Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
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Chapter 12, Problem 12.25E
Interpretation Introduction
Interpretation:
The four possible slater determinants for helium atom having electron configuration
Concept introduction:
The wavefunctions can be represented in the form of Slater determinants. The terms in the wavefunction is equal to
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2.) 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?
You have the excited states of He with the configuration 2p1 3p1, in which the two electrons
have different principal quantum numbers. The electrons are coupled by a Russell-Saunders
spin-orbit coupling term in the Hamiltonian, § ' Ľ · S, where § ' is a positive constant.
1. What are the possible term symbols for the energy eigenstate states associated with this
He configuration? Show your work.
Write down the normalized determinantal wave function (slater determinant) of a He atom at its ground
energy state. He atom has an electron configuration of 1s^2.
Using the Slater determinant you ovtained above, prove that the He wave function is anti-symmetric
Chapter 12 Solutions
Physical Chemistry
Ch. 12 - In the Stern-Gerlach experiment, silver atoms were...Ch. 12 - Prob. 12.2ECh. 12 - Prob. 12.3ECh. 12 - Suppose s=12 for an electron. Into how many parts...Ch. 12 - Using and labels, write two possible...Ch. 12 - List all possible combinations of all four quantum...Ch. 12 - What are the degeneracies of the H atom...Ch. 12 - Prob. 12.8ECh. 12 - a Differentiate between the quantum numbers s and...Ch. 12 - Is the spin orbital 1s for the H atom still...
Ch. 12 - Draw a diagram analogous to Figure 11.15, but now...Ch. 12 - Are mathematical expressions for the following...Ch. 12 - Prob. 12.13ECh. 12 - Prob. 12.14ECh. 12 - a Assume that the electronic energy of Li was a...Ch. 12 - Spin orbitals are products of spatial and spin...Ch. 12 - If 1 and 2 are the individual wavefunctions for...Ch. 12 - Show that the correct behavior of a wavefunction...Ch. 12 - Prob. 12.19ECh. 12 - Why isnt the electron configuration of beryllium,...Ch. 12 - Prob. 12.21ECh. 12 - Write a Slater determinant for the lithide ion,...Ch. 12 - Why does the concept of antisymmetric...Ch. 12 - a Construct Slater determinant wavefunctions for...Ch. 12 - Prob. 12.25ECh. 12 - Prob. 12.26ECh. 12 - Prob. 12.27ECh. 12 - Suppose an electron had three possible values of...Ch. 12 - Using a periodic table or Table 12.1, find the...Ch. 12 - Write an acceptable electron configuration for...Ch. 12 - Prob. 12.31ECh. 12 - Prob. 12.32ECh. 12 - Prob. 12.33ECh. 12 - An anharmonic oscillator has the potential...Ch. 12 - Prob. 12.35ECh. 12 - In a particle-in-a-box having length a, the...Ch. 12 - Prob. 12.37ECh. 12 - Prob. 12.38ECh. 12 - Prob. 12.39ECh. 12 - The Stark effect is the change in energy of a...Ch. 12 - Prob. 12.41ECh. 12 - Prob. 12.42ECh. 12 - Prob. 12.43ECh. 12 - Show that a variation theory treatment of H using...Ch. 12 - Prob. 12.45ECh. 12 - Explain why assuming an effective nuclear charge,...Ch. 12 - Prob. 12.47ECh. 12 - Consider a real system. Assume that a real...Ch. 12 - Prob. 12.49ECh. 12 - Prob. 12.50ECh. 12 - Prob. 12.51ECh. 12 - Prob. 12.52ECh. 12 - State the Born-Oppenheimer approximation in words...Ch. 12 - Prob. 12.54ECh. 12 - Spectroscopy deals with differences in energy...Ch. 12 - Prob. 12.56ECh. 12 - What is the bond order for the lowest excited...Ch. 12 - The helium atom was defined as two electrons and a...Ch. 12 - Explain how we know that the first in equation...Ch. 12 - Prob. 12.60ECh. 12 - Prob. 12.61ECh. 12 - Use molecular orbital arguments to decide whether...Ch. 12 - Prob. 12.63ECh. 12 - Prob. 12.65ECh. 12 - Prob. 12.67ECh. 12 - Prob. 12.68E
