Full set of Notes with Fill-Ins - San Jose State University

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This came out a bit tedious again.Chem 155 Unit 10 Page 180 of 316We need a coherent section with the layer-bylayerapproach.The whole derivation needs to be scrapped.Extinction Cross Section Exercise:Relate the cross-section “a” to the molar extinctioncoefficient, ε, in Beer’s law. Use this to answer thequestion: can the absorption cross section of amolecule be bigger than the molecule itself?Beer’s law: A = εbC = -Log(P/Po)Basic theory: P = Po⋅exp(-aNx)Recall: Ln(x) = 2.303Log(x)Molar : C = N(cm -3 )(1000cm 3 /L)/(6.023⋅10 23 /mol) =C = 1000 N / N A1. Let x = b (the full path length), solve for aNb,convert to Log from Ln.P = Po exp(-aNb)ln(P/Po) = -aNbaNb = -ln(P/Po) = -2.303Log(P/Po)2. Substitute εbC for –Log(P/Po)aNb = 2.303εbC3. Substitute 1000 N / N A for C, cancel terms, solvefor ε.aNb = 2.303εb (1000 N / N A )aNb = 2.303εb (1000 N / N A )a = 2303 ε / N APage 180 of 316
Chem 155 Unit 10 Page 181 of 3164. Is the light absorption cross section “a” bigger orsmaller than the physical size of the proteinβ-phycoerythrin, a 240,000g/mol protein withε = 2.4x10 6 M -1 cm -1 at λ = 540nm?The physical size of this protein is probably 10 nm(diameter).Recall that a has the dimensions of cm 2a = 2303 ε / N Aa = 2303 (2.4x10 6 ) / 6.02x10 23 = 9.2x10 -15 cm²size ~ a 1/2 = 9.5x10 -8 cm = 0.95 nmPage 181 of 316
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Full set of Notes with Fill-Ins - San Jose State University

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