Lecture8-9

The gyromagne2c ra2o g2 implies what about the

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Unformatted text preview: or example) we keep every pair of electrons possible in the triplet state to make the space wave func2on an2symmetric and thus lower energy. u༇For large enough Z, the order of the states is changed due to the Coulomb repulsion term. o  We will deal with this by considering “Screening” 58 Consider Gauss’s Law for an Atom Filled inner shells give spherically symmetric charge distribu2on of electrons surrounding nucleus. u༇  Valence electrons in the outer shell see the full nuclear charge near r=0 but a reduced (screened) charge at larger r. u༇  Thus the states with more probability to be at large r, are higher in energy due to screening. u༇  Due to the psuedopoten2al term in the Schrodinger equa2on, higher l states are pushed to large r, so the lowest l states are preferred. u༇  o  we saw this in Helium u༇  At some point this “screening” effect will overcome the effect of the principle quantum number. o  it happens first with the 4s states being of lower energy than the 3d. 59 Order of the Energy Levels u༇ Due to screening, the shell order is u༇ lowest n+l; if n+l same, lowest n u༇ This gives us the shape of the periodic table. o  the 4s and 3d are very close in energy. 60 Atomic Shell Model u༇  Filled shell is completely spherically symmetric and it “screens” the charge of the nucleus. o  use Gauss’s law o  poten2al at large r is much weaker than it would be without inner shells. u༇  Filled shells have total L=0, S=0 and J=0. u༇  Outer electrons s2ll see a spherically symmetric poten2al and behave in a similar way as inner electrons. o  valence electrons in 4p are like 3p or 2p… o  periodic table is easy to explain from atomic shells 61 Atomic Shell Model u༇  Closed shells are spherically symmetric. o  Implies closed shells are simple and we can treat closed shells like a symmetric poten2al that a few addi2onal electrons move in. o  Closed shells are 2ghtly bound. o  One electron outside a closed shell is simple like one electron… o  Explains periodic table o  valence electrons similar in 2p, 3p, 4p… u༇  Screening increases Energy of higher l states since they are farther from the nucleus. 62 Ioniza2on Energies Peak for Closed Shells 63 Atomic Volume Drops as we add Unpaired Electrons 64 Atomic Energy Levels u༇  Use the Hydrogen- like states to describe the basic states of atoms. u༇  Screening of nuclear charge favors low angular momentum l. u༇  We can put two electrons into each state (two spin states). u༇  Big energy gaps at Z=2,10,18,36,54,96 o  Helium, Neon, Argon, Krypton, Xenon, Radon 65 Filling Up the Atomic Shells Electron configura2on determines chemical proper2es of elements. 66 Clicker: the 4s state u༇  Why are the outer electrons in K and Ca atoms in the 4s state rather than the (unfilled) 3d state? A.  B.  So that the periodic table will be periodic. Because the Hydrogen 4s state is lower in energy than the 3d state. C.  To...
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