Construct the wavefunction V(r, 0, ø) for an H atoms' electron in the state 2p,. Please note that in order to have a real-valued wavefunction of p, orbital(see below), you need to do a linear superposition of the corresponding spherical harmonics for the angular part. Use the spherical harmonics table below. Show that the superposition you selected indeed results in a real orbital; however, you do not need to simplify the expressions further or normalize the wavefunction.

Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Construct the wavefunction V(r, 0, ø) for an H atoms' electron in the state 2p. Please
note that in order to have a real-valued wavefunction of p, orbital(see below), you need
to do a linear superposition of the corresponding spherical harmonics for the angular
part. Use the spherical harmonics table below. Show that the superposition you selected
indeed results in a real orbital; however, you do not need to simplify the expressions
further or normalize the wavefunction.
y8 = )
Y =
1/2
%3D
Px
3 12
1/2
cos 0
YO = G6)" (5 cos 0-3 cos 0)
%3D
4x
Y1 =7()2 sin Be*io
Y =7(2112 sin 0 (5 cos 6-1)etio
%3D
647)
-y
Yg = G)" (3 cos²0- 1)
Y = " sin? o cos de2i¢
105 1/2
!3!
327
1бл
Y =7
(15 1/2
87
35 12
sin 6e*3i0
1647
sin e cos detie
%3D
%3D
Transcribed Image Text:Construct the wavefunction V(r, 0, ø) for an H atoms' electron in the state 2p. Please note that in order to have a real-valued wavefunction of p, orbital(see below), you need to do a linear superposition of the corresponding spherical harmonics for the angular part. Use the spherical harmonics table below. Show that the superposition you selected indeed results in a real orbital; however, you do not need to simplify the expressions further or normalize the wavefunction. y8 = ) Y = 1/2 %3D Px 3 12 1/2 cos 0 YO = G6)" (5 cos 0-3 cos 0) %3D 4x Y1 =7()2 sin Be*io Y =7(2112 sin 0 (5 cos 6-1)etio %3D 647) -y Yg = G)" (3 cos²0- 1) Y = " sin? o cos de2i¢ 105 1/2 !3! 327 1бл Y =7 (15 1/2 87 35 12 sin 6e*3i0 1647 sin e cos detie %3D %3D
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