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 11.75E
Why does the wavefunction
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Construct the wavefunction for an excited state of the He atom with configuration 1s12s1. Use Zeff = 2 for the 1s electron and Zeff = 1 for the 2s electron.
8. Show that the wavefunction ₁ is normalized over all space. The wavefunction is given
by,
√3
2√2π
ei sin 0
¥1,1 =
7
The wavefunction for the motion of a particle on a ring is of the form ψ = Neimlϕ. Evaluate the normalization constant, N.
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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- 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_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
- What are the degeneracies of the H atom wavefunctions when spin is accounted for? Give a general formula.arrow_forwardSuppose 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_forwardFor a He atom in the excited state with atomic electronic configuration 1s1 2s1: write out the symmetric and antisymmetric spatial wavefunctions. These two are linear combination of ψ1s and ψ2s each with an electron in them. combine each spatial wavefunction with the appropriate spin wavefunctions for two electrons (there are four of them) such that the total wavefunction is antisymmetric.arrow_forward
- 2. Calculate the amount of energy required to go from the ground state to the first excited state of an electron moving in a circular orbit with a radius of 100 pm. 3. The wavefunction of a particle on a ring can also be written in terms of sines and cosines as Y (4) = eimiø = cos(m¡4) + i sin(m¡4). How many nodes exist in the real part of the wavefunction for m=2 and m=4? At what values of p are they located?arrow_forward8. The wavefunction, y(p), for the motion of a particle in a = Neimlo. Determine the ring is of the form normalization constant, N.arrow_forwardQuantum mechanicsarrow_forward
- The ground state of the Li atom has the electronic configuration 1S2 2S1. What is its spectroscopic term? If the 2S electron is excited to the 2p state, what terms are then possible?arrow_forwardWrite the wavefunction for the n = 3 excited state of the particle in a box terms of h, m, and L. Make sure your wavefunction is properly normalized. Use the editor to format your answerarrow_forwardc) What is the ground state energy and wave function of the system, and how can they be interpreted? Explain the difference with respect to the ground state of the particle in 1D box. d) What is the degree of degeneracy in the system, and how do the possible solutions for the same energy differ? Interpret that difference.arrow_forward
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The Bohr Model of the atom and Atomic Emission Spectra: Atomic Structure tutorial | Crash Chemistry; Author: Crash Chemistry Academy;https://www.youtube.com/watch?v=apuWi_Fbtys;License: Standard YouTube License, CC-BY