Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
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Question
Chapter 44, Problem 10SP
To determine
The four quantum numbers for each electron in the ground state of a helium atom.
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Find the position expected value for an electron in the ground state of hydrogen. Express your
answers in terms of the Bohr radius a.
A partio
a ground
nd
A Construct the wavefunction V(r, 0, ¢) for an H atoms' electron in the state 2pz. Please
note that in order to have a real-valued wavefunction of pr 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.
Px
1/2
Yg = ()"" (5 cos 0 -3 cos 0)
cos e
%3D
(4x
21 12
64л/
1/2
sin e (5 cos? e- 1)eti
87
-y
Y =
(3 cos²0 – 1)
105 1/2
32
sin e cos de2ie
(167
15 12
sin e cos betie
35 12
(647
sin de i
B Now consider an excited state of He atom with electron configuration 1s 2s'. In general,
the wavefunction is a state:
V(r, 0, 0, 02) = V(r,0, ø)V..
where V(r, 0, 6) and V,, represent the spatial and the spin part. The spatial part is
constructed from the wavefunctions of the 1s' and 2s' orbitals denoted as o (r, 0, ø)
and o (r, 0,…
What are the total angular momentum and the spectroscopic notation for the ground state of helium?
Chapter 44 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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