1. Kinetic energy (we use the classical formula since
v
is much less than
c
) is converted
into potential energy (see Eq. 24-43). From Appendix F or G, we find
Z
= 3 for Lithium
and
Z
= 90 for Thorium; the charges on those nuclei are therefore 3
e
and 90
e
,
respectively. We manipulate the terms so that one of the factors of
e
cancels the “e” in the
kinetic energy unit MeV, and the other factor of
e
is set to be 1.6
×
10
–19
C. We note that
k
=
1 4
0
π
ε
can be written as 8.99
×
10
9
V·m/C. Thus, from energy conservation, we
have
(
)(
)
(
)
9
19
V m
C
1
2
6
8.99
10
3 1.6
10
C
90
3.00
10 eV
e
kq q
K
U
r
K
−
⋅
×
×
×
=
⇒
=
=
×
which yields
r
= 1.3
×
10
– 13
m (or about 130 fm).

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