Le Fevre High School
SACE Stage 2 Physics
Nuclear Fission and Fusion
1. Nuclear fission is the splitting of a heavy nucleus by a neutron into two lighter nuclei. Since the binding
energy in these daughter nuclei is greater the nucleons are on average in a lower energy state. This results is a
release of energy.
2. (a) LHS : U235
1
on
RHS :
3.9027 x 10-25 kg
0.016748 x 10-25 kg
3.919448 x 10-25 kg
Ba141
2.3397 x 10-25 kg
Kr92
1.5259 x 10-25 kg
1
3 x on 0.050244 x 10-25 kg
3.9158 x 10-25 kg
mass defect = 3.604 x 10-28 kg
Calculate energy released using :
E = mc2
= 3.604 x 10-26 x (3 x 108)2
= 43.24 x 10 -11 J
= 203 MeV
(b) A chemical reaction such as is the effect of burning coal involves the binding energy of the valence
electron interactions – an energy of the order of eV. However nuclear reactions involve nuclear binding
energies which is of the order of Mev – a million times greater energy output.
3.
(a) Each fission reaction produces more neutrons than cause it. The average number of neutrons
produced per reaction is 2.5. I will assume 3 for the following diagrams: A chain reaction occurs when
one fission reaction triggers further fission reactions.
STEADY STATE chain reaction only one neutron from each reaction causes further reaction. Consider 3
reactions to start with. We see that the number of reactions per unit time remains constant. This is the
situation we aim for in a nuclear reactor.
lost
lost
n
U
U
lost
U
lost
lost
lost
UNCONTROLLED or DIVERGENT chain reaction more than one neutron per reaction causes further
reactions. The number of reactions per unit time increases rapidly. This is the condition set up in atomic
bombs.
lost
U
(b)
MODERATORS are used to moderate or slow down the neutron speeds.
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The neutrons are slowed down by allowing them to undergo elastic collisions with light nuclei which do
not tend to absorb neutrons. They have to be light otherwise they won't carry off a very high proportion
of the neutron's energy. The best moderators are heavy water (ie. deuterium oxide D2O) graphite,
beryllium or beryllium oxide. Ordinary water is fairly satisfactory as well. Consequently aqueous
solutions of uranium compounds have relatively low critical masses. It is possible to attain a critical
mass for natural uranium if it is interspersed with graphite and water moderators. The critical mass is
about 100 tonne!
(c)
CRITICAL MASS
We will consider a mixture of U
238
235
and U
and consider the chances of sustaining a chain reaction in the
235
material. On average 2.5 neutrons are produced per fission of U . If on average 1 out of these 2.5
neutrons produces a further fission we will have a steady chain reaction. If more than 1 then the reaction
will be divergent. Neutrons released in a fission reaction can do one of four things:
(1) Escape Neutrons may escape from the uranium mixture altogether without causing fission. This is
quite likely as neutrons have to pass very close to the nucleus of an atom to be absorbed and as we have
seen nuclei are small! Escape becomes less likely if the volume of material is increased and if spherical
shapes are used rather than long flat ones.
238
(2) Be Captured by U
(this eventually produces plutonium).
(3) Be captured by non fissionable nuclei.
235
(4) Cause fission in U
nucleus
escape
Absorbed X
n
3
1
n
238
2
4
Captured
n
n
235
n
Fission
n
n
Normal uranium is only .7% U hence options (1) and (2) are the most likely.
CRITICAL MASS: This is the amount of mass of the nuclear fuel that is large enough to produce a
steady state chain reaction.
235
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4.
The kinetic energy transferred from one particle to another depends on the ratio of their masses.(This was
covered in tutorial 45.3 and 49.2.) If the masses are approximately equal (as in the case of a neutron and
hydrogen nucleus) then a large transfer of kinetic energy and momentum occurs. This results in a slow
speed neutron after interaction. Normal water consists of hydrogen (nucleus is a proton) and
consequently absorbs a large quantity of kinetic energy from the incident neutron, but is too effective in
slowing down the neutron. Deuterium is an isotope of hydrogen and its nucleus consists of a proton and
a neutron, approximately twice the mass of the neutron. Hence less kinetic energy will transfer to the
deuterium on collision than in the case of “normal” hydrogen. This slows to neutron down to a speed
required to produce further fission reactions with uranium nuclei.
5.
Nuclear reactor consists of the following components.
Fuel Rods: Uranium or Plutonium
Control rods: Materials such as cadmium or Boron which act as neutron absorbers. Lowered into the pile
of the reactor when the neutron flux becomes greater than one.
Moderators: Placed within the nuclear pile to slow down some of the high energy neutrons and so increase
the probability of these initiating fission when they do collide with the fuel. (Heavy water is more
effective but costly)
Shielding: materials: surrounding the nuclear pile to absorb radioactive emissions from the nuclear pile.
Typically Ferro-concrete materials.
Coolant: Sodium (molten) or Helium (gas) absorbs the heat generated in the nuclear reactions and then
flows through a heat exchanger where the high temperature converts water to super-heated steam and
this then drives the turbines and generates electricity.
Fuel
rods
Control
super heated steam out
rods
Cool
Sodium in
Heat
exchanger
electricity
Turbines output
Heated
Sodium out
Shielding
Moderator
cold water in
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Select any two advantages from the following:
Negligible greenhouse gas emission, relatively cheap when established on a large scale energy production,
can be used to produce medical-isotopes, relatively abundant fuel supplies.
7.
Fusion is the joining together of light nuclei to form heavier nuclei of higher binding energy with a
consequent release of energy.
8.
When two hydrogen nuclei fuse, the mass of the reactants is less than the mass of the products. This mass
defect is converted into kinetic energy of the products. The kinetic energy is converted to heat energy and
raises the temperature of the material.
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9.
The reactions in the proton cycle are as follows:
1
+ 1H1  1H2 + +1e0 + 00
1H
1
1H
+
1
1H
+
3
2He
+

1
1H
+
1
1H

2
1H
3
2He
+
0
+1e
+
0
 2He4 +
1
1H
+
1
1H
2
1H

2
1H
3
2He
Hence net effect
41H1  2He4
0
3
2He
+ 2+1e0 + 2
The reactions in the carbon cycle are:
1
12
+
 7N13
1H
6C
13
7N

13
6C
+
1
1H
0
+1e
+
6C
+
0
o
 7N14
13
1
1H
+
14
7N
 8O15
15
8O

15
7N
+
0
+1e
+
0
0
+ 7N15  6C12 + 2He4
Hence net effect
41H1  2He4 + 2+1e0 + 2
1
1H
(b) From above the other particles emitted are two positrons and two neutrinos.
.
4