Lecture 16 - Oct. 10, 2003 Todays Lecture Quantum Mechanics...

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Oct. 10, 2003 Today’s Lecture Quantum Mechanics and Atomic Theory • 12.9 Orbitals (Quantum Numbers)
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12.7 Schrodinger’s equation for H atom gives gives rise to 3 quantum numbers (see :Section 12.6 for a fuller description) n: principal quantum number l : angular momentum (azimuthal) quantum number m l : magnetic quantum number • allowed energies: • Note that E depends only on the principal quantum number (true for 1 e - species) • exactly the same equation as in Bohr model 2 42 18 n 2 2 22 o Z m eZ E 2.178x 1 0J n 8 hn - = - =- e Ll
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12.8 What is the physical significance of atomic orbital? • in spherical polar coordinates: Y 2 indicates the probability of finding an e - near a particular point in 3D space • graphically: e - density map, e - density or e - probability – probability distribution » plot Y 2 vs r (or R 2 r ) » greatest probability of finding the e - near the nucleus (r ,, ) R(r ) () () Y qf = QqFf
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– probability distribution » plot Y 2 vs r (or R 2 r ) » greatest probability of finding the e - near the nucleus Probability ( R 2 ) Distance from nucleus ( r ) Fig. 12.16
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– radial probability distribution » plot 4 π r 2 Y 2 vs r Radial probability (4 πρ 2 R ) Distance from nucleus ( r ) (b) (a)
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» observe a maximum at r = 5.29 x 10 -2 nm for 1s in H » this is the distance where the e - is most likely to be found » this distance is exactly the radius of inner most orbit as predicted by Bohr’s model » Bohr’s model predicts to always find e - at this distance » quantum mechanics predicts this is the most probable distance – define size of orbital: » the radius of a sphere that contains 90% of the total e - probability
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• 12.9 Quantum numbers:
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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 16 - Oct. 10, 2003 Todays Lecture Quantum Mechanics...

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