Give the equation for quantum yield j.rate of formation of the singlet staterate of ith decay mechanismrate of ith decay mechanismrate of removal of the singlet staterate of ith decay mechanismrate of formation of the singlet staterate of removal of the singlet staterate of ith decay mechanismStep 4 of 6Give the quantum yield ;. (Use the following as necessary: kj, k1, k2, k3, and t.)k1 + k, + k=ki3k1 + k2 + k3Recalling the relationship between the overall rate constant, k, and the mean lifetime, T, give the quantum yield D; in terms of T and Tj. (Use the following as necessary: T and T;)iStep 5 of 6(c) If T1 = 1×10-7 s, T2 = 4x10-8 s, and T3 =1x10-8 s, calculate the lifetime of the singlet state and the quantum yield for the path that has T2. (Enter an unrounded value with at least 3 digits.)1using the equation given in (b).Calculate= 7.407e-9s-1Solve for T, the lifetime of the singlet state.T =.185175X SSubmit Suppose that an excited singlet, S1, can be deactivated by three different mechanisms whose rate constants are k1, k2, and k3. The rate of decay is given by -d[S1]/dt = (k1 + k2 + k3)[S1].(a) If t is the mean lifetime, that is, the time required for [S1] to decrease to 1/e0.368 of the original value, show that (k1 + k2 + k3)T = 1.(b) The overall rate constant, k, is given by the equation below.1= k = k1 + k2 + k3 =T11++T21T3Show that the quantum yield ; is given bykjkiTiwhere i denotes the ith decay mechanism.(c) If T1 = 1×10-7S, T2 = 4×10-8s, and T3 = 1×10-8s, calculate the lifetime of the singlet state and the quantum yield for the path that has T2.Step 1 of 6(a) If T is the mean lifetime, that is, the time required for [S1] to decrease to 1/e or 0.368 of the original value, show that (k, + kɔ + k3)T = 1.Give the integrated rate law. (Use the following as necessary: k1, k2, k3, and t.)(k1 +kg +k3)ª[S1]t = [S1]o ·ee-(ki+k2+k3)tStep 2 of 6We are given the relationship between [S1]t and [S1]o, when t = T.Set this equation equal to the equation from Step 1 and solve for t = t. (Use the following as necessary: k1, k2, and k3.)(k1 + k2 + k3)T =Step 3 of 6(b) The overall rate constant, k, is given by the equation below.11= k = k1 + k2 + k3 =T11++T21T3Show that the quantum yield ; is given bykiO; ==where i denotes the ith decay mechanism.

Answered: Image /qna-images/answer/9c65419b-0278-46e1-a7e9-1454764ea40a.jpg

(c) If T, = 1x10-7 s, T, = 4x 10-8 s, and T3 = 1x10-8 s, calculate the lifetime of the singlet state and the quantum yield for the path that has T7. (Enter an unrounded value with at least 3 digits.) Calculate using the equation given in (b). = 7.407e-9 X s-1 Solve for T, the lifetime of the singlet state. T=.185175

(c) If T, = 1x10-7 s, T, = 4x 10-8 s, and T3 = 1x10-8 s, calculate the lifetime of the singlet state and the quantum yield for the path that has T7. (Enter an unrounded value with at least 3 digits.) Calculate using the equation given in (b). = 7.407e-9 X s-1 Solve for T, the lifetime of the singlet state. T=.185175

Principles of Instrumental Analysis

7th Edition

ISBN:9781305577213

Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch

Publisher:Douglas A. Skoog, F. James Holler, Stanley R. Crouch

Chapter21: Surface Characterization By Spectroscopy And Microscopy

Section: Chapter Questions

Problem 21.4QAP

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