1. AP Physics B Montwood High School R. Casao
Nuclear Fission
AP Physics B
Montwood High School
R. Casao

2. Nuclear Fission
Nuclear fission is a decay process in which an unstable nucleus splits into two fragments of comparable mass.
Fission was discovered through experiments in which uranium was bombarded with neutrons to produce two massive fragments (called fission fragments) and two or three free neutrons.
Occasionally a light nuclide, such as H-3 is produced.

3. Fission resulting from neutron absorption is called induced fission.
Both the common isotope U-238 (99.3%) and the uncommon isotope U-235 (0.7%) can be easily split by neutron bombardment.
U-235 by slow neutrons
U-238 by neutrons with a minimum of 1 MeV of energy.
Fission resulting from neutron absorption is called induced fission.
Some nuclides can undergo spontaneous fission without initial neutron absorption

4. When U-235 absorbs a neutron, the resulting U-236
When U-235 absorbs a neutron, the resulting U-236* nuclide is in a highly excited state and splits into two fragments almost immediately.
It is usually denoted as the fission of U-235 even though it is really U-236* that undergoes fission.
Over 100 different nuclides, representing more than 20 different elements, have been found among the fission products.

5. Distribution of mass numbers for fission fragments from the fission of U-235.
Most of the fragments have mass numbers from 90 to 100 and from 135 to 145.
Fission into two fragments with nearly equal mass is unlikely.

6. Two Typical Fission Reactions:
Total kinetic energy of the fission fragments is enormous (about 200 MeV), compared to typical a and b energies of a few MeV.
Reason: nuclides at the high end of the mass spectrum (near A = 240) are less tightly bound than those nearer the middle (near A = 90 to 145).

7. The average binding energy per nucleon is about 7
The average binding energy per nucleon is about 7.6 MeV at A = 240 but about 8.5 MeV at A = 120.
A rough estimate of the expected increase in binding energy during fission is about 8.5 MeV – 7.6 MeV = 0.9 MeV per nucleon, or a total of 235 nucleons·0.9 MeV/nucleon = MeV.
It may seem to be a violation of conservation of energy to have an increase in both the binding energy and the kinetic energy during a fission reaction.

8. Relative to the total rest energy Eo of the separated nucleons, the rest energy of the nucleus is Eo –EB. Rest energy corresponds to mass.
An increase in binding energy corresponds to a decrease in rest energy as rest energy is converted to kinetic energy of the fission fragments.
Fission fragments always have too many neutrons to be stable.
The neutron/proton ratio for stable nuclei is about 1 for light nuclides but almost 1.6 for the heaviest nuclides because of the increasing influence of the electrical repulsion of the protons.

9. The neutron/proton ratio for stable nuclides is about 1
The neutron/proton ratio for stable nuclides is about 1.3 at A = 100 and 1.4 at A = 150.
The fission fragments have about the same neutron/proton ratio as U-235, about 1.55.
They usually respond to this surplus of neutrons by undergoing a series of b- decays until a stable neutron/proton ratio is reached.
Example:
The Ce-140 nuclide is stable.
This series of b- decays produces about 15 MeV of additional kinetic energy.

10. Liquid-Drop Model A. U-235 nucleus absorbs a neutron.
B. The resulting U*-236 nucleus has excess energy which causes violent oscillations during which a neck between two lobes develops (C).

11. D. Electrical repulsion of these two lobes stretches the neck farther apart until the two lobes separate.
E. The separated lobes are fission fragments.
F. Neutrons are emitted from the fission fragments at the time of fission or a few seconds later.
Liquid-Drop Model

12. U-235 Fission

13. U-235 Fission

14. Chain Reactions
Fission of a uranium nucleus, triggered by neutron bombardment, releases other neutrons that can trigger more fissions, creating a chain reaction.
AtomicArchive.com Nuclear Fission Animation
If an least one neutron from U-235 fission strikes another nucleus and causes it to fission, then the chain reaction will continue.

15. Chain Reactions
If the reaction will sustain itself, it is said to be "critical", and the mass of U-235 required to produced the critical condition is said to be a “critical mass".
A critical chain reaction can be achieved at low concentrations of U-235 if the neutrons from fission are moderated to lower their speed, since the probability for fission with slow neutrons is greater.

16. Chain Reactions
The chain reaction may be made to proceed slowly and in a controlled manner in a nuclear reactor or explosively in a bomb.
The energy released in a chain reaction is enormous, far greater than that in any chemical reaction.

