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 11.94E
Interpretation Introduction
Interpretation:
The three-dimensional plots of the first three families of spherical harmonics are to be drawn. The values of
Concept introduction:
Spherical harmonics show the movement of electron around a sphere. This includes three coordinates which are known as polar coordinates. These are represented as
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4.
Given these operators A=d/dx and B=x², can you measure the expectation
values of the corresponding observables to infinite precision simultaneously?
Part A
In normalizing wave functions, the integration is over all space in which the wave function is defined. Normalize the wave function x(a − x)y(b − y) over the range 0 ≤ x ≤ a,
0 ≤ y ≤ b. The element of area in two-dimensional Cartesian coordinates is dx dy; a and b are constants.
Match the items in the left column to the appropriate blanks in the equations on the right. Make certain each equation is complete before submitting your answer.
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2. Give expressions which determine the most probable position for
the electron in region of space.
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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- Let's choose a sine function. We need to figure out the limits of this function. Plug in the limits. Sin Cax) =0 When x =L, sin (ax) = 0. For what values of ax does sin(ax) = 0? List 5. Solve for a for each of these 5 values. Using n as an integer, determine the general expression for a. Write the general formula for the particle in the box.arrow_forwardConsider a 1D particle in a box confined between a = 0 and x = 3. The Hamiltonian for the particle inside the box is simply given by Ĥ . Consider the following normalized wavefunction 2m dz² ¥(2) = 35 (x³ – 9x). Find the expectation value for the energy of the particle inside the box. Give your 5832 final answer for the expectation value in units of (NOTE: h, not hbar!). In your work, compare the expectation value to the lowest energy state of the 1D particle in a box and comment on how the expectation value you calculated for the wavefunction ¥(x) is an example of the variational principle.arrow_forwardThe 4fz(x2-y2) orbital has the angular function Y = (constant)z(x^2-y^2)/r^3a. How many radial nodes does this orbital have?b. How many angular nodes does it have?c. Write equations to define the angular nodal surfaces. What shapes are these surfaces?arrow_forward
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- 8. Do the linear momentum operator px and angular momentum operator Lx commute. Can the velocity in the x direction (vx) and angular momentum in the x direction (Lx) be measured simultaneously to an arbitrary precision?arrow_forwardCalculate the average distance of the electron from the nucleus in a hydrogen atom when the electron is in the 2s orbital. Repeat the calculation for an electron in the 2p orbital.arrow_forward10. (a) Use the radial wave function for the 3p orbital of a hydrogen atom to calculate the value of r for which a node exists. (b) Find the values of r for which nodes exist for the 3s wave function of the hydrogen atom.arrow_forward
- The wave functions p and d are linear combinations of the spherical harmonic functions, which are eigenfunctions of the operators ÂÎ, î², and Î ₂ for rotation in three dimensions. The combinations have been chosen to yield real functions. ▼ Part A Are these functions still eigenfunctions of 1₂? Answer this question by applying the operator to the functions. Match the items in the left column to the appropriate blanks in the sentences and the equations on the right. Make certain each sentence and equation is complete before submitting your answer. 3 V4π sin | 15 V4T 4 15TT 4 √3π COS is not is Î₂px îzdxz ə ap p. This shows that pr -iħ- ə = -iħ. ao 0 0 0 p = iħ an eigenfunction of Îz. 0 0 p. This shows that dxz Reset 0 6 = iħ an eigenfunction of 1 z. Helparrow_forwardHow do I solve this in respect to n=2arrow_forwardHow many maxima would you expect to find in the radial probabilityfunction for the 4s orbital of the hydrogen atom? How many nodes wouldyou expect in this function?arrow_forward
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