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24.1Nuclear fission
We will now discuss nuclear fission, a special kind of nuclear reaction in which the ideas we learned in SectionÂ 23.1 will come to be applied. Nuclear fission is the process in which a heavy nucleus splits up into two lighter nuclei. This can happen when the nucleus is bombarded by a neutron, and in this case we speak of induced fission. When a neutron is absorbed by a nucleus of uranium-235, the nucleus momentarily turns into uranium-236. It then splits into lighter nuclei plus neutrons. One possibility is:
n01+UÂ Â 92235âUÂ Â 92236âBaÂ Â 56144+Kr3689+3n01
In spontaneous fission a nucleus may split into two smaller nuclei without neutron absorption. An example is the reaction: CfÂ Â 98254âPdÂ Â 46118+TeÂ Â 52132+4n01.
The production of neutrons is a key feature of fission reactions, and use is made of this in a nuclear reactor (see next section).
The energy released can be calculated through mass differences as follows:
Îm=(235.0439299+1.008665îîîîîîîîîîîîîîîîîîîîîîîîîîîîtotal mass of reactantsÂ )Â uâ(143.92292+88.91781+3Ã1.008665îîîîîîîîîîîîîîîîîîîîîîîîîîîîîîîîîîîîîîîîîîîîtotal mass of productsÂ )Â u=0.18587Â u
Thus for this reaction, the energy released is:
Q=Îmc2=0.18587Ã931.5â173Â MeV.
This energy appears as kinetic energy of the products, mostly for the produced neutrons. The energy can be released in a controlled way, as in a fission reactor (see next section), or explosively in a very short time, as in a nuclear bomb (Figure 24.1a).

Figure 24.1: a Vast amounts of energy are released in the detonation of a nuclear weapon. b The results are catastrophic, as this photograph of Hiroshima shows.

WORKED EXAMPLE 24.1
One fission reaction of uranium-235 releases 173 MeV for each reaction. Estimate the energy released by 1 kg of uranium-235.
Answer
A quantity of 1 kg of uranium-235 is 1000235 mol of uranium.
The number of nuclei is therefore:
number of nucleiÂ =1000235Ã6Ã1023
Each nucleus produces about 173 MeV of energy, so:
total energyÂ =1000235Ã6Ã1023Ã173Â MeV
This is 4.4 Ã 1026 MeV or about 7 Ã 1013 J.
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Fission and the binding energy curve
The release of energy in fission is expected on the basis of the binding energy per nucleon graph, Figure 23.1 and Figure 24.2, as we will now explain. For the fission reaction n01+UÂ Â 92235âBaÂ Â 56144+Kr3689+3n01 we calculated the energy released by finding the total mass of the reactants on the left and subtracting the total mass of the products on the right. But this energy can also be calculated in a different way.
We know that
Q=((mn+MU)â(MBa+MKr+3mn)c2=(MUâMBaâMKr)c2â2mnc2
Recalling the definition of binding energy,
BbÂ U=(92mp+143mnâMU)c2âMUc2=(92mp+143mn)c2âBbÂ U
BbÂ Ba=(56mp+88mnâMBa)c2âMBac2=(56mp+88mn)c2âBbÂ Ba
BbÂ Kr=(36mp+53mnâMKr)c2âMKrc2=(36mp+53mn)c2âBbÂ Kr
We now substitute these values for the masses in the expression for Q to get
Q==(92mp+143mn)c2âBbÂ Uâ(56mp+88mn)c2+BbÂ Baâ(36mp+53mn)c2+BbÂ Krâ2mnc2BbÂ Ba+BbÂ KrâBbÂ U
We have the result that the energy released can also be calculated by subtracting from the total binding energy on the right of the reaction the total binding energy on the left of the reaction. The binding energy curve involves binding energy per nucleon, so let us express the energy released in terms of binding energy per nucleon, b:
We find that
Q=144bBa+89bKrâ235bU
This is where the binding energy curve comes in: krypton and barium are to the left of uranium in the graph and so have higher binding energy per nucleon, bKr bBa > bU. These inequalities of binding energy per nucleon are enough to show that Q > 0, i.e. energy will be released. The actual numbers are bKr = 8.616959 MeV, bBa = 8.265467 MeV and bU = 7.590907 MeV so that
Q=144Ã8.265467+89Ã8.616959â235Ã7.590907=173Â MeV.
The dashed vertical line at nickel-62 in Figure 24.2 is at the peak of the binding energy curveâthis is the most energetically stable nucleus. Fission means heavy nuclei split into lighter nuclei with higher binding energy per nucleon. Fusion (see next chapter) means light nuclei join to form heavier nuclei with higher binding energy per nucleon. By the argument of the previous paragraph, in both cases energy is released.

