Download Fundamentals of Spectroscopy: Understanding Molecular Interactions with Light and more Study notes Physical Chemistry in PDF only on Docsity! Spectrum
Photon energy (J)
10-12 40-14 40-18 840-18 407-29 40-22 149-24 407-28 40°28 40-39 19°32 197-34
l ] l 1 I | | 1 J |
Wavelength (m)
407% qo7 40-7 jor fo-® t0r4* 4074 1 10° 104 10° 108
| | I I i I
Gamma X rays Microwaves Radio waves
rays
Copyright © 2008 Pearson Education. Inc., publishing as Benjamin Cummings
2 Key equation in spectroscopy is 2 1h E Eω ν≡ = − Electronic> 400>30,000> 10<300Ultra violet Electronic~250~20,000~6~450Visible (blue) Electronic~160~13,000~4~700Visible (red) Vibrational< 120< 10,000< 3.0>1000Infrared Rotational< 0.1< 30< 10-2>100,000Micro wave NMR~1 x 10-4~0.01~10-6~1 x 109Radio SpectroscopyEnergy/ (kJ/mol) Wave number/ (cm-1) ν / 1014 /(Hz) λ/ (nm)Spectral Range 5 N1 (N2) atoms in lower (upper state) Absorption Spontaneous Emission Stimulated Emission E ne rg y ( ) ( )12 1 21 2 21 2B N B N A Nρ ν ρ ν= + 2 3 12 21 21 213 16 and vB B B A c π = = 3 possible processes: absorption, spontaneous emission and stimulated emission There is a spontaneous rate constant (A) that can only relax the system. The stimulated rates are driven by the strength of the light field, and the stimulated rate constants (B) for the up and down transfers are the same and proportional to the spontaneous rate constant, so they are driven by the same processes. 6 Vibrational spectroscopy transitions • Transition probability zero unless transition dipole moment not zero • At 300K, usually only n=0 (ground vibrational) state occupied. ( ) ( ) ( )* 0mnx m x nx x x dµ ψ µ ψ τ ∞ −∞ = ≠∫ 0 H1x H0 H3x H0 H5x H0 +- X Allowed transitions: ∆n=±1 n=0 to n=1 dominant transition In a molecule 3n-5 (linear) or 3n-6 (nonlinear) vibrational modes; Each mode acts as its own harmonic oscillator 7 Anharmonicity allows ∆n = ±2, ±3 (very weak). ∆E between adjacent levels not all same. V(x) xe x 0 DoDe Different level spacings don’t give rise to multiple peaks level spacing are not the same. The Morse potential is realistic potential and allows dissociation 10 m on oc hr om et er sa m pl e ce ll de te ct or light source 1000 1500 2000 2500 3000 3500 A bs or ba nc e CH4 CO 3n-6 = 9 for CH4 and 3n-5 = 1 for CO. Why is number of observed peaks different? Experimental setup and spectra 11 for diatomic molecules is ∆J = ± 1 + + + + + - - - - - time E Permanent dipole needed to couple molecular rotations to EM field. 2 0 2 B I I r π µ = = Rotational spectroscopy selection rule 12 ∆E for transitions starting at J given by ( ) ( ) ( ) ( ) ( )( ) ( ){ } ( ) ( )( ) ( ){ } 2 1 1 2 for 1 1 2 1 2 1) and for 1 1 1 2 final initial E J J hBJ J I E E J E J J E hB J J J J hB J J E hB J J J J hBJ + − = + = + ∆ = − ∆ = + ∆ = + + − + = + ∆ = − ∆ = − − + = − Rotational Energy levels 15 n=1 J=10 n=1 J=5 n=0 J=10 n=0 J=5 29002800 3000 3100 3200 Frequency (cm-1) In te ns ity 0- 1 1- 2 2- 3 3- 4 4- 5 5- 6 6- 7 7- 8 8- 9 10 -9 9 -8 8 -7 7 -6 6- 5 5- 4 4- 3 3- 2 2- 1 1- 0 Peak frequencies (equally spaced!) determined by energy level spacing. Peak intensities determined by number of molecules of originating level. Rotational-vibrational spectroscopy 1 2 1HOlight J B Jπ ν ω = + + 16 ( ) ( ) 0 2 ( 1) 2 0 0 2 1 J J J I kTJ J kTn g e J e n g ε ε−− − += = + nJ/n0 J 5 10 15 20 25 2 4 6 8 10 12 700 K 300 K 100 K 700 K 300 K 100 K CO nJ/n0 J HD 2 4 6 8 0.5 0 1.0 1.5 2.0 2.5 J value of highest intensity depends sensitively on T Reconsider IR spectra for CO and CH4 High Resolution IR Rot-Vib Spectrum of CO
Absorbance Units
0.015 0.020
L 1
0.010
1
0.005
T T T T
2050 2100 2150 2200
Wavenumber cm-1
17
