Lec17_drobny_11-1 - Lecture 17: The Hydrogen Atom Reading:...

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Lecture 17: The Hydrogen Atom • Reading: Zumdahl 12.7-12.9 • Recommended Problems: 12.5312.55, 12.57, 12.59, 12.61 • Outline – The wavefunction for the H atom – Quantum numbers and nomenclature – Orbital shapes and energies
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Summary of Particle in a Box Dimensions Energy Δ E =E n+1 -E n Momentum Wave Function Probability Line Length=a a = 12 Å
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Chromophore Problems: 1D Particle in a Box Chromophore: The portion of a molecule that strongly absorbs light, usually visible light . If visible light is absorbed, the molecular substance will be colored (complementary visible light is reFected). Conjugated chain chromophores: retinal, carotene, etc. β -carotene is a precursor of retinal, contains 11 conjugated double bonds, and 22 electrons which ±ll the ±rst 11 energy levels Calculate Δ E when an electron absorbs light and makes a transition from n=11 to n=12. Calculate the wavelength of light adsorbed. Assume β - carotene is a 20 Angstrom long box.
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Solving … • Use Δ E for particle in the box…n=11 to n=12. • Observed wavelength: λ =450nm…corresponds to a=18 Angstroms
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Particles in Flat Square Boxes Electronic properties of molecular systems can also be modeled as particles in ±at, square boxes. Another class of chromophore is a metal complex e.g. porphyrins. Porphyrins are planar metal complexes found in chlorophylls, and heme proteins like hemoglobin. A heme group in hemoglobin contains iron, binds oxygen and imparts to blood its red color. Delocalized electron transitions in such chromophores can be approximated as particles in ±at, square boxes: Note there are two quantum numbers n x and n y which express the probability of ²nding the particle at a location (x,y) and which quantize the energy. .
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Particles in Cubic Boxes
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Lec17_drobny_11-1 - Lecture 17: The Hydrogen Atom Reading:...

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