The overlap between an H 1 s a n d a n H 2 p depends on their separation has to be sketched. Concept Introduction: The overlap of atomic orbital of one atom with the atomic orbital of another atom is called the overlap integral. The overlap integral between H1s orbital and H2p orbital on nuclei can be written as S = (R/a 0 ){1 + (R/a 0 ) + 1 3 (R/a 0 ) 2 }e -R/a 0 , where R is the distance between the nuclei.

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Answer 1

Question

Chapter 9, Problem 9.3PR

(a)

Interpretation Introduction

Interpretation:

The overlap between an H1s and an H2p depends on their separation has to be sketched.

Concept Introduction:

The overlap of atomic orbital of one atom with the atomic orbital of another atom is called the overlap integral.

The overlap integral between H1s orbital and H2p orbital on nuclei can be written as S = (R/a0){1 + (R/a0) + 13 (R/a0)2}e-R/a0, where R is the distance between the nuclei.

(b)

Interpretation Introduction

Interpretation:

The graph of overlap versus separation between nuclei has to be plotted. Also the separation at which maximum overlap is obtained has to be mentioned.

Concept Introduction:

The overlap of atomic orbital of one atom with the atomic orbital of another atom is called the overlap integral.

The overlap integral between H1s orbital and H2p orbital on nuclei can be written as S = (R/a0){1 + (R/a0) + 13 (R/a0)2}e-R/a0, where R is the distance between the nuclei.

(c)

Interpretation Introduction

Interpretation:

A linear combination of orbital A and B which is not overlapping with the given wave function has to be found.

Concept Introduction:

Two functions are said to be orthogonal if the integral of their product is zero.

Consider two functions X and Y. If these functions are orthogonal then ∫X .Y dz=0.

A function is said to be normalized if the integral of its product to itself is 1.

Consider a function X, if this function is normalized then ∫X.X dz=1.

(d)

Interpretation Introduction

Interpretation:

The given wave function has to be normalized in terms of λ and S.

Concept Introduction:

Two functions are said to be orthogonal if the integral of their product is zero.

Consider two functions X and Y. If these functions are orthogonal then ∫X .Y dz=0.

A function is said to be normalized if the integral of its product to itself is 1.

Consider a function X, if this function is normalized then ∫X.X dz=1.

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Answer 2

Question

Chapter 9, Problem 9.3PR

(a)

Interpretation Introduction

Interpretation:

The overlap between an H1s and an H2p depends on their separation has to be sketched.

Concept Introduction:

The overlap of atomic orbital of one atom with the atomic orbital of another atom is called the overlap integral.

The overlap integral between H1s orbital and H2p orbital on nuclei can be written as S = (R/a0){1 + (R/a0) + 13 (R/a0)2}e-R/a0, where R is the distance between the nuclei.

(b)

Interpretation Introduction

Interpretation:

The graph of overlap versus separation between nuclei has to be plotted. Also the separation at which maximum overlap is obtained has to be mentioned.

Concept Introduction:

The overlap of atomic orbital of one atom with the atomic orbital of another atom is called the overlap integral.

The overlap integral between H1s orbital and H2p orbital on nuclei can be written as S = (R/a0){1 + (R/a0) + 13 (R/a0)2}e-R/a0, where R is the distance between the nuclei.

(c)

Interpretation Introduction

Interpretation:

A linear combination of orbital A and B which is not overlapping with the given wave function has to be found.

Concept Introduction:

Two functions are said to be orthogonal if the integral of their product is zero.

Consider two functions X and Y. If these functions are orthogonal then ∫X .Y dz=0.

A function is said to be normalized if the integral of its product to itself is 1.

Consider a function X, if this function is normalized then ∫X.X dz=1.

(d)

Interpretation Introduction

Interpretation:

The given wave function has to be normalized in terms of λ and S.

Concept Introduction:

Two functions are said to be orthogonal if the integral of their product is zero.

Consider two functions X and Y. If these functions are orthogonal then ∫X .Y dz=0.

A function is said to be normalized if the integral of its product to itself is 1.

Consider a function X, if this function is normalized then ∫X.X dz=1.

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Answer 3

Question

Chapter 9, Problem 9.3PR

(a)

Interpretation Introduction

Interpretation:

The overlap between an H1s and an H2p depends on their separation has to be sketched.

Concept Introduction:

The overlap of atomic orbital of one atom with the atomic orbital of another atom is called the overlap integral.

The overlap integral between H1s orbital and H2p orbital on nuclei can be written as S = (R/a0){1 + (R/a0) + 13 (R/a0)2}e-R/a0, where R is the distance between the nuclei.

