Bundle: Physical Chemistry, 2nd + Student Solutions Manual
Bundle: Physical Chemistry, 2nd + Student Solutions Manual
2nd Edition
ISBN: 9781285257594
Author: David W. Ball
Publisher: Cengage Learning
Question
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Chapter 16, Problem 16.43E
Interpretation Introduction

(a)

Interpretation:

The diagram that represents the z components of nuclear spin for 1H(I=12) is to be drawn.

Concept introduction:

Nuclear spin shows the complete angular momentum corresponding to the nucleus. It is represented by I. The nucleus consists of protons and neutrons. It depends on the mass number of a nucleus. The odd mass number shows that the nucleus has half-integer spin like an electron. The even mass number shows that the nucleus has integer spin.

Expert Solution
Check Mark

Answer to Problem 16.43E

The diagram that represents the z components of nuclear spin for 1H(I=12) is shown below.

Bundle: Physical Chemistry, 2nd + Student Solutions Manual, Chapter 16, Problem 16.43E , additional homework tip  1

Explanation of Solution

The z component of nuclear spin is given by the formula shown below.

Lz=mI…(1)

Where,

mI is the magnetic quantum number.

The value of mI is given by the formula shown below.

ImI+I

The value of I for 1H is given as 12. Therefore, the possible values of mI for 1H are

 12, 0 and  +12.

Substitute value of mI=12 for 1H in equation (1).

Lz= 12

Substitute value of mI=0 for 1H in equation (1).

Lz= 0

Substitute value of mI=12 for 1H in equation (1).

Lz= +12

Therefore, the Lz values for 1H are  12, 0 and  +12.

The diagram that represents the z components of nuclear spin for 1H(I=12) is shown below.

Bundle: Physical Chemistry, 2nd + Student Solutions Manual, Chapter 16, Problem 16.43E , additional homework tip  2

Figure 1

Conclusion

The diagram that represents the z components of nuclear spin for 1H(I=12) is shown in Figure 1.

Interpretation Introduction

(b)

Interpretation:

The diagram that represents the z components of nuclear spin for 35Cl(I=32) is to be drawn.

Concept introduction:

Nuclear spin shows the complete angular momentum corresponding to the nucleus. It is represented by I. The nucleus consists of protons and neutrons. It depends on the mass number of a nucleus. The odd mass number shows that the nucleus has half-integer spin like an electron. The even mass number shows that the nucleus has integer spin.

Expert Solution
Check Mark

Answer to Problem 16.43E

The diagram that represents the z components of nuclear spin for 35Cl(I=32) is shown below.

Bundle: Physical Chemistry, 2nd + Student Solutions Manual, Chapter 16, Problem 16.43E , additional homework tip  3

Explanation of Solution

The z component of nuclear spin is given by the formula shown below.

Lz=mI…(1)

Where,

mI is the magnetic quantum number.

The value of mI is given by the formula shown below.

ImI+I

The value of I for 35Cl is given as 32. Therefore, the possible values of mI for 35Cl are 32,  12, 0,  +12 and +32.

Substitute value of mI=32 for 35Cl in equation (1).

Lz= 32

Substitute value of mI=12 for 35Cl in equation (1).

Lz= 12

Substitute value of mI=0 for 35Cl in equation (1).

Lz= 0

Substitute value of mI=+12 for 35Cl in equation (1).

Lz= +12

Substitute value of mI=+32 for 35Cl in equation (1).

Lz= +32

Therefore, the Lz values for 35Cl are 32,  12, 0,  +12 and +32.

The diagram that represents the z components of nuclear spin for 35Cl(I=32) is shown below.

Bundle: Physical Chemistry, 2nd + Student Solutions Manual, Chapter 16, Problem 16.43E , additional homework tip  4

Figure 2

Conclusion

The diagram that represents the z components of nuclear spin for 35Cl(I=32) is shown in Figure 2.

Interpretation Introduction

(c)

Interpretation:

The diagram that represents the z components of nuclear spin for 118Sn(I=0) is to be drawn.

Concept introduction:

Nuclear spin shows the complete angular momentum corresponding to the nucleus. It is represented by I. The nucleus consists of protons and neutrons. It depends on the mass number of a nucleus. The odd mass number shows that the nucleus has half-integer spin like an electron. The even mass number shows that the nucleus has integer spin.

Expert Solution
Check Mark

Answer to Problem 16.43E

The diagram that represents the z components of nuclear spin for 118Sn(I=0) is shown below.

Bundle: Physical Chemistry, 2nd + Student Solutions Manual, Chapter 16, Problem 16.43E , additional homework tip  5

Explanation of Solution

The z component of nuclear spin is given by the formula shown below.

Lz=mI…(1)

Where,

mI is the magnetic quantum number.

The value of mI is given by the formula shown below.

ImI+I

The value of I for 118Sn is given as 0. Therefore, the possible value of mI for 118Sn is 0.

Substitute value of mI=0 for 118Sn in equation (1).

Lz= 0

Therefore, the Lz value for 118Sn is 0.

The diagram that represents the z components of nuclear spin for 118Sn(I=0) is shown below.

Bundle: Physical Chemistry, 2nd + Student Solutions Manual, Chapter 16, Problem 16.43E , additional homework tip  6

Figure 3

Conclusion

The diagram that represents the z components of nuclear spin for 118Sn(I=0) is shown in Figure 3.

Interpretation Introduction

(d)

Interpretation:

The diagram that represents the z components of nuclear spin for 14N(I=1) is to be drawn.

Concept introduction:

Nuclear spin is the total angular momentum of the nucleus. It is represented by I. The nucleus consists of protons and neutrons. It depends on the mass number of a nucleus. The odd mass number shows that the nucleus has half-integer spin like an electron whereas the even mass number shows that the nucleus has integer spin.

Expert Solution
Check Mark

Answer to Problem 16.43E

The diagram that represents the z components of nuclear spin for 14N(I=1) is shown below.

Bundle: Physical Chemistry, 2nd + Student Solutions Manual, Chapter 16, Problem 16.43E , additional homework tip  7

Explanation of Solution

The z component of nuclear spin is given by the formula shown below.

Lz=mI…(1)

Where,

mI is the magnetic quantum number.

The value of mI is given by the formula shown below.

ImI+I

The value of I for 14N(I=1) is given as 0. Therefore, the possible values of mI for 14N are 1, 0 and +1.

Substitute value of mI=1 for 14N in equation (1).

Lz=1

Substitute value of mI=0 for 14N in equation (1).

Lz= 0

Substitute value of mI=1 for 14N in equation (1).

Lz=+1

Therefore, the Lz values for 14N are 1, 0 and +1.

The diagram that represents the z components of nuclear spin for 14N(I=1) is shown below.

Bundle: Physical Chemistry, 2nd + Student Solutions Manual, Chapter 16, Problem 16.43E , additional homework tip  8

Figure 4

Conclusion

The diagram that represents the z components of nuclear spin for 14N(I=1) is shown in Figure 4.

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