C566lecture1_000

C566lecture1_000 - C566 Master Lecture Notes Lecture 1...

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C566 Master Lecture Notes Lecture 1 Units and Physical Constants- See page xvii in Hollas Speed of light = 3 x 10 8 m s 1 =  Visible light is on the order of 500 nm = 5 x 10 -7 m Molecular sizes are on the order of 10 10 m (1 Å) Units of energy typically used in spectroscopy: 1 c m 1 = 1.986 x 10 -23 J = 0.01196 kJ mol -1 = 1.12398 x 10 -4 eV Energy in “Hz” via c (in cm s 1 ) (energy in cm 1 ) Energies in NMR generally 10 2 MHz (depending on field) Few quick mathematical reminder Euler Relationship: e ikx = cos kx + i sin kx e ikx = cos kx i sin kx And 1/i = i
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Chapter 1 of Hollas: Typical introduction to QM Examples of the failure of classical mechanics Blackbody radiation Photoelectric effect Heat capacity anomaly at low temperature Electron diffraction Atomic spectra- Bohr model Schrodinger equation H-atom solution Rigid rotor Electron spin, nuclear spin Harmonic oscillator Time-dependent Schrödinger Equation for a conservative system (note that units on both sides are energy): E x x t f dt d t f i x t f t f dt d x i t f x t f x dt d i t x t x dt d i ) ( ) ( 1 ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) , ( ) , ( H H H H Time-independent Schr. Eqn: H (x) = E (x) H-like atom: a single electron bound by a nucleus, V(r) = -Ze 2 /4  o r H ( r, , ) = 2 2 2 m ( r, , ) (Ze 2 /4  o r) ( r, , ) = E ( r, , ) We get atomic orbitals: (r, , )= R n,l (r)Y l,m ( , ) (n = 1, 2, …; l = 0, …, n 1, etc.) And the eigenvalues: E n = R H /n 2 But, from the time-dependent Schr. Eqn., we also have f(t) = exp( iE n t/ )
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nlm ( x , t) = nlm (r, , ) f(t) E total = E trans R H /n 2 ; ( X, x ) = trans ( X) e (r, , ) Spectroscopy- Interaction between light and matter Chapter 2 of Hollas: Interaction of E-M radiation with atoms and molecules Part 1. The absorption and emission of radiation Additional References G.M. Barrow, Introduction to Molecular Spectroscopy Pages 61 - 70 J.D. Graybeal, Molecular Spectroscopy Pages 181 - 190 Linearly polarized light: E and B fields in phase, propagating orthogonally. Propagating in x direction, E
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C566lecture1_000 - C566 Master Lecture Notes Lecture 1...

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