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Lecture 28
Hydrogen 3d, 4s and 4p
3d
4s
4p
We can get some insight into the relative
Energies of these three orbitals from
the website:
http://keisan.casio.com/
http://www.corrosionsource.com/handbook/periodic/periodic_table.gif
Lecture 28
The periodic Table
Lecture 28
Atomic Radii
http://www.mhhe.com/physsci/chemistry/essentialchemistry/flash/atomic4.swf
See also:
http://en.wikipedia.org/wiki/Atomic_radii_of_the_elements_(data_page)
Lecture 28
Combining angular momentum
Lecture 27
Energy splitting for 2 electrons
in the 4p/4d states
This corresponds to the case of two electrons in a 4p,4d level in which inner
electrons are not providing any separation between the two; it considers only
the interaction between these two electrons and relativity (only relevant to excited
States of Helium or ions with only two electrons, not terribly realistic).
Lecture 28 Relativistic effects
(S-O coupling, mass increase)
f=2.46x1015 Hz~ 2.5 PHz.
Fine structure effects
are on the order of ppm
http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html
P301 Exam II Review
•NO CALM QUESTION FOR FRIDAY!!!
•Exam Mechanics:
•Covers material from sections 5.2 thru 8.3 (but of course, some
material from earlier sections may come in as well).
•1 side of 8.5x11” formula sheet is allowed. It is not to be a
general note sheet
•4 questions with 9 parts (each worth 6 points)
•All have computational/short answer this time (no expt.
descriptions).
•Tables from the inside front lay-out of the text will be provided.
•Exam will start at 11:10.
•Office Hours:
•Wednesday 2:30 to 3:30 (Forum)
•Thursday 4:00 to 5:00 ???
•Friday 8:45 to 10:00
•No office hours Friday afternoon.
P301 Exam I Review
•Important results/topics:
•Chapter 5 (4 lectures):
•Bragg’s law (as applied to particles)
•DeBroglie waves
•Fourier Analysis/ Wave packets /Group velocity
•Uncertainty Relations (position-momentum; time-energy)
•Wave-particle duality and the Copenhagen interpretation.
•Chapter 6 (5 lectures):
•Schrodinger Equation (time dependent and time-independent)
•Properties of wave functions and the application of boundary
conditions. (e.g. problem 2 (7-38) on today’s assignment)
•Expectation values and the physical significance of Y(x,t)
•Square wells (infinite and finite).
•Operators in quantum mechanics
•Confinement energy
•Quantum Simple Harmonic Oscillator
•Tunneling
P301 Exam I Review
•Important results/topics:
•Chapter 7 (3 lectures):
•Schrodinger Equation in spherical polar coordinates and angular/radial
separation of variables
•Principal and Angular momentum quantum numbers
•Differences between the “Schrodinger” and “Bohr” hydrogen atom.
•Properties of the radial wave functions for hydrogen
•Selection rules (Dl=+/-1,Dml=+/-1, DJ=0,+/-1 (J:0->0 forbidden), DS=0.
•Zeeman effect
•Intrinsic spin and the Stern-Gerlach experiment
•Chapter 8 (3 lecutres):
•Pauli Exclusion principle
•Structure of the periodic table and the role played therein by interelectron interactions (and radial wave function shapes) and Pauli.
•Angular momentum (magnitude and projection quantum numbers,
uncertainty relations, etc.)
•Addition of Angular momenta
•Spectroscopic Notation
•Hund’s rules (especially number 1).
Examples
Draw a sketch of the wave function
for two lowest energy states in this
potential (assuming that at least two
exit) and emphasizing any features
that are different for the two states.
The wave function for a potential given by a delta-function
(negative infinity at the origin, zero everywhere else) is given
by Aexp(-|x|/a). What is the probability that the particle will
be found at a distance greater than “a” from the origin?
Nitrogen has atomic number 7, what electronic states would
you expect to be occupied when a nitrogen atom is in its
ground state, and what might you expect to be the lowestlying excited state for this atom? {this is an example of a noncomputational question that you could be asked}
8-23 (sort of) The Ka x-ray line is actually a doublet (Ka1, Ka2) where the
Difference between the two is quite small (20 eV out of 8keV for Cu for
Instance). What is the origin of the energy splitting between these two lines
and why are there two (and only two) lines?
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5-
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