# FXA Candidates should be able to : UNIT G485 Module Fission and Fusion. Δm = m(separate nucleons) - m(nucleus) 1 u = 1.

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1 1 Candidates should be able to : MASS DEFECT Select and use Einstein s mass-energy equation : ΔE = Δmc 2 All atoms are lighter than the sum of the masses of their constituent protons, neutrons and electrons. Define binding energy and binding energy per nucleon. The difference in mass is called the MASS DEFECT (Δm) and it is in the nucleus that it is most apparent. Use and interpret the binding energy per nucleon against nucleon number graph. Determine the binding energy of nuclei using the masses of nuclei and ΔE = Δmc 2. The MASS DEFECT (Δm) of a nucleus is the difference between the total mass of all its separate nucleons and the mass of the nucleus itself. Δm = m(separate nucleons) - m(nucleus) Describe the process of induced nuclear fission. Describe and explain the process of nuclear chain reaction. Because the nuclear masses are very small, they are measured in a Unit called the ATOMIC MASS UNIT (u), rather than in kilograms. 1 u = x kg Describe the basic construction of a fission reactor and explain the role of the fuel rods, control rods and the moderator. Describe the use of nuclear fission as an energy source. The helium nucleus consists of 2 protons + 2 neutrons. + Describe the peaceful and destructive uses of nuclear fission. Describe the environmental effects of nuclear waste. Describe the process of nuclear fusion. m(2p + 2n) = (2 x ) + (2 x ) u = u. m(he nucleus) = u. Mass defect, Δm = m(separate nucleons) - m(nucleus) Δm = = u = x x Describe the conditions in the core of stars. = x kg

2 2 MASS-ENERGY EQUIVALENCE AND EINSTEIN S EQUATION As we have seen from our calculation with the helium nucleus, when a nucleus is separated into its constituent nucleons, there is an increase in mass. The question is, where does this extra mass come from?. The answer is that the energy which is needed to pull the nucleons apart against the strong nuclear forces which bind them together, is in effect converted into mass. It was Albert Einstein who suggested that mass and energy are equivalent, that is to say, they are interchangeable quantities. He expressed this idea mathematically in the very famous equation shown below : ENERGY EQUIVALENT OF 1 ATOMIC MASS UNIT 1 u = x kg. / c = x 10 8 m s -1. / 1 ev = x J. ΔE = Δmc 2 = x x ( x 10 8 ) 2 = x J. ΔE = x J = x 10 6 ev = MeV x J ev -1 1 u = MeV WORKED EXAMPLE The carbon-12 nucleus contains 6 protons and 6 neutrons. Given that : mass of carbon-12 nucleus = x kg. mass of a proton = x kg. mass of a neutron = x kg. 1 u = x kg. 1 u = MeV. ΔE = Δmc 2 Where ΔE is the energy change(in J) equivalent to a mass change Δm (in kg) and c is the speed of light in a vacuum (3.00 x 10 8 m s -1 ). Calculate : (a) The mass defect (Δm) (i) in kg, (ii) in u. (b) The energy in MeV needed to split the nucleus into its constituent protons and neutrons. (a) (i) Δm = m(6p + 6n) - m(c-12 nucleus) = = kg In Einstein s equation, mass is in KILOGRAM (kg) and energy in JOULE(J), but when we are working with nuclei these units are far too large and we are more likely to use the ATOMIC MASS UNIT (u) and the ELECTRON- VOLT (ev) instead. (ii) Δm = = x (b) ΔE = Δm x MeV u -1. = MeV. u.

3 3 PRACTICE QUESTIONS (1) BINDING ENERGY AND BINDING ENERGY PER NUCLEON Imagine a nucleus being dismantled by pulling each nucleon apart from its neighbour. To do this, work has to be done against the strong nuclear force which holds the nucleons together and each separated nucleon has increased potential energy as a result. The BINDING ENERGY of a nucleus is defined as the work that must be done to separate the nucleus into its constituent protons and neutrons. * The binding energy of a nucleus is the energy equivalent of the mass defect of the nucleus. When a nucleus forms from separate protons and neutrons, the strong nuclear force does work in pulling the nucleons together. An amount of energy equal to the binding energy of the nucleus, is released as a result. The total binding energy of a nucleus gives us some information about the stability of the nucleus, but a more useful indicator of nuclear stability is The binding energy per nucleon. The BINDING ENERGY PER NUCLEON is the average energy needed to remove each nucleon from a nucleus. 4 A gold nucleus contains 79 protons and 118 neutrons. Given the data shown below, calculate : (a) The mass defect in u. (b) The energy in MeV required to split the nucleus into its constituent protons and neutrons. BE per nucleon = total BE A Mass of gold nucleus = u. Mass of a proton = u. Calculate the binding energy per nucleon for the carbon-12 nucleus we considered on page 2. Mass of a neutron = u. 1u = MeV.

