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Give the equation for the quantum yield for the path that has T2, @2: (Use the following as necessary: T, T1, T2, and T3.) Calculate the quantum yield, 02, with the given values. (Enter an unrounded value with at least 3 digits.)

Give the equation for the quantum yield for the path that has T2, @2: (Use the following as necessary: T, T1, T2, and T3.) Calculate the quantum yield, 02, with the given values. (Enter an unrounded value with at least 3 digits.)

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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where i denotes the ith decay mechanism. (c) If T1 = 1x10-7 s, Tɔ = 4×10-8 s, and T3 = 1×10-8 s, 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 (k1 + k2 + k3)T = 1. Give the integrated rate law. (Use the following as necessary: k1, k2, k3, and t.) [Si]t = [S1]o · e e-(k1+k2+k3 )t Step 2 of 6 We are given the relationship between [S1]t and [S1]o, when t = T. [Si]7 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 = 1 Step 3 of 6 (b) The overall rate constant, k, is given by the equation below. 1 = k = k1 + k2 + k3 = T1 1 T2 T3 Show that the quantum yield ¤; is given by ki O; = ki Ti where i denotes the ith decay mechanism. Give the equation for quantum yield Þj. rate of formation of the singlet state O; = rate of ith decay mechanism rate of ith decay mechanism rate of removal of the singlet state 2 Dj = rate of ith decay mechanism rate of formation of the singlet state O D; =
Transcribed Image Text:where i denotes the ith decay mechanism. (c) If T1 = 1x10-7 s, Tɔ = 4×10-8 s, and T3 = 1×10-8 s, 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 (k1 + k2 + k3)T = 1. Give the integrated rate law. (Use the following as necessary: k1, k2, k3, and t.) [Si]t = [S1]o · e e-(k1+k2+k3 )t Step 2 of 6 We are given the relationship between [S1]t and [S1]o, when t = T. [Si]7 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 = 1 Step 3 of 6 (b) The overall rate constant, k, is given by the equation below. 1 = k = k1 + k2 + k3 = T1 1 T2 T3 Show that the quantum yield ¤; is given by ki O; = ki Ti where i denotes the ith decay mechanism. Give the equation for quantum yield Þj. rate of formation of the singlet state O; = rate of ith decay mechanism rate of ith decay mechanism rate of removal of the singlet state 2 Dj = rate of ith decay mechanism rate of formation of the singlet state O D; =
rate of ith decay mechanism rate of removal of the singlet state rate of ith decay mechanism rate of formation of the singlet state O P; = rate of removal of the singlet state rate of ith decay mechanism Step 4 of 6 Give the quantum yield D;. (Use the following as necessary: ki, k1, k2, k3, and t.) O; = k1 + k, + k ki 3 ki + k2 + k3 Recalling the relationship between the overall rate constant, k, and the mean lifetime, T, give the quantum yield ; in terms of T and tj. (Use the following as necessary: T and T;) Ф i Step 5 of 6 (c) If T1 = 1×10¬/ s, T2 = 4×10-8 s, and T3 = 1×10-8 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.) 1 using the equation given in (b). Calculate = 135e6 135000000| s-1 Solve for T, the lifetime of the singlet state. T = 7.407e-9 7.40740740740741e-09 s Step 6 of 6 Give the equation for the quantum yield for the path that has T2, P2. (Use the following as necessary: T, T1, T2, and T3.) Calculate the quantum yield, P2, with the given values. (Enter an unrounded value with at least 3 digits.) .185
Transcribed Image Text:rate of ith decay mechanism rate of removal of the singlet state rate of ith decay mechanism rate of formation of the singlet state O P; = rate of removal of the singlet state rate of ith decay mechanism Step 4 of 6 Give the quantum yield D;. (Use the following as necessary: ki, k1, k2, k3, and t.) O; = k1 + k, + k ki 3 ki + k2 + k3 Recalling the relationship between the overall rate constant, k, and the mean lifetime, T, give the quantum yield ; in terms of T and tj. (Use the following as necessary: T and T;) Ф i Step 5 of 6 (c) If T1 = 1×10¬/ s, T2 = 4×10-8 s, and T3 = 1×10-8 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.) 1 using the equation given in (b). Calculate = 135e6 135000000| s-1 Solve for T, the lifetime of the singlet state. T = 7.407e-9 7.40740740740741e-09 s Step 6 of 6 Give the equation for the quantum yield for the path that has T2, P2. (Use the following as necessary: T, T1, T2, and T3.) Calculate the quantum yield, P2, with the given values. (Enter an unrounded value with at least 3 digits.) .185
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