Physical Chemistry
Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
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Chapter 11, Problem 11.73E

What are the values of E , L , and L z for an F 8 + atom whose electron has the following wavefunctions, listed as Ψ n , l , m l ? (a) Ψ 1 , 0 , 0 (b) Ψ 3 , 2 , 2 (c) Ψ 2 , 1 , 1 (d) Ψ 9 , 6 , 3 .

Expert Solution
Check Mark
Interpretation Introduction

(a)

Interpretation:

The values of E, L, and Lz for an F8+ atom for the given wavefunctions are to be calculated.

Concept introduction:

In quantum mechanics, the wavefunction is given by Ψ. The wavefunction contains all the information about the state of the system. The wavefunction is the function of the coordinates of the particles and time.

Answer to Problem 11.73E

The value of E, L, and Lz for an F8+ atom for the given wavefunctions are 1.76×1016J, 0 and 0 respectively.

Explanation of Solution

The energy for the given wave function is given by the formula,

E=Z2e4μ8ε02h2n2(1)

Where,

Z is the atomic number.

E is the charge on electron.

μ is the reduced mass.

n is the number of shell.

The total angular momentum is calculated by the formula,

L=l(l+1)(2)

Where,

l is the angular momentum.

The Lz is calculated by the formula,

Lz=ml(3)

Where,

ml is the magnetic quantum number.

The given wavefunctions for electron of F8+ atom is Ψ1,0,0. Therefore, the value of n, l and ml is 1, 0 and 0 respectively.

Substitute the value of n, Z=9 for F8+ in equation (1).

E=(9)2(1.602×1019)4(9.1×1031)8(8.85×1012)2(6.626×1034)2(1)2=4854.857×1010727509.290×1092J=1.76×1016J

Thus, the value of E is 1.76×1016J.

Substitute the value of l in equation (2).

L=0(0+1)L=0

Thus, the value of L is 0.

Substitute the value of ml in equation (3).

Lz=0×=0

Thus, the value of Lz is 0.

Hence, the value of E, L, and Lz for an F8+ atom for the given wavefunctions are 1.76×1016J, 0 and 0 respectively.

Conclusion

The value of E, L, and Lz for an F8+ atom for the given wavefunctions are 1.76×1016J, 0 and 0 respectively.

Expert Solution
Check Mark
Interpretation Introduction

(b)

Interpretation:

The values of E, L, and Lz for an F8+ atom for the given wavefunctions are to be calculated.

Concept introduction:

In quantum mechanics, the wavefunction is given by Ψ. The wavefunction contains all the information about the state of the system. The wavefunction is the function of the coordinates of the particles and time.

Answer to Problem 11.73E

The value of E, L, and Lz for an F8+ atom for the given wavefunctions are 1.96×1017J, 6 and 2 respectively.

Explanation of Solution

The energy for the given wave function is given by the formula,

E=Z2e4μ8ε02h2n2(1)

Where,

Z is the atomic number.

E is the charge on electron.

μ is the reduced mass.

n is the number of shell.

The total angular momentum is calculated by the formula,

L=l(l+1)(2)

Where,

l is the angular momentum.

The Lz is calculated by the formula,

Lz=ml(3)

Where,

ml is the magnetic quantum number.

The given wavefunctions for electron of F8+ atom is Ψ3,2,2. Therefore, the value of n, l and ml is 3, 2 and 2 respectively.

Substitute the value of n, Z=9 for F8+ in equation (1).

E=(9)2(1.602×1019)4(9.1×1031)8(8.85×1012)2(6.626×1034)2(3)2=1.96×1017J

Thus, the value of E is 1.96×1017J.

Substitute the value of l in equation (2).

L=2(2+1)L=6

Thus, the value of L is 6.

Substitute the value of ml in equation (3).

Lz=2×=2

Thus, the value of Lz is 2.