4 4 Shown below is a graph of BINDING ENERGY PER NUCLEON against NUCLEON NUMBER (A) for all known nuclides. USING BE/A GRAPH TO ESTIMATE ENERGY RELEASED IN FISSION The graph below shows the variation of binding energy per nucleon with nucleon number (A). AVERAGE BINDING ENERGY PER NUCLEON (MeV) AVERAGE BINDING ENERGY PER NUCLEON (MeV) NUCLEON NUMBER (A) NUCLEON NUMBER (A) Use the graph to calculate a value for the energy which would be released from the fission of uranium-235 into a lanthanum-146 nucleus and a bromine-87 nucleus. POINTS TO NOTE The binding energy per nucleon is typically about 8 MeV. The lighter nuclei, hydrogen, helium-3, lithium etc. have low binding energy per nucleon. Helium-4 is a distinct spike on the curve, having a higher binding energy per nucleon than predicted by its nucleon number. The most stable nucleus, iron-56, has the highest binding energy per nucleon at 8.79 MeV.

5 5 The differences between values of binding energy per nucleon suggests a means of extracting energy from nuclear reactions. If heavy nuclei can be split, lighter nuclei will be formed, and the difference in binding energy per nucleon is released in the process (nuclear fission). INDUCED NUCLEAR FISSION AVERAGE BINDING ENERGY PER NUCLEON (MeV) FUSION FISSION Similarly, if two very light NUCLEON NUMBER (A) nuclei can be fused together, the resulting nucleus will be more stable, and again the difference in binding energy will be released (nuclear fusion). The diagram shows how fission of a uranium-235 nucleus occurs when it captures a slow-moving neutron and so becomes U-236. The absorption of the neutron deforms the nucleus which then starts to oscillate until it eventually acquires a dumbbell shape. At this point, the electrostatic repulsion between the protons in the two halves becomes greater than the short-range strong force between all the nucleons and the nucleus splits. There are many possible fission fragment combinations and a relatively large amount of energy ( 200 MeV) is released by each fission event. Several neutrons (typically 3) are also ejected at high speeds. The mass of the U-235 nucleus plus the captured neutron is greater than the mass of the fission fragments plus the ejected fission Neutrons and it is this mass difference which results in the release of energy, which appears as kinetic energy of the fragments and neutrons. The fission fragments have greater binding energy and are therefore more stable than the U-235 nucleus. The energy released is equal to the change in total binding energy. If the fast, high-energy fission neutrons are somehow slowed down so that they are captured by U-235 nuclei, they can then cause further fission, which in turn leads to further fission and so on. This is called a fission chain reaction (shown in the diagram below) and as each fission event occurs in a tiny fraction of a second, a huge amount of energy can be released in a very short time. CAPTURE U-236 FISSION INSTABILITY

6 6 The equation shown below is that for a typical nuclear fission reaction. A U-235 nucleus is split into a barium nucleus, a krypton nucleus and three fission neutrons, with the release of energy. GENERAL INTRODUCTION In a nuclear reactor, energy released from fission is extracted and used to produce steam which drive turbines to run generators which produce electricity n energy released U + Ba + Kr + 3 n + In order to harness the energy from fission, the chain reaction has to be perfectly controlled (i.e. CRITICAL). The energy released (ΔE) can be calculated using ΔE = Δmc 2, where Δm is the difference between the total mass before and after fission. If the masses are in kg, ΔE will be in JOULE (J). If the masses are in u, ΔE is calculated using : ΔE = Δm x MeV. A CRITICAL chain reaction is one in which the rate at which neutrons are produced by fissions = the rate at which neutrons are lost (By (1) further fissions, (2) absorption without fission, and (3) leaving the fissile material). If the rate of fission neutron production is greater than that at which they are lost, the chain reaction is said to be SUPERCRITICAL (this is what happens in nuclear fission bombs). If the rate of fission neutron production is less than that at which they are lost, the chain reaction dies out. FUEL RODS NUCLEAR FISSION REACTOR Uranium is a naturally-occurring metal which is mined in several parts of the world. Unfortunately it only contains 0.7 % of the fissile isotope U-235, the rest being the non-fissioning U-238. The uranium used in reactors is artificially enriched to increase the concentration of U-235 to about 3 %. The fuel is contained in cylindrical, stainless steel rods which are inserted into tubes in the reactor core. Once the uranium in a rod has been used up, it can easily be removed and replaced.

