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

Chemistry

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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

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Concept explainers

Quantum Chemistry

Quantum chemistry deals with the properties of chemical systems and their reactions. The branch of chemistry which is more concerned with quantum chemistry is physical chemistry. It is a more sophisticated field of theoretical physics which is concerned towards the application of physical concepts towards various chemical aspects such as, formation of atoms, chemical structure descriptions, chemical bond strength, hybridization, conjugation etc. Quantum chemistry mainly studies the various states i.e., ground state, excited state, transition states of the individual atoms or molecules taking place during any chemical reaction. The laws of motion explained by various scientists, which are termed as “classical mechanics” were not acceptable in terms of electrons, protons, atoms, light etc. Thus, a new theory named “quantum mechanics” emerged to understand the basic framework of various atomic and subatomic particles.

Question

100%

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.

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