PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH)
PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH)
11th Edition
ISBN: 9780198826910
Author: ATKINS
Publisher: Oxford University Press
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Chapter 10, Problem 10B.9P

(a)

Interpretation Introduction

Interpretation:

The irreducible representation spanned by the f orbital when its radial function is multiplied by a factor z(5z23r2) has to be identified in the point group C2v.

Concept introduction:

A representative in the group theory is the mathematical operator used for the representation of the physical symmetry operation.  The set of these mathematical operators representing all the symmetry operations of the group are represented in matrix form in the group theory.  The set of all matrices representing all the symmetry operations of the group are known as a representation.

(a)

Expert Solution
Check Mark

Answer to Problem 10B.9P

The irreducible representation spanned by the f orbital when its radial function is multiplied by a factor z(5z23r2) in the point group C2v is A1.

Explanation of Solution

The character table for the C2v point group is shown below.

  C2vEC2σvσvA11111z,z2,x2,y2A21111xyRzB11111x,xzRyB21111y,yzRx

The function x2, y2, z2 and r2 are invariant for all symmetry operations.  From the character table of C2v the function z(5z23r2) transforms as z(A1).  Therefore, the irreducible representation spanned by the function z(5z23r2) is A1.

(b)

Interpretation Introduction

Interpretation:

The irreducible representation spanned by the f orbital when its radial function is multiplied by a factor y(5y23r2) has to be identified in the point group C2v.

Concept introduction:

As mentioned in the concept of introduction in part (a).

(b)

Expert Solution
Check Mark

Answer to Problem 10B.9P

The irreducible representation spanned by the f orbital when its radial function is multiplied by a factor y(5y23r2) in the point group C2v is B2.

Explanation of Solution

The character table for the C2v point group is shown below.

  C2vEC2σvσvA11111z,z2,x2,y2A21111xyRzB11111x,xzRyB21111y,yzRx

The function x2, y2, z2 and r2 are invariant for all symmetry operations.  From the character table of C2v the function y(5y23r2) transforms as y(B2).  Therefore, the irreducible representation spanned by the function y(5y23r2) is B2.

(c)

Interpretation Introduction

Interpretation:

The irreducible representation spanned by the f orbital when its radial function is multiplied by a factor x(5x23r2) has to be identified in the point group C2v.

Concept introduction:

As mentioned in the concept of introduction in part (a).

(c)

Expert Solution
Check Mark

Answer to Problem 10B.9P

The irreducible representation spanned by the f orbital when its radial function is multiplied by a factor x(5x23r2) in the point group C2v is B1.

Explanation of Solution

The character table for the C2v point group is shown below.

  C2vEC2σvσvA11111z,z2,x2,y2A21111xyRzB11111x,xzRyB21111y,yzRx

The function x2, y2, z2 and r2 are invariant for all symmetry operations.  From the character table of C2v the function x(5x23r2) transforms as x(B1).  Therefore, the irreducible representation spanned by the function x(5x23r2) is B1.

(d)

Interpretation Introduction

Interpretation:

The irreducible representation spanned by the f orbital when its radial function is multiplied by a factor z(x2y2) has to be identified in the point group C2v.

Concept introduction:

As mentioned in the concept of introduction in part (a).

(d)

Expert Solution
Check Mark

Answer to Problem 10B.9P

The irreducible representation spanned by the f orbital when its radial function is multiplied by a factor z(x2y2) in the point group C2v is A1.

Explanation of Solution

The character table for the C2v point group is shown below.

  C2vEC2σvσvA11111z,z2,x2,y2A21111xyRzB11111x,xzRyB21111y,yzRx

The function x2, y2, z2 and r2 are invariant for all symmetry operations.  From the character table of C2v the function z(x2y2) transforms as z(A1).  Therefore, the irreducible representation spanned by the function z(x2y2) is A1.

(e)

Interpretation Introduction

Interpretation:

The irreducible representation spanned by the f orbital when its radial function is multiplied by a factor y(x2z2) has to be identified in the point group C2v.

Concept introduction:

As mentioned in the concept of introduction in part (a).

(e)

Expert Solution
Check Mark

Answer to Problem 10B.9P

The irreducible representation spanned by the f orbital when its radial function is multiplied by a factor y(x2z2) in the point group C2v is B2.

Explanation of Solution

The character table for the C2v point group is shown below.

  C2vEC2σvσvA11111z,z2,x2,y2A21111xyRzB11111x,xzRyB21111y,yzRx

The function x2, y2, z2 and r2 are invariant for all symmetry operations.  From the character table of C2v the function y(x2z2) transforms as y(B2).  Therefore, the irreducible representation spanned by the function y(x2z2) is B2.

