Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
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Chapter 11, Problem 11.81E
State how many radial, angular, and total nodes are in each of the following hydrogen-like wavefunctions. (a)
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Consider a fictitious one-dimensional system with one electron.The wave function for the electron, drawn below, isψ (x)= sin x from x = 0 to x = 2π. (a) Sketch the probabilitydensity, ψ2(x), from x = 0 to x = 2π. (b) At what value orvalues of x will there be the greatest probability of finding theelectron? (c) What is the probability that the electron willbe found at x = π? What is such a point in a wave functioncalled?
In each of the following cases, demonstrate that 2n² is the number of sets of quantum numbers (e, me, m) possible for a hydrogen atom in the n-th shell. In each case, accomplish this by specifying the number of states in each subshell.
Submit the numbers for all subshells, separated by spaces, in the single answer box for each case.
(a) n = 1
2
(b) n = 2
122
(c) n = 3
242
(d) n = 4
362
(e) n = 5
482
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(a) What are the possible values for mℓ when the principal quantum number (n) is 2 and the angular momentum quantum number (ℓ) is 0? (b) What are the possible values for mℓ when the principal quantum number (n) is 3 and the angular momentum quantum number (ℓ) is 2?
Chapter 11 Solutions
Physical Chemistry
Ch. 11 - Convert 3.558mdyn/A into units of N/m.Ch. 11 - Prob. 11.2ECh. 11 - Prob. 11.3ECh. 11 - Prob. 11.4ECh. 11 - Prob. 11.5ECh. 11 - Prob. 11.6ECh. 11 - Prob. 11.7ECh. 11 - Prob. 11.8ECh. 11 - Prob. 11.9ECh. 11 - Prob. 11.10E
Ch. 11 - Prob. 11.11ECh. 11 - Prob. 11.12ECh. 11 - a For a pendulum having classical frequency of...Ch. 11 - Prob. 11.14ECh. 11 - The OH bond in water vibrates at a frequency of...Ch. 11 - Show that 2 and 3 for the harmonic oscillator are...Ch. 11 - Prob. 11.17ECh. 11 - Prob. 11.18ECh. 11 - Prob. 11.19ECh. 11 - Use the expression for 1 in equations 11.17 and...Ch. 11 - Prob. 11.21ECh. 11 - Prob. 11.22ECh. 11 - Consider Figure 11.4 and choose the correct...Ch. 11 - Based on the trend shown in Figure 11.5, draw the...Ch. 11 - Prob. 11.25ECh. 11 - Prob. 11.26ECh. 11 - Prob. 11.27ECh. 11 - Prob. 11.28ECh. 11 - Prob. 11.29ECh. 11 - Prob. 11.30ECh. 11 - Compare the mass of the electron, me, with a the...Ch. 11 - Reduced mass is not reserved only for atomic...Ch. 11 - Prob. 11.33ECh. 11 - An OH bond has a frequency of 3650cm1. Using...Ch. 11 - Prob. 11.35ECh. 11 - Prob. 11.36ECh. 11 - Prob. 11.37ECh. 11 - Prob. 11.38ECh. 11 - Prob. 11.39ECh. 11 - What are the energies and angular momenta of the...Ch. 11 - Prob. 11.41ECh. 11 - A 25-kg child is on a merry-go-round/calliope,...Ch. 11 - Prob. 11.43ECh. 11 - a Using the expression for the energy of a 2-D...Ch. 11 - Prob. 11.45ECh. 11 - Prob. 11.46ECh. 11 - Prob. 11.47ECh. 11 - The quantized angular momentum is choose one:...Ch. 11 - Prob. 11.49ECh. 11 - Prob. 11.50ECh. 11 - Prob. 11.51ECh. 11 - Can you evaluate r for the spherical harmonic Y22?...Ch. 11 - Show that 1,0 and 1,1 for 3-D rotational motion...Ch. 11 - Prob. 11.54ECh. 11 - Prob. 11.55ECh. 11 - a Using the he expression for the energy of a 3-D...Ch. 11 - Prob. 11.57ECh. 11 - In exercise 11.57 regarding C60, what are the...Ch. 11 - Draw the graphical representations see Figure...Ch. 11 - Prob. 11.60ECh. 11 - What is the physical explanation of the difference...Ch. 11 - List the charges on hydrogen-like atoms whose...Ch. 11 - Prob. 11.63ECh. 11 - Prob. 11.64ECh. 11 - Prob. 11.65ECh. 11 - Calculate the difference between the Bohr radius...Ch. 11 - To four significant figures, the first four lines...Ch. 11 - What would the wavelengths of the Balmer series...Ch. 11 - Construct an energy level diagram showing all...Ch. 11 - Prob. 11.70ECh. 11 - What is the degeneracy of an h subshell? An n...Ch. 11 - What is the numerical value of the total angular...Ch. 11 - What are the values of E, L, and Lz for an F8+...Ch. 11 - Prob. 11.74ECh. 11 - Why does the wavefunction 4,4,0 not exist?...Ch. 11 - Prob. 11.76ECh. 11 - What is the probability of finding an electron in...Ch. 11 - What is the probability of finding an electron in...Ch. 11 - Prob. 11.79ECh. 11 - Prob. 11.80ECh. 11 - State how many radial, angular, and total nodes...Ch. 11 - Prob. 11.82ECh. 11 - Prob. 11.83ECh. 11 - Verify the specific value of a, the Bohr radius,...Ch. 11 - Prob. 11.85ECh. 11 - Prob. 11.86ECh. 11 - Evaluate Lz for 3px, Compare it to the answer in...Ch. 11 - Calculate V for 1s of the H atom and compare it to...Ch. 11 - Prob. 11.89ECh. 11 - Prob. 11.90ECh. 11 - Prob. 11.91ECh. 11 - Prob. 11.92ECh. 11 - Graph the first five wavefunctions for the...Ch. 11 - Prob. 11.94ECh. 11 - Set up and evaluate numerically the integral that...Ch. 11 - Prob. 11.96E
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