13. If an electron is in the ground state of the hydrogen atom, the probability that its distance from the proton is more than one Bohr radius is approximately.
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Answer:
15.a
Explanation:
The radial probability function for the ground state of hydrogen is
P(r)=(4r
2
/a
3
)e
−2r/a
where a is the Bohr radius.
The integral table of Appendix E may be used to evaluate the integral r
avg
=∫
0
∞
rP(r)dr.
Setting n=3 and
replacing a in the given formula
with 2/a (and x with r), we obtain
r
avg
=∫
0
∞
rP(r)dr=
a
3
4
∫
0
∞
r
3
e
−2r/a
dr
=
a
3
4
(2/a)
4
6
=1.5a
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