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 11.23E
Consider Figure 11.4 and choose the correct phrase: As the vibrational quantum number increases, the extension of the vibration (increases/decreases/stays the same) while the average length of the oscillator itself (increases/decreases/stays the same). Explain your choices.
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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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- Why does the wavefunction 4,4,0 not exist? Similarly, why does a 3f subshell not exist? See exercise 11.73 for notation definition.arrow_forwardThe following are sets of rotational quantum numbers (J,MJ,K). Label each indicated transition as either allowed or forbidden. Hint: Remember the rules for allowed values of the various quantum numbers. a (5,4,0)(3,6,0)b (8,2,2)(9,2,2) c (7,4,2)(7,4,2)d (4,2,5)(3,2,5)arrow_forwardChapter 3 introduced the concept of a double bond between carbon atoms, represented by C=C , with a length near 1.34 Å. The motion of an electron in such a bond can be treated crudely as motion in a one-dimensional box. Calculate the energy of an electron in each of its three lowest allowed states if it is confined to move in a one-dimensional box of length 1.34 Å. Calculate the wavelength of light necessary to excite the electron from its ground state to the first excited state.arrow_forward
- The following are sets of rotational quantum numbers (J,MJ,K). Label each indicated transition as either allowed or forbidden. Hint: Remember the rules for allowed values of the various quatum numbers. a (0,0,0)(1,1,0)b (0,0,0)(1,0,0) c (3,2,1)(3,1,1)d (4,4,1)(2,4,1)arrow_forwardExplain why X-ray lasers would be extremely difficult to build.arrow_forwardQuantum mechanicsarrow_forward
- We have a HCl molecule, with H and Cl have atomic mass of 1.0 and 35.5 amu, respectively. The force constant is 480 N/m for this H-Cl bond, what is the photon frequency when the HCl molecule decay from its second excited vibrational state to its ground vibrational state?arrow_forwardWhich statement correctly compares what occurs when molecules absorb photons in the microwave region with what occurs when molecules absorb photons in the infrared region? a.) Microwave photons cause the molecules to increase their rotational energy states, whereas infrared photons cause the molecules to increase their vibrational energy states. b.) Microwave photons cause electrons in the molecules to increase their electronic energy states, whereas infrared photons cause the molecules to increase their rotational energy states. c.) Microwave photons cause the molecules to increase their vibrational energy states, whereas infrared photons cause electrons in the molecules to increase their electronic energy states. d.) Microwave photons cause the molecules to increase their rotational energy states, whereas infrared photons cause electrons in the molecules to increase their electronic energy states.arrow_forward1arrow_forward
- Carbon dioxide is a linear molecule. The carbon-oxygen bonds in this molecule act very much like springs. Figure 11–58 shows one possible way the oxygen atoms in this molecule can oscillate: the oxygen atoms oscillate symmetrically in and out, while the central carbon atom remains at rest. Hence each oxygen atom acts like a simple harmonic oscillator with a mass equal to the mass of an oxygen atom. It is observed that this oscillation occurs at a frequency ƒ = 2.83 × 1013 Hz. What is the spring constant of the C-O bond?arrow_forwardThe lowest absorption energy of simple organic molecules can often be predicted by approximating the molecule as a 1D particle in a box. Consider the molecule 1,3-butadiene, which consist of four Carbon atoms in a conjugated chain. Butadiene absorbs light at a wavelength of 310 nm. Assume we can model this molecule by only considering its T electrons occupying the energy levels of a 1D particle in a box. Approximating the absorption energy as a highest occupied to lowest unoccupied (HOMO to LUMO) orbital transition, find the size of the "box" that would correspond to an excitation wavelength of 310 nm (you have just found an estimate for the length of the 1,3 butadiene molecule!). Give your final answer in units of angstrom. In your work, also comment on whether you would expect the molecule octatetraene, which contains 8 C atoms in a conjugated chain, to absorb light at a higher or lower wavelength.arrow_forward2. Calculate the bond length of the OH molecule in the gas phase if the first two lines of the microwave spectrum occur at 8.562 cm1 and 17.124 cm.arrow_forward
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