p40_053.pdf
(
53 KB
)
Pobierz
Chapter 40 - 40.53
the Bohr radius. (See Eq. 40-31.) We want to evaluate the integral
0
P
(
r
)
dr
. Eq. 15 in the integral
table of Appendix E is an integral of this form. We set
n
= 2 and replace
a
in the given formula with
2
/a
and
x
with
r
.Then
∞
a
3
∞
0
4
a
3
2
(2
/a
)
3
=1
.
P
(
r
)
dr
=
r
2
e
−
2
r/a
dr
=
0
53. The radial probability function for the ground state of hydrogen is
P
(
r
)=(4
r
2
/a
3
)
e
−
2
r/a
,where
a
is
4
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p40_004.pdf
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p40_005.pdf
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