5. Using a table of Hermite Polynomials, provide the property normalized 42. You may1(asverify your answer with: n(x) =(21)² H₂ (α²x) e-x²2nn!2.

To find the properly normalized 4th Hermite polynomial (ψ₄(x)), we need to use the following steps:…

Answered: 5. Using a table of Hermite…

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter12: Atoms And Molecules

Section: Chapter Questions

Problem 12.22E: Write a Slater determinant for the lithide ion, Li.

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E7B.3(b) Which of the following functions can be normalized (in all cases the range for x is from x = -∞ to ∞, and a is a positive constant): (i) sin(ax); (ii) cos(ax) ex²? Which of these functions are acceptable as wavefunctions?
The cyclobutadienyl cation (C4H4+) may be treated using the Huckel MO approach. The roots to the secular determinant are α+ 2β, α and α- 2β. The middle level is doubly degenerate. (a) Determine the energy for this system in terms of α and β. (b) The ionization energy for C4H4 has been determined to be 0.22 eV. Calculate α in kJ mol-1. (c) Predict the ground state multiplicities for C4H4, C4H4+, and C4H4-.
for C2H2 1- Calculate the separation at which the minimum of the potential energy occur.2- verify that at this minimum the potential energy V = ─  .3- Choose values of r such that all characteristic points and areas are shown clearly on the graph. Let the x-axis be r in pm
Consider the molecules: CH2=CH-CH=CH-CH=CH-CH=CH-CH=CH2. let’s assume that the 10 electrons that make up the double bonds can exist everywhere along the carbon chains. The electrons can then be considered as particles in a box; the ends of the molecule correspond to the boundaries of the box with a finite or zero potential energy inside. In this “molecular box”, 2 electrons can occupy an energy level. What are quantum states that the electrons from this molecule can occupy in the ground state? What’s the smallest frequency of light that can excite the electron? Briefly explain why. Note that the length of a C-C bond is about 1.54A and the length of a C=C bond is 1.34A to allow you to estimate the length of the “molecular box”
4h The chlorophylls that participate in photosynthesis and the haem groups of cytochromes are derived from the porphine dianine group (1), which belongs to the D point group. The ground electronic state is A and the lowest-lying excited state is E. Is a photon-induced transition allowed from the ground state to the excited state? Explain your answer. u : NH (1) HN:
3. Sketch xy-plane cross-section diagrams for the orbitals listed below. Indicate nodal planes and spheres by dashed lines, and regions of high electron probability by shading. Show the x and y axes. Indicate the positive and the negative parts of the wave function with plus and minus signs. (a) 4px; (b) 3s; (c) 4dxy; (d) 3d,2-2; and (e) 4s.
2. (a) Calculate the spin only magnetic moment of: 0= V O SO₂
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Proton 1 moves with a speed v from theeast coast to the west coast in the continental United States; proton 2 moves with the same speed from the southern United Statestoward Canada. (a) Is the magnitude of the magnetic force experienced by proton 2 greater than, less than, or equal to the forceexperienced by proton 1? (b) Choose the best explanation fromamong the following:I. The protons experience the same force because the magneticfield is the same and their speeds are the same.II. Proton 1 experiences the greater force because it moves atright angles to the magnetic field.III. Proton 2 experiences the greater force because it moves in thesame direction as the magnetic field.
(a) The trace of an n x n matrix A is defined as tr[A] = E;=1 Ai that is, summing over all the diagonal elements of Ä. Prove: tr[ÂB] = tr[BÂ] (b) Based on this, prove the “cyclic" relation of the trace. That is tr[ÂÊĈD] = tr[DÂBĈ| = tr[ĈDÂB]
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The Morse potential energy is very useful as a simple representation of the actual molecular potential energy. When 85Rb1H was studied, it was found that ˜ν = 936.8 cm−1 and x_eν˜ = 14.15 cm−1. Plot the potential energy curve from 50 pm to 800 pm aroundRe = 236.7 pm. Then go on to explore how the rotation of a molecule may weaken its bond by allowing for the kinetic energy of rotation of a molecule and plotting V∗ = V + hcBJ˜ (J + 1) with B˜. Plot these curves on the same diagram for J = 40, 80, and 100, and observe how the dissociation energy is affected by the rotations. Hints: Taking B˜ = 3.020 cm−1 as the equilibrium bond length will greatly simplify the calculation. The mass of 85Rb is 84.9118mu

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5. Using a table of Hermite Polynomials, provide the property normalized 42. You may 1 (as verify your answer with: n(x) = (21)² H₂ (α²x) e-x² 2nn! 2.