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-.
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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? 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”
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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.
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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.