Figure 24.2: When a heavy nucleus splits up, energy is released because the produced nuclei have a higher binding energy per nucleon than the original nucleus. When two light nuclei fuse, energy is produced because the products again have a higher binding energy per nucleon.

WORKED EXAMPLE 24.2
Consider the fission reaction: UÂ Â 92238âLaÂ Â 57145+Br3590+xn01.
Is this an example of induced or spontaneous fission? What is x? What is the energy released? Data available:
Binding energy per nucleon for UÂ Â 92238=7.57Â MeV, LaÂ Â 57145=8.26Â MeV and for Br3590=8.48Â MeV.
Answer
No neutrons are used to bombard uranium, so it is a spontaneous fission reaction. Balancing mass numbers gives x = 3. The energy released is Q = 145 Ã 8.26 + 90 Ã 8.48 â 238 Ã 7.57 = 159 MeV.
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Nuclear fission reactors
A nuclear reactor is a machine in which nuclear fission reactions take place, producing energy.
Schematic diagrams of the cores of two types of nuclear reactor are shown in Figure 24.3.

Figure 24.3: Schematic diagrams of two types of fission reactor.

The fuel of a nuclear reactor is typically uranium-235. Neutrons initiate the reaction. One possible fission reaction is:
n01+UÂ Â 92235âXeÂ Â 54140+Sr3894+2n01
The energy released is about 185 MeV.
The neutrons produced can be used to collide with other nuclei of uranium-235 in the reactor, producing more fission, more energy and more neutrons. The reaction is thus self-sustaining; it is called a chain reaction. For the chain reaction to get going, a certain minimum mass of uranium-235 must be present, otherwise the neutrons escape without causing further reactions. This minimum mass is called the critical mass (for pure uranium-235, this is about 15 kg and rises to 130 kg for fuels containing 10% uranium-235). Uranium-235 will only capture neutrons if the neutrons are not too fast. The neutrons produced in the fission reactions are much too fast and so must be slowed down before they can initiate further reactions.
The slowing down of neutrons is achieved through collisions of the neutrons with atoms of the moderator, the material surrounding the fuel rods (the tubes containing uranium). The moderator material can be graphite or water, for example. As the neutrons collide with moderator atoms, they transfer energy to the moderator, increasing its temperature. A heat exchanger is therefore needed to extract the heat from the moderator. This can be done using cold water that circulates in pipes throughout the moderator. The water is turned into steam at high temperature and pressure. The steam is then used to turn the turbines of a generator, finally producing electricity.
The rate of the reactions is determined by the number of neutrons available to be captured by uranium-235. Too few neutrons would result in the reactions stopping, while too many neutrons would lead to an uncontrollably large release of energy. Thus control rods are introduced into the moderator. These absorb neutrons when too many neutrons are present, thus decreasing the rate of reactions. If the rate of reactions needs to be increased, the control rods are removed. The core of the reactor where the fission reactions take place has to be shielded (by thick concrete walls) to prevent radiation leaking to the surroundings.
CHECK YOURSELF 1
aWhat would happen to a nuclear reactor if a moderator was not present?
bWhat would happen to a nuclear reactor if the mass of the fuel were less than the critical mass?
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WORKED EXAMPLE 24.3
aAssuming the energy released in one fission reaction involving U-235 is 185 MeV, show that one kilogram of uranium-235 will release an energy equal to about 8 Ã 1013 J.
bNatural uranium (mainly uranium-238) contains about 0.7% of uranium-235 (by mass). Calculate the energy released by 1 kg of natural uranium.
Answer
aThe energy released by one nucleus of U-235 is 185 Ã 106 Ã 1.6 Ã 10â19 = 2.96 Ã 10â11 J. One kilogram of U-235 contains 1000235Ã6.02Ã1023=2.56Ã1024 nuclei of uranium and so the energy released by 1 kg of U-235 is 2.96 Ã 10â11 Ã 2.56 Ã 1024 = 7.58 Ã 1013 J.
