Lecture 17 - 07_105 Nodes Node 1s 2s (a) 3s 1s 2s (b) 3s p...

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07_105 Nodes Node 1 s 2 s 3 s (a) 1 s 2 s 3 s (b)
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p orbitals: n = 2, 3, 4… (not for n = 1) • not spherical: 2 lobes separated by a node at p orbitals are named according to the axis along which lobes lie: 2 p x , 2 p y , 2 p z • same shape • same energy • different orientation 07_107 x x y z x y z 2 p x 2 p y 2 p z z y Fig. 12.19 3p Orbital Fig. 12.19
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Standing Waves for 1- and 2-Dimensional Models of the Atom Guitar Strings Standing waves in 1-D Kettle Drums Standing waves in 2-D
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Drum skin n=1 l=0 n=2 l=0 n=2 l=1,x n=2 l=1,y n=3 l=0 n=3 l=1,x n=3 l=1,y n=3 l=2,x2-y2 n=3 l=2,xy
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+ + + + - - - - E 0 -ve n n 2 3 2 1 1 4 9 Bohr Atom Schrodinger Atom Full 3-D Waves for the Hydrogen Atom; the Schrodinger Model E ’ ! R H 1 n 2 No. of co-energetic waves = n 2 d-wave s-wave p-wave
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Oct. 15, 2003 Today’s Lecture Quantum Mechanics and Atomic Theory • 12.13 The Aufbau Principle and the Periodic Table • 12.14 Further Developments (review if interested) • 12.15 Periodic Trends in Atomic Properties
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• The Aufbau principle and the periodic table: • quantum mechanical model of the atom accounts for the organization of the periodic table – Assume: • all atoms have the same type of orbitals as hydrogen
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1 s 2 s 3 s (b) x x y z x y z 2 p x 2 p y 2 p z z y 07_108B x y d yz x y x y z y z z z z x y d xz d xy d x 2 - y 2 d z 2 x (b) 07_109 z z z y x z z z z f z 3 3 5 zr f xyz f y(x 2 - z 2) f x(z 2 - y 2) f z(x 2 - y 2) y x y x y x y x y x f x 3 3 5 xr 2 f y 3 3 5 yr 2 y x - - - 2
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3s — 3p — — — 3d — — — — — 2s — 2p — — — 1s — H atomic orbitals 4p — — — 4s — 3d 3p — — — 3s — 2p — — — 2s — 1s — H-like atomic orbitals note: energy 3d 4s order: 1s,2s,2p,3s,3p,4s,3d,4p,5s,4d,5p,6s,4f,5d… Energy
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– Aufbau principle: • as protons are added to the nucleus to build up the elements, e - ’s are added to hydrogen-like orbitals – Use orbital diagrams: • for example: 1s 2s 2p 3s – Steps in filling orbitals: • Fill orbitals in succession, starting with lowest energy (1s) orbital • Place a maximum of 2 e - ’s in each orbital (with opposite spin sign ) Represents orbitals
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• For degenerate orbitals: place one e - per orbital until all orbitals of the same type have at least 1 e - , then add remainder e - ’s until orbitals are filled. Unpaired e - ’s must have a positive spin sign • Fill orbitals of the same type before moving onto the next one • Note: in polyelectronic atoms, only orbitals with the same n and l quantum #’s are degenerate – Hund’s rule: • “The lowest energy configuration for an atom is one having maximum # of unpaired e - ’s allowed by the Pauli’s Principle in a particular set of degenerate orbitals”
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– Examples: • H: 1s 1 1s 2s 2p 3s • He: 1s 2 1s 2s 2p 3s • Li: 1s 2 2s 1 1s 2s 2p 3s • C: 1s 2 2s 2 2p 2 1s 2s 2p 3s • O: 1s 2 2s 2 2p 4 1s 2s 2p 3s • Ne: 1s 2 2s 2 2p 6 1s 2s 2p 3s
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– for Na (11 e - ’s): • 1s 2 2s 2 2p 6 3s 1 [Ne]3s 1 Ne – for Mg (12 e - ’s): • 1s 2 2s 2 2p 6 3s 2 [Ne]3s 2
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– Valence vs Core electrons: Valence e - ’s: the e - ’s in the outer most principal
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This note was uploaded on 01/16/2010 for the course CHEM CHEM 121 taught by Professor Peggy during the Spring '09 term at Simon Fraser.

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Lecture 17 - 07_105 Nodes Node 1s 2s (a) 3s 1s 2s (b) 3s p...

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