Physical Chemistry
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 12.40E

The Stark effect is the change in energy of a system due to the presence of an electric field (discovered by German physicist Johannes Stark in 1913). Consider the hydrogen atom. Its normally spherical 1 s orbital distorts slightly when exposed to an electric field. If the electric field is considered to be in the z direction, then the field acts to introduce, or mix, some 2 p z character in with the 1 s orbital. The atom is said to be polarizable, and the extent to which it changes is considered a measure of the atom’s polarizability (which is designated by the letter α , not to be confused with the spin function α !). The perturbation Hamiltonian is defined as H ^ = e E r cos θ , where e is the charge on the electron, E is the strength of the electric field, and r and θ represent coordinates of the electron. Evaluate the perturbation energy of the hydrogen atom. You will have to integrate all the three spherical polar coordinates in your evaluation of H ^ . (A similar effect, the Zeeman effect, exists for magnetic fields. It too can be treated using perturbation theory.)

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1. The angular portions of the wave functions for the px and dxz orbitals of the hydrogen atom are linear combinations of the spherical harmonics and are given by the expressions below. 3 YP. = √(x²+x¹) = -sin coso 4T Wd₂ = 1/2 (Y/² + X/₂ ¹) = eigenfunctions of 15 4π These combinations are chosen to yield real functions. Are these functions a Ĺ sincoscoso -iħ. do ?
3- 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 %3D
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 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 answer

Chapter 12 Solutions

Physical Chemistry

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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