(b)

Interpretation Introduction

Interpretation:

The graph of overlap versus separation between nuclei has to be plotted. Also the separation at which maximum overlap is obtained has to be mentioned.

Concept Introduction:

The overlap of atomic orbital of one atom with the atomic orbital of another atom is called the overlap integral.

The overlap integral between H1s orbital and H2p orbital on nuclei can be written as S = (R/a0){1 + (R/a0) + 13 (R/a0)2}e-R/a0, where R is the distance between the nuclei.

(c)

Interpretation Introduction

Interpretation:

A linear combination of orbital A and B which is not overlapping with the given wave function has to be found.

Concept Introduction:

Two functions are said to be orthogonal if the integral of their product is zero.

Consider two functions X and Y. If these functions are orthogonal then ∫X .Y dz=0.

A function is said to be normalized if the integral of its product to itself is 1.

Consider a function X, if this function is normalized then ∫X.X dz=1.

(d)

Interpretation Introduction

Interpretation:

The given wave function has to be normalized in terms of λ and S.

Concept Introduction:

Two functions are said to be orthogonal if the integral of their product is zero.

Consider two functions X and Y. If these functions are orthogonal then ∫X .Y dz=0.

A function is said to be normalized if the integral of its product to itself is 1.

Consider a function X, if this function is normalized then ∫X.X dz=1.

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Answer 4

Question

Chapter 9, Problem 9.3PR

(a)

Interpretation Introduction

Interpretation:

The overlap between an H1s and an H2p depends on their separation has to be sketched.

Concept Introduction:

The overlap of atomic orbital of one atom with the atomic orbital of another atom is called the overlap integral.

The overlap integral between H1s orbital and H2p orbital on nuclei can be written as S = (R/a0){1 + (R/a0) + 13 (R/a0)2}e-R/a0, where R is the distance between the nuclei.

(b)

Interpretation Introduction

Interpretation:

The graph of overlap versus separation between nuclei has to be plotted. Also the separation at which maximum overlap is obtained has to be mentioned.

Concept Introduction:

The overlap of atomic orbital of one atom with the atomic orbital of another atom is called the overlap integral.

The overlap integral between H1s orbital and H2p orbital on nuclei can be written as S = (R/a0){1 + (R/a0) + 13 (R/a0)2}e-R/a0, where R is the distance between the nuclei.

(c)

Interpretation Introduction

Interpretation:

A linear combination of orbital A and B which is not overlapping with the given wave function has to be found.

Concept Introduction:

Two functions are said to be orthogonal if the integral of their product is zero.

Consider two functions X and Y. If these functions are orthogonal then ∫X .Y dz=0.

A function is said to be normalized if the integral of its product to itself is 1.

Consider a function X, if this function is normalized then ∫X.X dz=1.

(d)

Interpretation Introduction

Interpretation:

The given wave function has to be normalized in terms of λ and S.

Concept Introduction:

Two functions are said to be orthogonal if the integral of their product is zero.

Consider two functions X and Y. If these functions are orthogonal then ∫X .Y dz=0.

A function is said to be normalized if the integral of its product to itself is 1.

Consider a function X, if this function is normalized then ∫X.X dz=1.

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See solution

Answer 5

Chapter 9, Problem 9.3PR

(a)

Interpretation Introduction

Interpretation:

The overlap between an H1s and an H2p depends on their separation has to be sketched.

Concept Introduction:

The overlap of atomic orbital of one atom with the atomic orbital of another atom is called the overlap integral.

The overlap integral between H1s orbital and H2p orbital on nuclei can be written as S = (R/a0){1 + (R/a0) + 13 (R/a0)2}e-R/a0, where R is the distance between the nuclei.

(b)

Interpretation Introduction

Interpretation:

The graph of overlap versus separation between nuclei has to be plotted. Also the separation at which maximum overlap is obtained has to be mentioned.

Concept Introduction:

The overlap of atomic orbital of one atom with the atomic orbital of another atom is called the overlap integral.

The overlap integral between H1s orbital and H2p orbital on nuclei can be written as S = (R/a0){1 + (R/a0) + 13 (R/a0)2}e-R/a0, where R is the distance between the nuclei.

(c)

Interpretation Introduction

Interpretation:

A linear combination of orbital A and B which is not overlapping with the given wave function has to be found.

Concept Introduction:

Two functions are said to be orthogonal if the integral of their product is zero.

Consider two functions X and Y. If these functions are orthogonal then ∫X .Y dz=0.

A function is said to be normalized if the integral of its product to itself is 1.

Consider a function X, if this function is normalized then ∫X.X dz=1.

(d)

Interpretation Introduction

Interpretation:

The given wave function has to be normalized in terms of λ and S.