Hence, the value of E, L, and Lz for an F8+ atom for the given wavefunctions are 1.96×1017J, 6 and 2 respectively.

Conclusion

The value of E, L, and Lz for an F8+ atom for the given wavefunctions are 1.96×1017J, 6 and 2 respectively.

Expert Solution
Check Mark
Interpretation Introduction

(c)

Interpretation:

The values of E, L, and Lz for an F8+ atom for the given wavefunctions are to be calculated.

Concept introduction:

In quantum mechanics, the wavefunction is given by Ψ. The wavefunction contains all the information about the state of the system. The wavefunction is the function of the coordinates of the particles and time.

Answer to Problem 11.73E

The value of E, L, and Lz for an F8+ atom for the given wavefunctions are 4.41×1017J, 2 and respectively.

Explanation of Solution

The energy for the given wave function is given by the formula,

E=Z2e4μ8ε02h2n2(1)

Where,

Z is the atomic number.

E is the charge on electron.

μ is the reduced mass.

n is the number of shell.

The total angular momentum is calculated by the formula,

L=l(l+1)(2)

Where,

l is the angular momentum.

The Lz is calculated by the formula,

Lz=ml(3)

Where,

ml is the magnetic quantum number.

The given wavefunctions for electron of F8+ atom is Ψ2,1,1. Therefore, the value of n, l and ml is 2, 1 and 1 respectively.

Substitute the value of n, Z=9 for F8+ in equation (1).

E=(9)2(1.602×1019)4(9.1×1031)8(8.85×1012)2(6.626×1034)2(2)2=4.41×1017J

Thus, the value of E is 4.41×1017J.

Substitute the value of l in equation (2).

L=1(1+1)L=2

Thus, the value of L is 2.

Substitute the value of ml in equation (3).

Lz=1×=

Thus, the value of Lz is .

Hence, the value of E, L, and Lz for an F8+ atom for the given wavefunctions are 4.41×1017J, 2 and respectively.

Conclusion

The value of E, L, and Lz for an F8+ atom for the given wavefunctions are 4.42×1017J, 2 and respectively.

Expert Solution
Check Mark
Interpretation Introduction

(d)

Interpretation:

The values of E, L, and Lz for an F8+ atom for the given wavefunctions are to be calculated.

Concept introduction:

In quantum mechanics, the wavefunction is given by Ψ. The wavefunction contains all the information about the state of the system. The wavefunction is the function of the coordinates of the particles and time.

Answer to Problem 11.73E

The value of E, L, and Lz for an F8+ atom for the given wavefunctions are 2.18×1018J, 42 and 3 respectively.

Explanation of Solution

The energy for the given wave function is given by the formula,

E=Z2e4μ8ε02h2n2(1)

Where,

Z is the atomic number.

E is the charge on electron.

μ is the reduced mass.

n is the number of shell.

The total angular momentum is calculated by the formula,

L=l(l+1)(2)

Where,

l is the angular momentum.

The Lz is calculated by the formula,

Lz=ml(3)

Where,

ml is the magnetic quantum number.

The given wavefunctions for electron of F8+ atom is Ψ9,6,3. Therefore, the value of n, l and ml is 9, 6 and 3 respectively.

Substitute the value of n, Z=9 for F8+ in equation (1).

E=(9)2(1.602×1019)4(9.1×1031)8(8.85×1012)2(6.626×1034)2(9)2=2.18×1018J

Thus, the value of E is 2.18×1018J.

Substitute the value of l in equation (2).

L=6(6+1)L=42

Thus, the value of L is 42.

Substitute the value of ml in equation (3).

Lz=3×=3

Thus, the value of Lz is 3.

Hence, the value of E, L, and Lz for an F8+ atom for the given wavefunctions are 2.18×1018J, 42 and 3 respectively.

Conclusion

The value of E, L, and Lz for an F8+ atom for the given wavefunctions are 2.18×1018J, 42 and 3 respectively.

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