Concept explainers
(a) Construct Slater determinant wavefunctions for
(b) How many different Slater determinants can be constructed for
(a)
Interpretation:
The slater determinant wavefunctions for
Concept introduction:
The wavefunctions can be represented in the form of Slater determinants. The terms in the wavefunction is equal to
Answer to Problem 12.24E
The slater determinant wavefunctions for
The total slater determinants possible for boron is
Explanation of Solution
The number of electrons in
Where,
•
•
The number of electrons in
Where,
•
•
In boron, the electron can be placed in any of the three
The slater determinant wavefunctions for
The total slater determinants possible for boron is
(b)
Interpretation:
The number of different Slater determinants that can be constructed for
Concept introduction:
The wavefunctions can be represented in the form of Slater determinants. The terms in the wavefunction is equal to
Answer to Problem 12.24E
The number of different Slater determinants that can be constructed for
Explanation of Solution
The number of electrons in
In carbon, the two electrons can be placed in any of the three
The number of electrons in
In fluorine, the one unpaired electron can be placed in any of the three
The number of different Slater determinant that can be constructed for
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Chapter 12 Solutions
Student Solutions Manual for Ball's Physical Chemistry, 2nd
- Consider an electron in the N shell. (a) What is the smallest orbital angular momentum it could have? (b) What is the largest orbital angular momentum it could have? Express your answers in terms of h and in SI units. (c) What is the largest orbital angular momentum this electron could have in any chosen direction? Express your answers in terms of h and in SI units. (d) What is the largest spin angular momentum this electron could have in any chosen direction? Express your answers in terms of h and in SI units. (e) For the electron in part (c), what is the ratio of its spin angular momentum in the z-direction to its orbital angular momentum in the z-direction?arrow_forward2.) Neglecting electron-electron repulsion, write down the singlet and triplet excited states of with the electron configuration, 1s^ 1 2s^ 1 . Make sure the wave function including spin and space parts) is antisymmetric under the interchange of the two electrons. What are the energies of the singlet and triplet states? What are the term symbols for the singlet and triplet states?arrow_forwardConstruct the Slater determinant for the 6C atom.arrow_forward
- The cyclobutadienyl cation (C4H4+) may be treated using the Huckel MO approach. The roots to the secular determinant are α+ 2β, α and α- 2β. The middle level is doubly degenerate. (a) Determine the energy for this system in terms of α and β. (b) The ionization energy for C4H4 has been determined to be 0.22 eV. Calculate α in kJ mol-1. (c) Predict the ground state multiplicities for C4H4, C4H4+, and C4H4-.arrow_forward2. Commuting operators. (a) Show whether the operator of the kinetic energy operator K and the momentum operator Px for a one-dimensional system commute (show every step). (b) What does the result mean (physical interpretation)?arrow_forward(1) (2) (b) Look very carefully at the picture below. Give the relevant quantum numbers. Explain your answer. y-axis (c) (1) What is a wavefunction? (ii) What are the two parts of a wavefunction?arrow_forward
- Construct a slater determinant for the ground state He atom and show that is gives you, Ψ=1s α(2)1s β(1) - 1s α(1)1s β(2) where "1s" represents the "Ψooo" Hydrogenic 1s spatial wavefunction and α(1), β(1) represents spin up and spin down for electron 1, respectively. (Note that there is a normalization factor missing in the text. You can ignore this normalization factor also)arrow_forwardc) What is the ground state energy and wave function of the system, and how can they be interpreted? Explain the difference with respect to the ground state of the particle in 1D box. d) What is the degree of degeneracy in the system, and how do the possible solutions for the same energy differ? Interpret that difference.arrow_forwardSince spin can have 2 possible orientations, what does this mean for the degeneracy?arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Chemistry: Principles and PracticeChemistryISBN:9780534420123Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward MercerPublisher:Cengage Learning