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- What are the degeneracies of the H atom wavefunctions when spin is accounted for? Give a general formula.arrow_forwardWhat is the physical explanation of the difference between a particle having the 3-D rotational wavefunction 3,2 and an identical particle having the wavefunction 3,2?arrow_forwardSuppose that the spin quantum number had three allowed values (ms=0,+12,12) . Give the atomic numbers of the first three noble-gas atoms in this case.arrow_forward
- Write a Slater determinant for the lithide ion, Li.arrow_forwardWhat is the probability of finding an electron in the 1s orbital within 0.1A of an Ne9+ nucleus? Compare your answer to the answer to exercise 11.77 and justify the difference.arrow_forward3- Consider the atom having the electron configuration 1s 2s2 2p 3s 3p. Assume that the z components of both the orbital and spin angular momenta of the electron in the 3p subshell are positive. What are the quantum numbers that describe the state of this electron? On=3,1= 1, m = 1, s = 1/2 n = 3,1 = 2, m = 1, s = 1/2 On= 3,1= 2, m 2, s =-1/2 On=3,13D 1, m = 2, s = 1/2 On=3,1 1, m = -1, s = 1/2 %3Darrow_forward
- 2. Consider a helium atom. (a) Sketch the system and write the Hamiltonian. Denote the term(s) in the operator that make(s) the Schrödinger equation unsolvable. (b) Given an excited-state configuration 1s 2s', express all possible excited-state wavefunctions in terms of spatial and spin functions for the two electrons. For each, denote the symmetry of the overall wavefunction, the spatial component, and the spin component with respect to exchange.arrow_forwardNow consider an excited state of He atom with electron configuration 1s' 2s'. In general, the wavefunction is a state: V (r, 0, 6, 02) = V(r, 0, ø)Vo. where V(r, 0, ø) and V, represent the spatial and the spin part. The spatial part is constructed from the wavefunctions of the 1s' and 2s' orbitals denoted as o (r, 0, 6) and ø (r, 0, 6), where subscript k denotes which electron it belongs to (i.e., k is either 1 or 2 since we have two electrons). • The spatial part of the wavefunction can be written 1*(r, 0, 4)o3* (r, 0, 4) + o(r, 0, ¢)o²*(r, 0, 4) V2 F (r, 0, 4)«3"(r, 0, ø) – 05" (r, 0, 4)o²°(r, 0, ø) V2 V2(r, 0, 6) = Vī2(r, 0, 6) = Explain (and demonstrate) which spatial wavefunction (V2(r, 0, 0) or V2(r, 0, 0)) is symmetric with respect to exchange of two electrons? Which one corresponds to the singlet and triplet state (defined by the spin multiplicity)? • Based on you response to the previous question, write down the wavefunction for the (i) ground state of He and the (ii) singlet…arrow_forwardConstruct the wavefunction for an excited state of the He atom with configuration 1s12s1. Use Zeff = 2 for the 1s electron and Zeff = 1 for the 2s electron.arrow_forward
- Consider a single particle with rest mass m residing in a one-dimensional space, x. This particle experiences a potential energy V(x) = ∞ for x a, and a potential energy V(x) = 0 for 0 < x < a. The solutions to the Schrödinger Equation for this system are 12. 2 Vn(x) : sin a where n is the state's quantum number. Show that the ground state wave function is normalized.arrow_forward2. Calculate the amount of energy required to go from the ground state to the first excited state of an electron moving in a circular orbit with a radius of 100 pm. 3. The wavefunction of a particle on a ring can also be written in terms of sines and cosines as Y (4) = eimiø = cos(m¡4) + i sin(m¡4). How many nodes exist in the real part of the wavefunction for m=2 and m=4? At what values of p are they located?arrow_forwardConsider 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 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? E and d no answerarrow_forward
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