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 12.18E
Show that the correct behavior of a wavefunction for
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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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- Based on the trend shown in Figure 11.5, draw the probability distribution of a harmonic oscillator wavefunction that has a very high value of n. Explain how this is consistent with the correspondence principle.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_forwardHow is the Bohr theory of the hydrogen atom inconsistent with the uncertainty principle? In fact, it was this inconsistency, along with the theorys limited application to non-hydrogen-like systems, that limited Bohrs theory.arrow_forward
- Suppose 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_forwardWhy does the concept of antisymmetric wavefunctions not need to be considered for the hydrogen atom?arrow_forwardWhat are the degeneracies of the H atom wavefunctions when spin is accounted for? Give a general formula.arrow_forward
- Where are the nodes in the wavefunction for a particle confined to a box with 0 < x < a and n=3?arrow_forwardConstruct the wavefunction V(r, 0, ø) for an H atoms' electron in the state 2p. Please note that in order to have a real-valued wavefunction of p, orbital(see below), you need to do a linear superposition of the corresponding spherical harmonics for the angular part. Use the spherical harmonics table below. Show that the superposition you selected indeed results in a real orbital; however, you do not need to simplify the expressions further or normalize the wavefunction. y8 = ) Y = 1/2 %3D Px 3 12 1/2 cos 0 YO = G6)" (5 cos 0-3 cos 0) %3D 4x Y1 =7()2 sin Be*io Y =7(2112 sin 0 (5 cos 6-1)etio %3D 647) -y Yg = G)" (3 cos²0- 1) Y = " sin? o cos de2i¢ 105 1/2 !3! 327 1бл Y =7 (15 1/2 87 35 12 sin 6e*3i0 1647 sin e cos detie %3D %3Darrow_forwardWithout evaluating any integrals, state the value of the expectation value of x for a particle in a box of length L for the case where the wavefunction has n = 2. Explain how you arrived at your answer.arrow_forward
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