bOne kilogram of natural uranium contains 0.7% of uranium-235 and so the energy E of natural uranium that can be extracted from 1 kg is:
E=0.7100Ã7.58Ã1012=5.3Ã1011Â JÂ kgâ1
E=530GJkgâ1
This value is substantially higher than that of fossil fuels.
Risks with nuclear power
The fast neutrons produced in a fission reaction may be used to bombard uranium-238 and produce plutonium-239. The reactions leading to plutonium production are:
n01+UÂ Â 92238âUÂ Â 92239
UÂ Â 92239âNpÂ Â 93239+eâ1Â Â Â 0+Î½Â¯
NpÂ Â 93239âPuÂ Â 94239+eâ1Â Â Â 0+Î½Â¯
The importance of these reactions is that non-fissionable material (uranium-238) is being converted to fissionable material (plutonium-239) as the reactor operates. The plutonium-239 produced can then be used as the nuclear fuel in other reactors. It can also be used in the production of nuclear weapons, which therefore raises serious concerns.
The spent fuel in a nuclear reactor and the products of the reactions are all highly radioactive with long half-lives. There are now about 400 000 tons of radioactive waste worldwide, and about one third of this has been reprocessed. Radioactive waste is broadly classified as higher level and low level waste.
Higher level waste is mainly the left-over uranium fuel in a reactorâs fuel rods and the lighter elements produced in the fission of the uranium fuel, such as strontium-90 and cesium-137 and others that we looked at in fission reactions earlier. These elements are highly radioactive. The radiation produced when they decay is very penetrating and delivers fatal doses even during short exposures, decades after they have been removed from the reactor. Leakage of this material into groundwater, lakes and rivers may enter the food chain, contaminating a large number of people. The energy produced when they decay produces heat, and so their storage must ensure cooling to avoid fires. As we saw, the absorption of neutrons by uranium-238 eventually produces plutonium-239 and other heavy elements. These produce less heat and penetrating radiation, but they have very long half-lives which means they pose a danger even after thousands of years. Higher level waste products are kept in steel containers surrounded by thick reinforced concrete which are filled with water. The water serves both as a coolant as well as a radiation shield. After many years in these containers, the waste can be moved into dry casks; these are steel vessels surrounded by concrete. These storage facilities are temporary until satisfactory permanent storage is found. Many countries are considering burying the material in containers in special facilities deep into the earth.
Low level waste includes material that has become radioactive due to neutron absorption or has been contaminated with radioactive material. It includes protective clothing, plastic shoe covers, cleaning materials such as mops and filters, tools and other equipment. These are not very radioactive, and after storage for some time, so that their radioactivity drops to below background, they can be disposed of as ordinary trash. Also included in low level waste are products generated in the mining of uranium and in the process of extracting the uranium from the ore.
In addition, there is always the possibility of an accident due to uncontrolled heating of the moderator, which might start a fire or explosion. This would be a conventional explosionâthe reactor cannot explode in the way a nuclear weapon does. In the event of an explosion, radioactive material would leak from the sealed core of a reactor, dispersing radioactive material into the environment. Both explosions shown in Figure 24.4 resulted in widespread contamination.
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Figure 24.4: The effects of two of the worldâs worst nuclear accidents. a The devastation after the explosion at the Fukushima nuclear plant in Japan on March 11, 2011. b Reactor number 4 in the Chernobyl nuclear power plant after the explosion on April 26, 1986.

