic levels and atomic states (in a magnetic field) for the 1s22s22p3
configuration of carbon.
Ionization Energies (again)
4) When UV radiation of wavelength 58.4 nm from a He lamp is directed on to a sample
of Krypton gas, electrons are ejected with a maximum speed of 1.59x106 m/s. What is
the ionization energy of Krypton?
Reviewing the Rigid Rotor (again)
5) A rotating linear diatomic molecule with reduced mass, µ, and bond length, d, is found
in a state specified by the wave function:
1/ 2
 15 
2
− 2 iφ
 (sin θ )e
 32π 
ψ (θ , φ ) = 
What are the values of the angular momentum, energy, and degeneracy of this state.