Chapter 32 Medical Applications of Nuclear Physics
32.6 Fission
Summary
- Define nuclear fission.
- Discuss how fission fuel reacts and describe what it produces.
- Describe controlled and uncontrolled chain reactions.
Nuclear fission is a reaction in which a nucleus is split (or fissured). Controlled fission is a reality, whereas controlled fusion is a hope for the future. Hundreds of nuclear fission power plants around the world attest to the fact that controlled fission is practical and, at least in the short term, economical, as seen in Figure 1. Whereas nuclear power was of little interest for decades following TMI and Chernobyl (and now Fukushima Daiichi), growing concerns over global warming has brought nuclear power back on the table as a viable energy alternative. By the end of 2009, there were 442 reactors operating in 30 countries, providing 15% of the world’s electricity. France provides over 75% of its electricity with nuclear power, while the US has 104 operating reactors providing 20% of its electricity. Australia and New Zealand have none. China is building nuclear power plants at the rate of one start every month.

Fission is the opposite of fusion and releases energy only when heavy nuclei are split. As noted in Chapter 32.5 Fusion, energy is released if the products of a nuclear reaction have a greater binding energy per nucleon (
Example 1: Calculating Energy Released by Fission
Calculate the energy released in the following spontaneous fission reaction:
given the atomic masses to be
Strategy
As always, the energy released is equal to the mass destroyed times
Solution
The products have a total mass of
The mass lost is the mass of
so the energy released is
Discussion
A number of important things arise in this example. The 171-MeV energy released is large, but a little less than the earlier estimated 240 MeV. This is because this fission reaction produces neutrons and does not split the nucleus into two equal parts. Fission of a given nuclide, such as
Spontaneous fission can occur, but this is usually not the most common decay mode for a given nuclide. For example,
where
An example of a typical neutron-induced fission reaction is
Note that in this equation, the total charge remains the same (is conserved):


Not every neutron produced by fission induces fission. Some neutrons escape the fissionable material, while others interact with a nucleus without making it fission. We can enhance the number of fissions produced by neutrons by having a large amount of fissionable material. The minimum amount necessary for self-sustained fission of a given nuclide is called its critical mass. Some nuclides, such as
The reason
Most fission reactors utilize

Control rods containing nuclides that very strongly absorb neutrons are used to adjust neutron flux. To produce large power, reactors contain hundreds to thousands of critical masses, and the chain reaction easily becomes self-sustaining, a condition called criticality. Neutron flux should be carefully regulated to avoid an exponential increase in fissions, a condition called supercriticality. Control rods help prevent overheating, perhaps even a meltdown or explosive disassembly. The water that is used to thermalize neutrons, necessary to get them to induce fission in
Example 2: Calculating Energy from a Kilogram of Fissionable Fuel
Calculate the amount of energy produced by the fission of 1.00 kg of
Strategy
The total energy produced is the number of
Solution
The number of
So the total energy released is
Discussion
This is another impressively large amount of energy, equivalent to about 14,000 barrels of crude oil or 600,000 gallons of gasoline. But, it is only one-fourth the energy produced by the fusion of a kilogram mixture of deuterium and tritium as seen in Chapter 32.5 Fusion Example 1. Even though each fission reaction yields about ten times the energy of a fusion reaction, the energy per kilogram of fission fuel is less, because there are far fewer moles per kilogram of the heavy nuclides. Fission fuel is also much more scarce than fusion fuel, and less than 1% of uranium ([latex]{\text{the} \;{^{235} \text{U}}) is readily usable.
One nuclide already mentioned is
Uranium-239 then
Neptunium-239 also
Plutonium-239 builds up in reactor fuel at a rate that depends on the probability of neutron capture by
Plutonium-239 has advantages over
PhET Explorations: Nuclear Fission
Start a chain reaction, or introduce non-radioactive isotopes to prevent one. Control energy production in a nuclear reactor!

