# Medical Applications of Nuclear Physics

## Fission


### Learning Objectives

By the end of this section, you will be able to:
1. Define nuclear fission.
2. Discuss how fission fuel reacts and describe what it produces.
3. 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 . 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 Fusion, energy is released if the products of a nuclear reaction have a greater binding energy per nucleon () than the parent nuclei.  shows that  is greater for medium-mass nuclei than heavy nuclei, implying that when a heavy nucleus is split, the products have less mass per nucleon, so that mass is destroyed and energy is released in the reaction. The amount of energy per fission reaction can be large, even by nuclear standards. The graph in  shows  to be about 7.6 MeV/nucleon for the heaviest nuclei ( about 240), while  is about 8.6 MeV/nucleon for nuclei having  about 120. Thus, if a heavy nucleus splits in half, then about 1 MeV per nucleon, or approximately 240 MeV per fission, is released. This is about 10 times the energy per fusion reaction, and about 100 times the energy of the average , , or  decay.
Spontaneous fission can occur, but this is usually not the most common decay mode for a given nuclide. For example, 
        
          
     can spontaneously fission, but it decays mostly by  emission. Neutron-induced fission is crucial as seen in . Being chargeless, even low-energy neutrons can strike a nucleus and be absorbed once they feel the attractive nuclear force. Large nuclei are described by a liquid drop model with surface tension and oscillation modes, because the large number of nucleons act like atoms in a drop. The neutron is attracted and thus, deposits energy, causing the nucleus to deform as a liquid drop. If stretched enough, the nucleus narrows in the middle. The number of nucleons in contact and the strength of the nuclear force binding the nucleus together are reduced. Coulomb repulsion between the two ends then succeeds in fissioning the nucleus, which pops like a water drop into two large pieces and a few neutrons. Neutron-induced fission can be written as
where  and  are the two daughter nuclei, called fission fragments, and  is the number of neutrons produced. Most often, the masses of the fission fragments are not the same. Most of the released energy goes into the kinetic energy of the fission fragments, with the remainder going into the neutrons and excited states of the fragments. Since neutrons can induce fission, a self-sustaining chain reaction is possible, provided more than one neutron is produced on average — that is, if  in . This can also be seen in .
An example of a typical neutron-induced fission reaction is 
Note that in this equation, the total charge remains the same (is conserved): 
        
          
    . Also, as far as whole numbers are concerned, the mass is constant: 
        
          
    . This is not true when we consider the masses out to 6 or 7 significant places, as in the previous example.

      
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 
        
          
    , produce more neutrons per fission than others, such as 
        
          
    . Additionally, some nuclides are easier to make fission than others. In particular, 
        
          
     and 
        
          
     are easier to fission than the much more abundant 
        
          
    . Both factors affect critical mass, which is smallest for 
        
          
    .
The reason 
        
          
     and 
        
          
     are easier to fission than 
        
          
     is that the nuclear force is more attractive for an even number of neutrons in a nucleus than for an odd number. Consider that 
        
          
     has 143 neutrons, and 
        
          
     has 145 neutrons, whereas 
        
          
     has 146. When a neutron encounters a nucleus with an odd number of neutrons, the nuclear force is more attractive, because the additional neutron will make the number even. About 2-MeV more energy is deposited in the resulting nucleus than would be the case if the number of neutrons was already even. This extra energy produces greater deformation, making fission more likely. Thus, 
        
          
     and 
        
          
     are superior fission fuels. The isotope 
        
          
     is only 0.72 % of natural uranium, while 
        
          
     is 99.27%, and 
        
          
     does not exist in nature. Australia has the largest deposits of uranium in the world, standing at 28% of the total. This is followed by Kazakhstan and Canada. The US has only 3% of global reserves. 
Most fission reactors utilize 
        
          
    , which is separated from 
        
          
     at some expense. This is called enrichment. The most common separation method is gaseous diffusion of uranium hexafluoride () through membranes. Since 
        
          
     has less mass than 
        
          
    , its  molecules have higher average velocity at the same temperature and diffuse faster. Another interesting characteristic of 
        
          
     is that it preferentially absorbs very slow moving neutrons (with energies a fraction of an eV), whereas fission reactions produce fast neutrons with energies in the order of an MeV. To make a self-sustained fission reactor with 
        
          
    , it is thus necessary to slow down (“thermalize”) the neutrons. Water is very effective, since neutrons collide with protons in water molecules and lose energy.  shows a schematic of a reactor design, called the pressurized water reactor.
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 
        
          
    , and achieve criticality, provides a negative feedback for temperature increases. In case the reactor overheats and boils the water to steam or is breached, the absence of water kills the chain reaction. Considerable heat, however, can still be generated by the reactor’s radioactive fission products. Other safety features, thus, need to be incorporated in the event of a loss of coolant accident, including auxiliary cooling water and pumps.
One nuclide already mentioned is 
        
          
    , which has a 24,120-y half-life and does not exist in nature. Plutonium-239 is manufactured from 
        
          
     in reactors, and it provides an opportunity to utilize the other 99% of natural uranium as an energy source. The following reaction sequence, called breeding, produces 
        
          
    . Breeding begins with neutron capture by 
        
          
    :
Uranium-239 then  decays:
Neptunium-239 also  decays:
Plutonium-239 builds up in reactor fuel at a rate that depends on the probability of neutron capture by 
        
          
     (all reactor fuel contains more 
        
          
     than 
        
          
    ). Reactors designed specifically to make plutonium are called breeder reactors. They seem to be inherently more hazardous than conventional reactors, but it remains unknown whether their hazards can be made economically acceptable. The four reactors at Chernobyl, including the one that was destroyed, were built to breed plutonium and produce electricity. These reactors had a design that was significantly different from the pressurized water reactor illustrated above.
Plutonium-239 has advantages over 
        
          
     as a reactor fuel — it produces more neutrons per fission on average, and it is easier for a thermal neutron to cause it to fission. It is also chemically different from uranium, so it is inherently easier to separate from uranium ore. This means 
        
          
     has a particularly small critical mass, an advantage for nuclear weapons.

### Test Prep for AP Courses


### Section Summary

1. Nuclear fission is a reaction in which a nucleus is split.
2. Fission releases energy when heavy nuclei are split into medium-mass nuclei.
3. 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. 
4. A minimum mass, called the critical mass, should be present to achieve criticality.
5. More than a critical mass can produce supercriticality.
6. 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


### Problem Exercises
