Physical Chemistry
Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
Question
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Chapter 16, Problem 16.22E
Interpretation Introduction

(a)

Interpretation:

The spin and number of equivalent nuclei required to produce the given ESR spectrum are to be stated.

Concept introduction:

Electron spin resonance is the method to study the materials with an unpaired electron. An unpaired electron absorbs the microwave radiation under the strong magnetic field. The difference between two energy levels is calculated by the formula shown below.

ΔEmag=geμBB

Expert Solution
Check Mark

Answer to Problem 16.22E

The spin and number of equivalent nuclei required to produce the given ESR spectrum are 12 and 1 respectively.

Explanation of Solution

The give ESR spectrum is shown below.

Physical Chemistry, Chapter 16, Problem 16.22E , additional homework tip  1

Figure 1

The number of spins in the ESR spectrum is shown below.

number of signals=Πi=numberof atoms2NiIi+1…(1)

Where,

Ni is the number of equivalent nuclei ith atom.

I is the nuclear spin of equivalent nuclei ith atom.

The total number of signal in the given ESR spectrum is 3.

Three different peaks with same intensity indicate that 2 nuclei are present of the same atom and have of nuclear spin are present.

Substitute the values of N and number of signal in the equation (1).

3=2(1)I+1+2(1)I3=4I+12=4I

The above equation is further simplified for the value of I as shown below.

I=12

Therefore, the spin and number of equivalent nuclei required to produce the given ESR spectrum are 12 and 1 respectively.

Conclusion

The spin and number of equivalent nuclei required to produce the given ESR spectrum are 12 and 1 respectively.

Interpretation Introduction

(b)

Interpretation:

The spin and number of equivalent nuclei required to produce the given ESR spectrum are to be stated.

Concept introduction:

Electron spin resonance is the method to study the materials with an unpaired electron. An unpaired electron absorbs the microwave radiation under the strong magnetic field. The difference between two energy levels is calculated by the formula shown below.

ΔEmag=geμBB

Expert Solution
Check Mark

Answer to Problem 16.22E

The spin and number of equivalent nuclei required to produce the given ESR spectrum are 12 and 2 respectively.

Explanation of Solution

The give ESR spectrum is shown below.

Physical Chemistry, Chapter 16, Problem 16.22E , additional homework tip  2

Figure 2

The number of spins in the ESR spectrum is shown below.

number of signals=Πi=numberof atoms2NiIi+1…(1)

Where,

Ni is the number of equivalent nuclei ith atom.

I is the nuclear spin of equivalent nuclei ith atom.

The total number of signal in the given ESR spectrum is 3.

Three peaks with different intensities indicate that two equivalent nuclei are present.

Substitute the values of N and number of signal in the equation (1).

3=2(2)I+13=4I+12=4I

The above equation is further simplified for the value of I as shown below.

I=12

Therefore, spin and number of equivalent nuclei required to produce the given ESR spectrum are 12 and 2 respectively.

Conclusion

The spin and number of equivalent nuclei required to produce the given ESR spectrum are 12 and 2 respectively.

Interpretation Introduction

(c)

Interpretation:

The spin and number of equivalent nuclei required to produce the given ESR spectrum are to be stated.

Concept introduction:

Electron spin resonance is the method to study the materials with an unpaired electron. An unpaired electron absorbs the microwave radiation under the strong magnetic field. The difference between two energy levels is calculated by the formula shown below.

ΔEmag=geμBB

Expert Solution
Check Mark

Answer to Problem 16.22E

The spin and number of equivalent nuclei required to produce the given ESR spectrum are 12 and 1 respectively.

Explanation of Solution

The give ESR spectrum is shown below.

Physical Chemistry, Chapter 16, Problem 16.22E , additional homework tip  3

Figure 3

The number of spins in the ESR spectrum is shown below.

number of signals=Πi=numberof atoms2NiIi+1…(1)

Where,

Ni is the number of equivalent nuclei ith atom.

I is the nuclear spin of equivalent nuclei ith atom.

The total number of signal in the given ESR spectrum is 5.

Five different peaks with same intensity represents that 4 nuclei are present of the same atom and have of nuclear spin are present.

Substitute the values of N and number of signal in the equation (1).

5=2(1)I+1+2(1)I+1+2(1)I+1+2(1)I+15=8I+14=8I

The above equation is further simplified for the value of I as shown below.

I=12

The spin and number of equivalent nuclei required to produce the given ESR spectrum are 12 and 1 respectively.

Conclusion

The spin and number of equivalent nuclei required to produce the given ESR spectrum are 12 and 1 respectively.

Interpretation Introduction

(d)

Interpretation:

The spin and number of equivalent nuclei required to produce the given ESR spectrum are to be stated.

Concept introduction:

Electron spin resonance is the method to study the materials with an unpaired electron. An unpaired electron absorbs the microwave radiation under the strong magnetic field. The difference between two energy levels is calculated by the formula shown below.

ΔEmag=geμBB

Expert Solution
Check Mark

Answer to Problem 16.22E

The spin and number of equivalent nuclei required to produce the given ESR spectrum are 12 and 4 respectively.

Explanation of Solution

The give ESR spectrum is shown below.

Physical Chemistry, Chapter 16, Problem 16.22E , additional homework tip  4

Figure 4

The number of spins in the ESR spectrum is shown below.

number of signals=Πi=numberof atoms2NiIi+1…(1)

Where,

Ni is the number of equivalent nuclei ith atom.

I is the nuclear spin of equivalent nuclei ith atom.

The total number of signal in the given ESR spectrum is 5.

Five different peaks with different intensities indicate that four equivalent nuclei are present.

Substitute the values of N and number of signal in the equation (1).

5=2(4)I+15=8I+14=8I

The above equation is further simplified for the value of I as shown below.

I=12

Therefore, the spin and number of equivalent nuclei required to produce the given ESR spectrum are 12 and 4 respectively.

Conclusion

The spin and number of equivalent nuclei required to produce the given ESR spectrum are 12 and 4 respectively.

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Students have asked these similar questions
6 of 15 Based on their corresponding nuclear spin number (reported within brackets), determine which of the following nuclei can be studied by NMR spectroscopy. Choose all correct answers. Please, be aware that incorrect answers will result in negative scores. O Nitrogen: 14N(1) O Fluorine: 19F(1/2) O Oxygen: 160(0) O Deuterium: 2H(1) O Carbon: 12c(0) O Proton: 'H(1/2) O Carbon 13: 13C(1/2) O Nitrogen 15: 15N(1/2)
True or False : The difference in energy, ΔE, between alfa (+1/2) and beta (–1/2) spin states of a proton is independent of the strength of the applied magnetic field. Could you explain detail?
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