Section Summary
- Nuclear fission is a reaction in which a nucleus is split.
- Fission releases energy when heavy nuclei are split into medium-mass nuclei.
- Self-sustained fission is possible, because neutron-induced fission also produces neutrons that can induce other fissions,
, where and are the two daughter nuclei, or fission fragments, and x is the number of neutrons produced. - A minimum mass, called the critical mass, should be present to achieve criticality.
- More than a critical mass can produce supercriticality.
- The production of new or different isotopes (especially
by nuclear transformation is called breeding, and reactors designed for this purpose are called breeder reactors.
Conceptual Questions
1: Explain why the fission of heavy nuclei releases energy. Similarly, why is it that energy input is required to fission light nuclei?
2: Explain, in terms of conservation of momentum and energy, why collisions of neutrons with protons will thermalize neutrons better than collisions with oxygen.
3: The ruins of the Chernobyl reactor are enclosed in a huge concrete structure built around it after the accident. Some rain penetrates the building in winter, and radioactivity from the building increases. What does this imply is happening inside?
4: Since the uranium or plutonium nucleus fissions into several fission fragments whose mass distribution covers a wide range of pieces, would you expect more residual radioactivity from fission than fusion? Explain.
5: The core of a nuclear reactor generates a large amount of thermal energy from the decay of fission products, even when the power-producing fission chain reaction is turned off. Would this residual heat be greatest after the reactor has run for a long time or short time? What if the reactor has been shut down for months?
6: How can a nuclear reactor contain many critical masses and not go supercritical? What methods are used to control the fission in the reactor?
7: Why can heavy nuclei with odd numbers of neutrons be induced to fission with thermal neutrons, whereas those with even numbers of neutrons require more energy input to induce fission?
8: Why is a conventional fission nuclear reactor not able to explode as a bomb?
Problems & Exercises
1: (a) Calculate the energy released in the neutron-induced fission (similar to the spontaneous fission in Example 1)
given
2: (a) Calculate the energy released in the neutron-induced fission reaction
given
(b) Confirm that the total number of nucleons and total charge are conserved in this reaction.
3: (a) Calculate the energy released in the neutron-induced fission reaction
given
(b) Confirm that the total number of nucleons and total charge are conserved in this reaction.
4: Confirm that each of the reactions listed for plutonium breeding just following Example 2 conserves the total number of nucleons, the total charge, and electron family number.
5: Breeding plutonium produces energy even before any plutonium is fissioned. (The primary purpose of the four nuclear reactors at Chernobyl was breeding plutonium for weapons. Electrical power was a by-product used by the civilian population.) Calculate the energy produced in each of the reactions listed for plutonium breeding just following Example 2. The pertinent masses are
6: The naturally occurring radioactive isotope
(a) What are
(b) Write the reaction equation for neutron captured by
(c) The product nucleus
(d) Confirm that the final nucleus has an odd number of neutrons, making it a better fission fuel.
(e) Look up the half-life of the final nucleus to see if it lives long enough to be a useful fuel.
7: The electrical power output of a large nuclear reactor facility is 900 MW. It has a 35.0% efficiency in converting nuclear power to electrical.
(a) What is the thermal nuclear power output in megawatts?
(b) How many
(c) What mass of
8: A large power reactor that has been in operation for some months is turned off, but residual activity in the core still produces 150 MW of power. If the average energy per decay of the fission products is 1.00 MeV, what is the core activity in curies?
Glossary
- breeder reactors
- reactors that are designed specifically to make plutonium
- breeding
- reaction process that produces 239Pu
- criticality
- condition in which a chain reaction easily becomes self-sustaining
- critical mass
- minimum amount necessary for self-sustained fission of a given nuclide
- fission fragments
- a daughter nuclei
- liquid drop model
- a model of nucleus (only to understand some of its features) in which nucleons in a nucleus act like atoms in a drop
- nuclear fission
- reaction in which a nucleus splits
- neutron-induced fission
- fission that is initiated after the absorption of neutron
- supercriticality
- an exponential increase in fissions
Solutions
Problems & Exercises
1: (a) 177.1 MeV
(b) Because the gain of an external neutron yields about 6 MeV, which is the average
(c)
3: (a) 180.6 MeV
(b)
5:
7: (a)
(b)
(c) 991 kg