17. Chain Reactions

18. Example of Energy Yield: Uranium-235 Fission
Nuclear fission of U-235 yields an enormous amount of energy from the fact that the fission products have less total mass than the uranium nucleus, a mass change that is converted to energy by E = mc2.

20. Chain Reactions
A fission chain reaction produces intermediate mass fragments which are highly radioactive and produce further energy by their radioactive decay. Some of them produce neutrons, called delayed neutrons, which contribute to the fission chain reaction.
On average, each fission of a U-235 nucleus produces 2.5 free neutrons, so 40% of the neutrons are needed to sustain a chain reaction.
A U-235 nucleus is more likely to absorb a low-energy neutron (less than 1 eV) than one of the higher energy (1 MeV) that are released during fission.

21. Chain Reactions
In a nuclear reactor, the higher energy neutrons are slowed down by collisions with nuclei in the surrounding material (called the moderator), so they are more likely to cause further fissions.
In nuclear power plants, the moderator is often water and sometimes graphite.
The rate of the reaction is controlled by inserting or withdrawing control rods made of elements (such as boron or cadmium) whose nuclei absorb neutrons without undergoing any additional reaction.

22. Chain Reactions
The isotope U-238 can also absorb neutrons, creating U*-239, but not with high enough probability for it to sustain a chain reaction by itself.
Uranium that is used in reactors is often “enriched” by increasing the proportion of U-235 above the natural value of 0.7%, typically to 3%.

23. Nuclear Fission Reactors
The most familiar application of nuclear reactors is for the generation of electric power.
The fission energy appears as kinetic energy of the fission fragments, and its intermediate result is to increase the internal energy of the fuel elements and the surrounding moderator.
The increase in internal energy is transferred as heat to boil water  produce steam  turn a turbine  run a generator  produce electricity.
The energy in the fission fragments heat the water surrounding the reactor core.
A steam generator is a heat exchanger that takes heat from this highly radioactive water and generates non-radioactive steam to run the turbines.

24. Boiling Water Reactor
In the boiling water reactor, the water which passes over the reactor core to act as moderator and coolant is also the steam source for the turbine.
The disadvantage of this is that any fuel leak might make the water radioactive and that radioactivity would reach the turbine and the rest of the loop.
A typical operating pressure for such reactors is about 70 atm at which pressure the water boils at about 285 °C. This operating temperature gives a Carnot efficiency of only 42% with a practical operating efficiency of around 32%, somewhat less than the pressurized water reactor.

25. Boiling Water Reactor

26. Pressurized Water Reactor
In the pressurized water reactor, the water which passes over the reactor core to act as moderator and coolant does not flow to the turbine, but is contained in a pressurized primary loop.
The primary loop water produces steam in the secondary loop which drives the turbine.
The obvious advantage to this is that a fuel leak in the core would not pass any radioactive contaminants to the turbine and condenser.
Another advantage is that the PWR can operate at higher pressure and temperature, about 160 atm and about 315 °C.
This provides a higher Carnot efficiency than the BWR, but the reactor is more complicated and more costly to construct.

27. Pressurized Water Reactor
Most of the U.S. reactors are pressurized water reactors.

28. Pressurized Water Reactor

29. Liquid-Metal Fast-Breeder Reactor
The plutonium-239 breeder reactor is commonly called a fast breeder reactor, and the cooling and heat transfer is done by a liquid metal.
The metals which can accomplish this are sodium and lithium, with sodium being the most abundant and most commonly used.
The construction of the fast breeder requires a higher enrichment of U-235 than a light-water reactor, typically 15 to 30%.
The reactor fuel is surrounded by a "blanket" of non-fissionable U-238.
No moderator is used in the breeder reactor since fast neutrons are more efficient in transmuting U-238 to Pu-239.
At this concentration of U-235, the cross-section for fission with fast neutrons is sufficient to sustain the chain-reaction.
Using water as coolant would slow down the neutrons, but the use of liquid sodium avoids that moderation and provides a very efficient heat transfer medium.

30. Breeding Plutonium-239
Fissionable plutonium-239 can be produced from non-fissionable uranium-238.
The bombardment of uranium-238 with neutrons triggers two successive beta decays with the production of plutonium.
The amount of plutonium produced depends on the breeding ratio (the amount of fissile plutonium-239 produced compared to the amount of fissionable fuel (like U-235) used to produced it .

31. Liquid-Metal Fast-Breeder Reactor