5. Show that the following wavefunctions areorthogonalY1 (r) =i() = 2(2)}efao142 (r) =(2 – p) e-?ao82

Given: Two wave function, whose orthogonality can be tested as follows:

Answered: 5. Show that the following…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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V7.
Solve Q12
The tables above show the radial wavefunctions and the spherical harmonics wavefunctions for Hydrogen atomic orbitals. a. Write down the complete wavefunction of a Hydrogen atomic orbital which has quantum numbers of (n, I, mi) = (3, 1, 1) and simplify it as much as possible. b. Draw the radial plot (R(r) vs r) and find out how many nodes it has. Calculate the distance of the radial node from the nucleus. Write down the real part wavefunction of this orbital and find out the angular node(s). d. How many total nodes does this orbital has? с.
21.47 For I2, V = 6.395×10¹2s¹ and the internuclear distance is 2.67 Å. For I₂(g), calculate (a) U500-U0; (b) H500-Uo; (c) S500 (d) G500-U0
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5. Show that the following wavefunctions are orthogonal v, (7) = 2(2)*e-f ao Y2 (r) = (2 – p) e-? ao 82