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 16.35E
Interpretation Introduction

Interpretation:

The ESR spectrum for the ND2 radical at a magnetic field of 3482gauss is to be stated.

Concept introduction:

The full form of ESR spectroscopy is electron-spin resonance spectroscopy. The ESR spectroscopy is used to observe those materials which contain unpaired electrons. ESR spectroscopy also works like NMR spectroscopy, but, in ESR, electron spin in spite of atomic nuclei spin gets excited.

Expert Solution & Answer
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Answer to Problem 16.35E

The ESR spectrum for the ND2 radical at a magnetic field of 3482gauss has 7 hyperfine absorptions at the values 3716gauss, 3638gauss, 3560gauss, 3482gauss, 3404gauss, 3326gauss and 3248gauss.

Explanation of Solution

The spin value of I(D) or I(2H) is 1.

The number of H atom is 2.

The spin value of I(N) is 1.

The number of N atom is 1.

The given hyperfine coupling constant a for deuterium, D is 78gauss.

The given magnetic field is 3482gauss.

The value of total mI for ND2 is (1)(2)+(1)(1)=3.

The expression that is use to calculate the ESR signals of the ND2 radical is given below.

Numberofsignal=2mI+1…(1)

Where,

mI is the total spin value.

Substitute the value of total spin values and number of atoms of N and D in equation (1).

Numberofsignal=2×(1)(2)+1+2×(1)(1)+1=5+3=7

So, the total signal of ND2 radical is 7.

Thus, the value of mI for ND2 varies from +3 to 3.

The value of BLocalenvironemnt for different values of mI=+3 is calculated by formula given below.

BLocalenvironemnt=BMagfield+amI…(1)

Where,

BMagfield is the magnetic field.

a is the hyperfine coupling constant.

Substitute the values BMagfield and a in equation (1).

BLocalenvironemnt=3482gauss+78gauss×3=3716gauss

The value of BLocalenvironemnt for different values of mI=+2 is calculated by formula given below.

Substitute the values BMagfield and a in equation (1).

BLocalenvironemnt=3482gauss+78gauss×2=3638gauss

The value of BLocalenvironemnt for different values of mI=+1 is calculated by formula given below.

Substitute the values BMagfield and a in equation (1).

BLocalenvironemnt=3482gauss+78gauss×1=3560gauss

The value of BLocalenvironemnt for different values of mI=0 is calculated by formula given below.

Substitute the values BMagfield and a in equation (1).

BLocalenvironemnt=3482gauss+78gauss×0=3482gauss

The value of BLocalenvironemnt for different values of mI=1 is calculated by formula given below.

Substitute the values BMagfield and a in equation (1).

BLocalenvironemnt=3482gauss+78gauss×1=3404gauss

The value of BLocalenvironemnt for different values of mI=2 is calculated by formula given below.

Substitute the values BMagfield and a in equation (1).

BLocalenvironemnt=3482gauss+78gauss×2=3326gauss

The value of BLocalenvironemnt for different values of mI=3 is calculated by formula given below.

Substitute the values BMagfield and a in equation (1).

BLocalenvironemnt=3482gauss+78gauss×3=3248gauss

Therefore, the ESR spectrum for the ND2 radical at a magnetic field of 3482gauss contains the 7 hyperfine absorptions at the values 3716gauss, 3638gauss, 3560gauss, 3482gauss, 3404gauss, 3326gauss and 3248gauss.

Conclusion

The ESR spectrum for the ND2 radical at a magnetic field of 3482gauss has 7 hyperfine absorptions at the values 3716gauss, 3638gauss, 3560gauss, 3482gauss, 3404gauss, 3326gauss and 3248gauss.

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