Nuclear Reactions
PHY 3101
D. Acosta
Nuclear Alchemy
n
First nuclear reaction performed by
Rutherford in 1919 using α-particles:
4
14
1
17
2 He + 7 N→1 H + 8 O
n
Reaction Energy:
a
f a
f
Q = M initial products − M final products × c 2
n
Exothermic: energy released in reaction
Endothermic: energy absorbed in reaction
– Goes into mass
n
Nuclear reactions take place in atmosphere:
n
1
14
1
14
0 n+ 7 N →1 H + 6 C
– Carbon binds to form CO 2 which is
absorbed by plants and animals
n
Carbon-14 dating:
– 14C is continually replenished until the
plant or animal dies
– 14C decays, and amount left gives age
– t1/2 = 5730 years
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PHY 3101 -- D. Acosta
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Nuclear Fission
n
Enrico Fermi and Italian groups bombard
nuclei with neutrons to produce new isotopes:
1
A
A +1
0 n + Z X→ Z X
n
In 1938, Hahn and Strassman in Germany
split uranium
Frisch and Lise Meitner call it fission
(like cell division) and observe that excess
energy is shed (exothermic)
Excess neutrons are released which may
catalyze more reactions
Niels Bohr points out that 235U (0.7% natural
abundance) is more likely than 238U (99.3%)
to fission because of odd number of neutrons
– Need to use enriched uranium
Many possible fission fragments are possible
For example:
99
134
n+ 235
92 U → 40 Zr + 52Te + 3n
Energy released is:
n
Average number of neutrons released is 2.3
n
n
n
n
n
n
1.0087u + 235.04u
– 98.92u –133.91u –3(1.0087u) = 0.2u ⇒ 185 MeV
4/13/2001
PHY 3101 -- D. Acosta
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Nuclear Fission
n
n
n
n
n
n
n
Uranium is on the downward slope of the
binding energy per nucleon curve
More energetically favorable for Uranium to
split into smaller nuclei
More neutrons are released than incident
If the released neutrons are absorbed, this
starts a chain reaction
Critical Mass:
– Larger mass sustains chain reaction
– Smaller mass implies neutrons escape
– Critical mass is a few kg for uranium
Controlled fission: moderators slow and
absorb neutrons
More efficient fission from plutonium, which
can be produced by bombarding 238U with
neutrons to get 239Pu
– Average of 2.7 neutrons per Pu fission
– t1/2 = 24,000 years
4/13/2001
PHY 3101 -- D. Acosta
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Atomic Bomb
n
Suppose 1 kg of enriched 235U fissions:
Q=
185 MeV 1 kg
1u
32
×
×
=
4
.
7
×
10
eV
fission
235 u 1.66 × 10 -27 kg
Q = 7.6 × 1013 J = 18 kT
(1 kT of TNT = 4.2 × 1012 J = 1012 calories)
n
Large as this is, it is still small compared to
the total rest mass energy:
a fd
E = mc = 1 kg 3 × 10 m / s
2
8
i
2
E = 9 × 1016 J = 21400 kT = 21.4 MT
n
Only 1/1000 of energy released in fission
4/13/2001
PHY 3101 -- D. Acosta
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Nuclear Fusion
n
n
Dividing high Z elements librates energy, but
so does fusing low Z elements (upward part
of binding energy per nucleon curve)
Consider the fusion of deuterium and
hydrogen (powers the Sun and H-bomb)
2
1
H +11H→ 23 He + γ
Q = 2.0141u +1.00783u - 3.01603u × c 2
Q = 0.0059 uc 2 = 5.5 MeV
4/13/2001
PHY 3101 -- D. Acosta
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Solar Reactions
n
The “burning” of hydrogen into helium and
higher Z materials in stars:
H.A.Bethe
n
PPI cycle:
1
1
2
+
H
+
H
→
H
+
β
+νe
1
1
1
2
1
3
H+
H
→
1
1
2 He + γ
3
3
4
1
1
He+
He
→
He+
H+
2
2
2
1
1H
n
Q = 1.44 MeV
Q = 5.5 MeV
Q = 12.9 MeV
PPII cycle:
3
4
7
He+
He
→
2
2
4 Be + γ
β - + 74 Be→ 73 Li + ν e
1
7
4
4
H+
Li
→
He+
1
3
2
2 He
n
PPIII cycle:
1
7
8
H
+
Be
→
1
4
5B + γ
8
8
+
B
→
Be
+
β
+νe
5
4
8
4
4
Be
→
He
+
4
2
2 He
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PHY 3101 -- D. Acosta
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Stars
n
n
n
n
n
Fusion of higher Z elements occurs when
lower Z fuel is exhausted
Continues until 56Fe is produced, which is at
the peak of the binding energy vs. Z curve
– Not energetically favorable to fuse
higher Z nuclei
Without energy source, star collapses and
may explode as a supernova
All elements in the periodic table besides H
and He are produced (and released) by stars
in the universe
Direct evidence for solar fusion is available
because we have detected the neutrinos
released in the solar reactions
4/13/2001
PHY 3101 -- D. Acosta
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