Ch1b08Lecture02

Ch1b08Lecture02 - 1 2 For allowed absorption or emission...

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Unformatted text preview: 1 2 For allowed absorption or emission processes, what determines absorption or emission intensity? Absorbance or emission , cm-1 , s-1 , or eVs Answer: Many things, but we will only discuss degeneracies 3 Degeneracies & Populations of Quantum Levels E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 7 particle in a box systems at temperature T The lowest energy state is the ground state An electron in this state can be spin up or spin down these two possibilities imply that the degeneracy of the ground state is 2. We say that g 1 = 2, where 1 means we are referring to the n= 1 quantum state. 4 Degeneracies & Populations of Quantum Levels E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 1 E 2 E 3 E 7 particle in a box systems at temperature T If we have a statistical number (more than the 7 shown) PiBox systems. At temperature T, what fraction of these systems have an electron in the n=2 state? 5 E 1 E 2 E 1 E 2 h = E 2 E 1 h = 6.626e-34 Js (kg m 2 s-1 ) = Plancks constant k B = 1.381e-23 JK-1 T = temperature (in K) For an energy level E k , the population of that level (for the case above, the probability that that level is occupied) is given by: T k E k k B k e g n Degeneracies & Populations of Quantum Levels This exponential function leads to what is called a Boltzmann distribution very important in many fields Chem Eng; Chem; Physics; Astronomy, (even Biology) etc. 6 Boltzmann Distributions Ludwig Boltzmann (shown here smiling) Molecular velocity, energy level, etc. 7 E 1 E 2 E 1 E 2 h = E 2 E 1 h = 6.626e-34 Js (kg m 2 s-1 ) = Plancks constant k B = 1.381e-23 JK-1 T = temperature (in K) A more relevant number is the population ratio between the ground and excited states, since this is what is typically measured: T k E B e g g n n = " ' " ' Degeneracies & Populations of Quantum Levels k B T at 298K 200 cm-1 If we plotted this for all of the states n of energy E n , we would have the Boltzmann distribution 8 h = 6.626e-34 Js (kg m 2 s-1 ) = Plancks constant k B = 1.381e-23 JK-1 T = temperature (in K) T k E B e g g n n = " ' " ' Rotational energy levels separated by a few cm-1 s ground and several higher (excited) levels will be populated at room T Vibrational energy levels 10 2-10 3 cm-1 s mostly just the ground state is populated at room T Electronic energy levels 10 4-10 5 cm-1 s pretty much only ground state is populated at room T k B T at 298K 200 cm-1 Degeneracies & Populations of Quantum Levels 9 Here is a pretty good problem to work out: Take a particle-in-a-1D-box system, at room temperature, in which the particle is an electron,...
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This note was uploaded on 06/05/2008 for the course CH 1a taught by Professor Lewis during the Winter '08 term at Caltech.

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Ch1b08Lecture02 - 1 2 For allowed absorption or emission...

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