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Ch1b08Lecture02

# Ch1b08Lecture02 - 1 For `allowed absorption or emission...

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2 For ‘allowed’ absorption or emission processes, what determines absorption or emission intensity? Absorbance or emission λ , cm -1 , s -1 , or eV’s 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 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.

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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 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 h ν = E 2 – E 1 h = 6.626e-34 J·s (kg m 2 s -1 ) = Planck’s constant k B = 1.381e-23 J·K -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.

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6 Boltzmann Distributions Ludwig Boltzmann (shown here smiling) Molecular velocity, energy level, etc.