Concept Introduction:

Two functions are said to be orthogonal if the integral of their product is zero.

Consider two functions X and Y. If these functions are orthogonal then ∫X .Y dz=0.

A function is said to be normalized if the integral of its product to itself is 1.

Consider a function X, if this function is normalized then ∫X.X dz=1.

Answer 6

Chapter 9, Problem 9.3PR

(a)

Interpretation Introduction

Interpretation:

The overlap between an H1s and an H2p depends on their separation has to be sketched.

Concept Introduction:

The overlap of atomic orbital of one atom with the atomic orbital of another atom is called the overlap integral.

The overlap integral between H1s orbital and H2p orbital on nuclei can be written as S = (R/a0){1 + (R/a0) + 13 (R/a0)2}e-R/a0, where R is the distance between the nuclei.

Answer 7

Chapter 9, Problem 9.3PR

(a)

Interpretation Introduction

Interpretation:

The overlap between an H1s and an H2p depends on their separation has to be sketched.

Concept Introduction:

The overlap of atomic orbital of one atom with the atomic orbital of another atom is called the overlap integral.

The overlap integral between H1s orbital and H2p orbital on nuclei can be written as S = (R/a0){1 + (R/a0) + 13 (R/a0)2}e-R/a0, where R is the distance between the nuclei.

Answer 8

(b)

Interpretation Introduction

Interpretation:

The graph of overlap versus separation between nuclei has to be plotted. Also the separation at which maximum overlap is obtained has to be mentioned.

Concept Introduction:

The overlap of atomic orbital of one atom with the atomic orbital of another atom is called the overlap integral.

The overlap integral between H1s orbital and H2p orbital on nuclei can be written as S = (R/a0){1 + (R/a0) + 13 (R/a0)2}e-R/a0, where R is the distance between the nuclei.

Answer 9

(b)

Interpretation Introduction

Interpretation:

The graph of overlap versus separation between nuclei has to be plotted. Also the separation at which maximum overlap is obtained has to be mentioned.

Concept Introduction:

The overlap of atomic orbital of one atom with the atomic orbital of another atom is called the overlap integral.

The overlap integral between H1s orbital and H2p orbital on nuclei can be written as S = (R/a0){1 + (R/a0) + 13 (R/a0)2}e-R/a0, where R is the distance between the nuclei.

Answer 10

(c)

Interpretation Introduction

Interpretation:

A linear combination of orbital A and B which is not overlapping with the given wave function has to be found.

Concept Introduction:

Two functions are said to be orthogonal if the integral of their product is zero.

Consider two functions X and Y. If these functions are orthogonal then ∫X .Y dz=0.

A function is said to be normalized if the integral of its product to itself is 1.

Consider a function X, if this function is normalized then ∫X.X dz=1.

Answer 11

(c)

Interpretation Introduction

Interpretation:

A linear combination of orbital A and B which is not overlapping with the given wave function has to be found.

Concept Introduction:

Two functions are said to be orthogonal if the integral of their product is zero.

Consider two functions X and Y. If these functions are orthogonal then ∫X .Y dz=0.

A function is said to be normalized if the integral of its product to itself is 1.

Consider a function X, if this function is normalized then ∫X.X dz=1.

Answer 12

(d)

Interpretation Introduction

Interpretation:

The given wave function has to be normalized in terms of λ and S.

Concept Introduction:

Two functions are said to be orthogonal if the integral of their product is zero.

Consider two functions X and Y. If these functions are orthogonal then ∫X .Y dz=0.

A function is said to be normalized if the integral of its product to itself is 1.

Consider a function X, if this function is normalized then ∫X.X dz=1.

Answer 13

(d)

Interpretation Introduction

Interpretation:

The given wave function has to be normalized in terms of λ and S.

Concept Introduction:

Two functions are said to be orthogonal if the integral of their product is zero.

Consider two functions X and Y. If these functions are orthogonal then ∫X .Y dz=0.

A function is said to be normalized if the integral of its product to itself is 1.

Consider a function X, if this function is normalized then ∫X.X dz=1.

Answer 14

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Answer 15

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Answer 16

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Answer 17

Ch. 9 - Prob. 9A.1ST Ch. 9 - Prob. 9A.2ST Ch. 9 - Prob. 9A.3ST Ch. 9 - Prob. 9A.5ST Ch. 9 - Prob. 9B.2ST Ch. 9 - Prob. 9B.3ST Ch. 9 - Prob. 9B.4ST Ch. 9 - Prob. 9C.1ST Ch. 9 - Prob. 9C.3ST Ch. 9 - Prob. 9D.1ST

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