Advantages of power by nuclear fission
âHigh power output
âLarge reserves of nuclear fuels
âNuclear power stations do not produce greenhouse gases
Disadvantages of power by nuclear fission
âRadioactive waste products difficult to dispose of
âMajor public health hazard should âsomething go wrongâ
âProblems associated with uranium mining
âPossibility of producing materials for nuclear weapons
WORKED EXAMPLE 24.4
A nuclear power plant produces 800 MW of electrical power with an overall efficiency of 35%. The energy released in the fission of one nucleus of uranium-235 is 170 MeV. Estimate the mass of uranium used per year.
Answer
Let P be the power produced from nuclear fission. Since the efficiency is 35%, then:
0.35=800P
âP=2286MW
The energy produced in one year is:
2286Ã106Ã365Ã24Ã3600=7.21Ã1016Â J
The energy produced in the fission of one nucleus is:
170Ã106Ã1.6Ã10â19=2.72Ã10â11Â J
and so the number of fission reactions in a year is:
7.21Ã10162.72Ã10â11=2.65Ã1027
The mass of uranium-235 used up in a year is therefore 2.65 Ã 1027 Ã 235 Ã 1.66 Ã 10â27, which is about 1000 kg.
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Ethics and morals
This section has shown how Einsteinâs famous formula E = mc2 applies to nuclear reactions. This formula describes the conversion of mass into energyâsomething that violates the law of conservation of mass as described by chemists. At the same time this formula made possible nuclear weapons that exploit the fission and fusion processes. Is this dangerous knowledge? J. R. Oppenheimer, who led the American effort to make the atomic bomb during World War II, said, quoting from the Hindu holy book The Bhagavad Gita: âI am become Death, the Destroyer of Worldsâ. If some knowledge is dangerous, can it ever be prevented from becoming widely available? If yes, by whom?

Figure 24.5: J. R. Oppenheimer (1904â1967).

TEST YOUR UNDERSTANDING
1Consider the nuclear fission reaction of uranium: UÂ Â 92235+n01âZr4098+TeÂ Â 52135+3n01.
aCalculate the energy released in two ways: using the masses, U = 235.0439 u, Zr = 97.9128 u, Te = 134.9165 u; and using the binding energies per nucleon, U = 7.5909 MeV, Zr = 8.5814 MeV, Te = 8.3465 MeV.
bUse the binding energy curve in Figure 23.1 to explain carefully why energy is released in fission reactions.
2Assume uranium-236 splits into two nuclei of palladium-117 (Pd).
The atomic mass of uranium is 236.0456 u; that of palladium is 116.9178 u.
aWrite down the reaction.
bWhat other particles must be produced?
cWhat is the energy released?
3Consider the decay UÂ Â 92238âThÂ Â 90234+Î±24.
Calculate the energy released.
(Binding energy per nucleon: U = 7.57 MeV; Th = 7.60 MeV; He = 7.07 MeV.)
4Consider the reaction UÂ Â 92235+n01âLaÂ Â 57145+Xxy+3n01.
What is x and y? Calculate the energy released.
(Binding energy per nucleon: UÂ Â 92235=7.59Â MeV, LaÂ Â 57145=8.26Â MeV, X = 8.56 MeV.)
5State and explain two advantages of energy production by nuclear fission over energy production by fossil fuels.
6State and explain two reasons for concern in the energy production by nuclear fission.
7aIn what form is the energy from a nuclear fission reactor produced?
bHow does the nuclear reactor produce electricity?
8A U-235 fission reaction involves the release of 170 MeV of energy which is used to light a 60 W light bulb for 12 hours. What mass of U-235 would be needed?
9What is meant by nuclear waste?
10Distinguish between higher level and low level nuclear waste.
11Outline some of the problems with nuclear waste storage.
