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82.
(a) At the smallest center-to-center separation
r
min
the initial kinetic energy
K
i
of the proton is entirely
converted to the electric potential energy between the proton and the nucleus. Thus,
K
i
=
1
4
πε
0
eq
lead
r
min
=
82
e
2
4
0
r
min
.
In solving for
r
min
using the eV unit, we note that a factor of
e
cancels in the middle line:
r
min
=
82
e
2
4
0
K
i
=
k
82
e
2
4
.
80
×
10
6
e
V
=
µ
8
.
99
×
10
9
N
·
m
2
C
2
¶
82(1
.
6
×
10
−
19
C)
4
.
80
×
10
6
V
=2
.
5
×
10
−
14
m=25fm
.
It is worth recalling that a volt is a Newton

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