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Magnetism
155
19.32
Since the centripetal acceleration is furnished by the magnetic force acting on the ions,
2
mv
qvB
r
=
or the radius of the path is
mv
r
qB
=
. Thus, the distance between the impact
points (that is, the difference in the diameters of the paths followed by the
U
and the
isotopes) is
238
235
U
()
238
235
238
235
5
27
19
2
2
23
.00 10 ms
kg
238 u
235 u
1.66
10
u
1.60
10
C
0.600 T
v
drr
mm
qB
−
−
∆=
−
=
−
×
=−
×
×
or
2
3.11
10
m
3.11 cm
d
−
×
=
19.33
In the perfectly elastic, head-on collision between the
-particle
α
and the initially
stationary proton, conservation of momentum requires that
mv
0
αα
pp
+
=
while
conservation of kinetic energy also requires that
( )
o
r
v
v
00
v
0
vv
v
−
−
=
+
. Using
the fact that
4
p
=
and combining these equations gives
( )
4
or
p
=
0
4
v
++
3
5
v
v
=
and
( )
0
35
85
p
vv vv
=+
=
Thus,
0
33
5 3
55
8 8
v v
==
=
After the collision, each particle follows a circular path in the horizontal plane with the

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