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lecture16_umn - Lecture 16 Atomic Spectroscopy Electron...

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Lecture 16 October 16, 2009 Atomic Spectroscopy Electron Spin Total Angular Momentum The Zeeman Effect and Electron Spin Resonance Spectroscopy
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Atomic Spectroscopy The hydrogenic atom has 3 quantum numbers. Two from the spherical harmonics. Selection rules on the spherical harmonics: (16-1) Without derivation selection rule for Δ n : absorption/emission is allowed for any change in n ( n must change from one value to another, or else E , which depends only on n , fails to change, and then there is no opportunity to absorb or emit a photon in the first place!) " l = ± 1 and " m l = 0, ± 1
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Allowed Transitions
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Allowed Transitions Actual measured spectrum would be relatively simple, because of the very small number of different Δ E values. A single photon frequency is associated with each Δ E : single ν for every n = 1 n = 2 transition ; single ν for every n = 2 n = 3 transition , irrespective of the actual orbitals involved at the particular principal quantum number level. If you make the experiment a bit more complicated: a lot of new lines in the spectrum (different photon frequencies) .
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Stern and Gerlach’s Experiment In 1922 1) Heat a block of silver (Ag) until it vaporizes 2) Arrange the pressure in the experimental system such that the gas of silver atoms collimates into a "beam" that passes through the poles of a magnet . 3) Observe where the silver atoms strike a target behind the magnet . What Stern and Gerlach expected: Ag atom is like a very big hydrogen atom. All electrons but one completely fill principal quantum number levels: 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 4d 10 5s 1
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Stern and Gerlach’s Experiment 5s 1 electron: ‘underneath’ it, it sees 47 protons and 46 electrons that are spherically symmetric. The total angular momentum of the electron/’nucleus’ system is L = 0 , just as is the case for H. In the absence of angular momentum, Ag should not interact with a magnetic field. The target should show a continuous smear of silver that drops off from the center, with the smearing attributable only to the beam not being perfectly collimated.
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What did they actually see? Instead of a single smear of atoms, reflecting zero electronic angular momentum, there are two distinct lines . They reflect some other angular momentum. The lines are distinct:
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This note was uploaded on 12/14/2010 for the course CHEM 3502 taught by Professor Staff during the Fall '08 term at Minnesota.

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lecture16_umn - Lecture 16 Atomic Spectroscopy Electron...

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