(f)

Interpretation Introduction

Interpretation:

The irreducible representation spanned by the f orbital when its radial function is multiplied by a factor x(z2y2) has to be identified in the point group C2v.

Concept introduction:

As mentioned in the concept of introduction in part (a).

(f)

Expert Solution
Check Mark

Answer to Problem 10B.9P

The irreducible representation spanned by the f orbital when its radial function is multiplied by a factor x(z2y2) in the point group C2v is B1.

Explanation of Solution

The character table for the C2v point group is shown below.

  C2vEC2σvσvA11111z,z2,x2,y2A21111xyRzB11111x,xzRyB21111y,yzRx

The function x2, y2, z2 and r2 are invariant for all symmetry operations.  From the character table of C2v the function x(z2y2) transforms as x(B1).  Therefore, the irreducible representation spanned by the function x(z2y2) is B1.

(g)

Interpretation Introduction

Interpretation:

The irreducible representation spanned by the f orbital when its radial function is multiplied by a factor xyz has to be identified in the point group C2v.

Concept introduction:

As mentioned in the concept of introduction in part (a).

(g)

Expert Solution
Check Mark

Answer to Problem 10B.9P

The irreducible representation spanned by the f orbital when its radial function is multiplied by a factor xyz in the point group C2v is A2.

Explanation of Solution

The character table for the C2v point group is shown below.

  C2vEC2σvσvA11111z,z2,x2,y2A21111xyRzB11111x,xzRyB21111y,yzRx

The function x2, y2, z2 and r2 are invariant for all symmetry operations.  From the character table of C2v the function xyz transforms as B1×B2×A1=A2.  Therefore, the irreducible representation spanned by the function xyz is A2.

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Chapter 10 Solutions

PHYSICAL CHEMISTRY. VOL.1+2 (LL)(11TH)

Ch. 10 - Prob. 10A.2AECh. 10 - Prob. 10A.2BECh. 10 - Prob. 10A.3AECh. 10 - Prob. 10A.3BECh. 10 - Prob. 10A.4AECh. 10 - Prob. 10A.4BECh. 10 - Prob. 10A.5AECh. 10 - Prob. 10A.5BECh. 10 - Prob. 10A.6AECh. 10 - Prob. 10A.6BECh. 10 - Prob. 10A.7AECh. 10 - Prob. 10A.1PCh. 10 - Prob. 10A.2PCh. 10 - Prob. 10A.3PCh. 10 - Prob. 10A.4PCh. 10 - Prob. 10A.5PCh. 10 - Prob. 10B.1DQCh. 10 - Prob. 10B.2DQCh. 10 - Prob. 10B.3DQCh. 10 - Prob. 10B.4DQCh. 10 - Prob. 10B.5DQCh. 10 - Prob. 10B.1AECh. 10 - Prob. 10B.1BECh. 10 - Prob. 10B.2AECh. 10 - Prob. 10B.2BECh. 10 - Prob. 10B.3AECh. 10 - Prob. 10B.3BECh. 10 - Prob. 10B.4AECh. 10 - Prob. 10B.4BECh. 10 - Prob. 10B.5AECh. 10 - Prob. 10B.5BECh. 10 - Prob. 10B.6AECh. 10 - Prob. 10B.6BECh. 10 - Prob. 10B.7AECh. 10 - Prob. 10B.7BECh. 10 - Prob. 10B.1PCh. 10 - Prob. 10B.2PCh. 10 - Prob. 10B.3PCh. 10 - Prob. 10B.4PCh. 10 - Prob. 10B.5PCh. 10 - Prob. 10B.6PCh. 10 - Prob. 10B.7PCh. 10 - Prob. 10B.8PCh. 10 - Prob. 10B.9PCh. 10 - Prob. 10B.10PCh. 10 - Prob. 10C.1DQCh. 10 - Prob. 10C.2DQCh. 10 - Prob. 10C.1AECh. 10 - Prob. 10C.1BECh. 10 - Prob. 10C.2AECh. 10 - Prob. 10C.2BECh. 10 - Prob. 10C.3AECh. 10 - Prob. 10C.3BECh. 10 - Prob. 10C.4AECh. 10 - Prob. 10C.4BECh. 10 - Prob. 10C.5AECh. 10 - Prob. 10C.6AECh. 10 - Prob. 10C.6BECh. 10 - Prob. 10C.7AECh. 10 - Prob. 10C.7BECh. 10 - Prob. 10C.8AECh. 10 - Prob. 10C.8BECh. 10 - Prob. 10C.9AECh. 10 - Prob. 10C.9BECh. 10 - Prob. 10C.1PCh. 10 - Prob. 10C.2PCh. 10 - Prob. 10C.3PCh. 10 - Prob. 10C.4PCh. 10 - Prob. 10C.5PCh. 10 - Prob. 10C.6P
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