Wavefunctions 3/2 1 (1s) = ,-Zrlao do 3/2 1 4 (2s) 2 4V27 \do.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 23E
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Show that the Hydrogenic Wavefunctions in Table 11.2 obey the Schrodinger Equation

 

TABLE 11.2 Hydrogenic Wavefunctions*
n
m,
3/2
1
p(1s) :
1
-Zrlao
e
V\ao.
3/2
1
4 (2s)
Zr
2
-Zr/2ao
e
%3D
-
4V2\ao.
do
5/2
1
-Zr/2ao
2
1
Y(2p;)
(z) e
4V2\ao.
Z 5/2
(х) е Zr/2a
1
Y(2px)
4V27\4o.
2
1
土1
Z 5/2
(y) e¯Zr/2ao
V(2p,)
4V27 \do.
= r cos 0
ao =
Bohr radius
0.529 Å
= 0.529×1010 m
me?
x = r sin 0 cos o
y = r sin 0 sin &
12 = x? + y? + z?
Note that the wavefunctions are separable, such that ¼(r,0,4) = g(r)h(0,4).
Z= charge on nucleus
%3D
||
||
Transcribed Image Text:TABLE 11.2 Hydrogenic Wavefunctions* n m, 3/2 1 p(1s) : 1 -Zrlao e V\ao. 3/2 1 4 (2s) Zr 2 -Zr/2ao e %3D - 4V2\ao. do 5/2 1 -Zr/2ao 2 1 Y(2p;) (z) e 4V2\ao. Z 5/2 (х) е Zr/2a 1 Y(2px) 4V27\4o. 2 1 土1 Z 5/2 (y) e¯Zr/2ao V(2p,) 4V27 \do. = r cos 0 ao = Bohr radius 0.529 Å = 0.529×1010 m me? x = r sin 0 cos o y = r sin 0 sin & 12 = x? + y? + z? Note that the wavefunctions are separable, such that ¼(r,0,4) = g(r)h(0,4). Z= charge on nucleus %3D || ||
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