Principles of Modern Chemistry
Principles of Modern Chemistry
8th Edition
ISBN: 9781305079113
Author: David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher: Cengage Learning
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Chapter 6, Problem 1P

Determine the number of nodes along the internuclearaxis for each of the σ molecular orbitals for H 2 + shown in Figure 6.5.

Expert Solution & Answer
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Interpretation Introduction

Interpretation: The number of nodes along the internuclear axis for each of the σ molecular orbitals for H2+ is to be determined.

Concept introduction: Born-Oppenheimer approximation state that nuclei are heavier than electrons that considered fixed in space whereas the electrons move constantly around them. The Born−Oppenheimer approximation solves the electronic Schrodinger equation for H2+ for fixed internuclear separation RAB . The result is one-electron MO (molecular orbitals), that is analogous to one-electron hydrogen AO (atomic orbital). The quantum picture for MO (molecular orbitals) of H2+ illustrates that first eight MO for H2+ that show their shapes and characterize them by their energies as well as symmetry The MO (molecular orbitals) are characterized by angular momentum along the internuclear axis and analogy to hydrogen atom These are called σ for orbital with cylindrical symmetry and π for molecular orbitals with one nodal plane that have internuclear axis.

Answer to Problem 1P

The number of nodes in 1σg is 0, in 1σu* is 1, in 2σg is 2, in 2σu* is 3, in 3σg is 2 and in 3σu* is 3.

Explanation of Solution

Node is point in molecular orbitals where probability to find the electron density is zero. Nodal plane is the imaginary plane where probability to find electrons is zero.

  Principles of Modern Chemistry, Chapter 6, Problem 1P

In the figure, node is the oval region. It is formed when plane white surface cut the spherical orbital into two equal halves having opposite symmetry. Also, there are six σ orbitals, 1σg , 1σu* , 2σg , 2σu* , 3σg and 3σu* .The energy level of σ orbital is that 1σg has the lowest energy and 3σu* has highest energy.

In 1σg orbital, there is no oval region on the spherical orbital. Hence number of nodes is 0.

In 1σu* orbital, there is one cut on the spherical orbital. Hence number of nodes is 1.

In 2σg orbital, there are two oval regions on the spherical orbital. Hence number of nodes is 2.

In 2σu* orbital, there are three oval regions formed by three cuts on the spherical orbital. Hence number of nodes is 3.

In 3σg orbital, there are two oval regions formed by two cuts on the spherical orbital. Hence number of nodes is 2.

In 3σu* orbital, there are three oval regions formed by three cuts on the spherical orbital. Hence number of nodes is 3.

Conclusion

Therefore, number of nodes in 1σg is 0, in 1σu* is 1, in 2σg is 2, in 2σu* is 3, in 3σg is 2 and in 3σu* is 3.

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Chapter 6 Solutions

Principles of Modern Chemistry

Ch. 6 - Without consulting tables of data, predict which...Ch. 6 - Without consulting tables of data, predict which...Ch. 6 - Without consulting tables of data, on the same...Ch. 6 - Without consulting tables of data, on the same...Ch. 6 - Suppose we supply enough energy to H2 to remove...Ch. 6 - Suppose we supply enough energy to He2+ to remove...Ch. 6 - Prob. 17PCh. 6 - When one electron is added to an oxygen molecule,...Ch. 6 - Predict the valence electron configuration and the...Ch. 6 - Predict the valence electron configuration and the...Ch. 6 - Prob. 21PCh. 6 - For each of the following valence electron...Ch. 6 - For each of the electron configurations in Problem...Ch. 6 - For each of the electron configurations in Problem...Ch. 6 - Following the pattern of Figure 6.21, work out the...Ch. 6 - Following the pattern of Figure 6.21, work out the...Ch. 6 - The bond length of the transient diatomic molecule...Ch. 6 - The compound nitrogen oxide (NO) forms when the...Ch. 6 - What would be the electron configuration for a HeH...Ch. 6 - The molecular ion HeH+ has an equilibrium bond...Ch. 6 - Prob. 31PCh. 6 - Predict the ground state electronic configuration...Ch. 6 - The bond dissociation energies for the species NO,...Ch. 6 - The ionization energy of CO is greater than that...Ch. 6 - Photoelectron spectra were acquired from a sample...Ch. 6 - Photoelectron spectra were acquired from a sample...Ch. 6 - Prob. 37PCh. 6 - From the n=0 peaks in the photoelectron spectrum...Ch. 6 - The photoelectron spectrum of HBr has two main...Ch. 6 - The photoelectron spectrum of CO has four major...Ch. 6 - Write simple valence bond wave functions for the...Ch. 6 - Write simple valence bond wave functions for the...Ch. 6 - Both the simple VB model and the LCAO method...Ch. 6 - Both the simple VB model and the LCAO method...Ch. 6 - Write simple valence bond wave functions for...Ch. 6 - Write simple valence bond wave functions for...Ch. 6 - Write simple valence bond wave functions for the...Ch. 6 - Write simple valence bond wave functions for the...Ch. 6 - Formulate a localized bond picture for the amide...Ch. 6 - Formulate a localized bond picture for the...Ch. 6 - Prob. 51PCh. 6 - Draw a Lewis electron dot diagram for each of the...Ch. 6 - Describe the hybrid orbitals on the chlorine atom...Ch. 6 - Describe the hybrid orbitals on the chlorine atom...Ch. 6 - The sodium salt of the unfamiliar orthonitrate ion...Ch. 6 - Describe the hybrid orbitals used by the carbon...Ch. 6 - Describe the bonding in the bent molecule NF2 ....Ch. 6 - Describe the bonding in the bent molecule OF2 ....Ch. 6 - The azide ion (N3) is a weakly bound molecular...Ch. 6 - Formulate the MO structure of (NO2+) for localized...Ch. 6 - Discuss the nature of the bonding in the nitrite...Ch. 6 - Discuss the nature of the bonding in the nitrate...Ch. 6 - The pyridine molecule (C5H5N) is obtained by...Ch. 6 - For each of the following molecules, construct the...Ch. 6 - (a) Sketch the occupied MOs of the valence shell...Ch. 6 - Calcium carbide (CaC2) is an intermediate in the...Ch. 6 - The B2 molecule is paramagnetic; show how this...Ch. 6 - The Be2 molecule has been detected experimentally....Ch. 6 - Prob. 69APCh. 6 - The molecular ion HeH+ has an equilibrium bond...Ch. 6 - The MO of the ground state of a heteronuclear...Ch. 6 - The stable molecular ion H3+ is triangular, with...Ch. 6 - According to recent spectroscopic results,...Ch. 6 - trans-tetrazene (N4H4) consists of a chain of four...
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