(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

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Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Give the equation for quantum yield j.
rate of formation of the singlet state
rate of ith decay mechanism
rate of ith decay mechanism
rate of removal of the singlet state
rate of ith decay mechanism
rate of formation of the singlet state
rate of removal of the singlet state
rate of ith decay mechanism
Step 4 of 6
Give the quantum yield ;. (Use the following as necessary: kj, k1, k2, k3, and t.)
k1 + k, + k
=
ki
3
k1 + k2 + k3
Recalling 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;)
i
Step 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.)
1
using the equation given in (b).
Calculate
= 7.407e-9
s-1
Solve for T, the lifetime of the singlet state.
T =
.185175
X S
Submit
Transcribed Image Text:Give the equation for quantum yield j. rate of formation of the singlet state rate of ith decay mechanism rate of ith decay mechanism rate of removal of the singlet state rate of ith decay mechanism rate of formation of the singlet state rate of removal of the singlet state rate of ith decay mechanism Step 4 of 6 Give the quantum yield ;. (Use the following as necessary: kj, k1, k2, k3, and t.) k1 + k, + k = ki 3 k1 + k2 + k3 Recalling 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;) i Step 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.) 1 using the equation given in (b). Calculate = 7.407e-9 s-1 Solve for T, the lifetime of the singlet state. T = .185175 X S Submit
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/e
0.368 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 =
T1
1
+
+
T2
1
T3
Show that the quantum yield ; is given by
kj
ki
Ti
where i denotes the ith decay mechanism.
(c) If T1 = 1×10-7
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.
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 ·
e
e-(ki+k2+k3)t
Step 2 of 6
We 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.
1
1
= k = k1 + k2 + k3 =
T1
1
+
+
T2
1
T3
Show that the quantum yield ; is given by
ki
O; =
=
where i denotes the ith decay mechanism.
Transcribed Image Text: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/e 0.368 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 = T1 1 + + T2 1 T3 Show that the quantum yield ; is given by kj ki Ti where i denotes the ith decay mechanism. (c) If T1 = 1×10-7 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. 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 · e e-(ki+k2+k3)t Step 2 of 6 We 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. 1 1 = k = k1 + k2 + k3 = T1 1 + + T2 1 T3 Show that the quantum yield ; is given by ki O; = = where i denotes the ith decay mechanism.
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