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75. A generalized formation reaction can be written X + x
→
Y, where X is the target nucleus, x is the
incident light particle, and Y is the excited compound nucleus (
20
Ne). We assume X is initially at rest.
Then, conservation of energy yields
m
X
c
2
+
m
x
c
2
+
K
x
=
m
Y
c
2
+
K
Y
+
E
Y
where
m
X
,
m
x
,and
m
Y
are masses,
K
x
and
K
Y
are kinetic energies, and
E
Y
is the excitation energy
of Y. Conservation of momentum yields
p
x
=
p
Y
.
Now,
K
Y
=
p
2
Y
/
2
m
Y
=
p
2
x
/
2
m
Y
=(
m
x
/m
Y
)
K
x
,so
m
X
c
2
+
m
x
c
2
+
K
x
=
m
Y
c
2
+(
m
x
/m
Y
)
K
x
+
E
Y
and
K
x
=
m
Y
m
Y
−
m
x
£
(
m
Y
−
m
X
−
m
x
)
c
2
+
E
Y
¤
.
(a) Let
x
represent the alpha particle and X represent the
16
O nucleus. Then, (
m
Y
−
m
X
−
m
x
)
c
2
=
(19
.
99244 u
−
15
.
99491 u
−
4
.
00260 u)(931
.
5MeV
/
u) =
−
4
.
722 MeV and
K
α
=
19
.
99244 u
19
.
99244 u
−
4
.
00260 u
(
−
4
.
722 MeV + 25
.
0MeV)=25
.
35 MeV
.
(b) Let
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics, Conservation Of Energy, Energy, Light

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