7 7 MODERATOR CONTROL RODS The neutrons released by each fission are travelling too fast to be captured by the U-235 nuclei and so cause further fission. They must therefore be slowed down by absorbing most of their kinetic energy. The moderator is a material which is incorporated into the reactor core in order to reduce the high speeds of the fission neutrons to thermal speeds and so enable them to cause further fission. Successive elastic collisions of the neutrons with the nuclei of the moderator material allows energy to be transferred to the material and so the neutrons are slowed down. Since in an elastic collision, energy is transferred most effectively if the two bodies are of equal mass, the nuclei of the moderator need to be of a size comparable to that of a neutron. Additional to this, the moderator material needs to have a low neutron absorbing capability. Otherwise fission neutrons would be removed from the reaction. The pressurised water reactor (PWR) employs water as both the moderator and coolant. Graphite is used in the Magnox and advanced gas cooled (AGR) reactors. As we already know, the reaction rate must be CRITICAL (i.e. on average each fission neutron must go on to cause a further fission). Anything less means that the reaction ceases and anything more causes the reaction to go out of control. A minimum mass of uranium, called the critical mass, is needed to set up a chain reaction. So if the uranium mass is too small, the fission neutrons will escape from the surface before they can cause further fissions. Each individual fuel rod is below the critical mass and their narrow, cylindrical shape means that fission neutrons escape into the moderator where they are slowed down sufficiently to enable them to cause fission in the next rod. The control rods are made of neutron-absorbing materials, such as boron and cadmium and they are used to control the number of neutrons available to cause fission. This control is achieved by raising or lowering the control rods into the reactor core. Lowering the rods increases the number of neutrons which are absorbed and so reduces the reaction rate, whereas raising them has the opposite effect. The reactor can be shut down completely by lowering the rods fully into the core.

8 8 COOLANT SHIELDING AND SAFETY The core of the reactor is contained within a steel pressure vessel which contains the highly pressurised coolant. A 5 metre thick concrete shield surrounds the reactor and this stops harmful radiation and neutrons from escaping and the whole system is housed in a steel and concrete containment building which is designed to prevent the escape of any radiation even in the extreme event of core meltdown. DESTRUCTIVE USE OF NUCLEAR FISSION The energy released in the fission reaction is almost entirely kinetic energy of the fission fragments and the neutrons. This kinetic energy increases the internal energy of all the components of the reactor, resulting in a temperature rise. To extract this heat energy, a coolant is pumped around the reactor core and this fluid gets heated through contact with the reactor components. It then passes to a heat exchanger where its heat energy is passed on to water to create steam. The coolant used must have the following properties : High specific heat capacity. Non-corrosiveness. Stability at the high reactor temperatures. Common coolants are carbon dioxide and water. In the pressurised water reactor (PWR) the water is pressurised so as to remain liquid at the high reactor temperatures. The coolant becomes radioactive as it passes through the core, so it must be fully contained. Loss of coolant could eventually result in meltdown (the core overheats and melts). This is because even if the reactor is quickly shut down, the core temperature will continue to rise as a result of radioactive decay of the fission fragments. The fission bomb (A-bomb) uses an uncontrolled chain reaction to unleash an immense amount of destructive energy. The first A-bomb used in warfare was dropped by the USA on August 6th Called Little Boy, it produced an explosion that devastated the Japanese city of Hiroshima, killing 130, 000 people in little over a minute. In this bomb, a mass of uranium about the size of a baseball produced an explosion equivalent to the instantaneous detonation of 15 kilotons of TNT! Little Boy was a gun-type fission bomb in which a small bullet of uranium was fired into a larger target piece of uranium and, upon impact, the two pieces fused together forming a supercritical mass. Neutrons were simultaneously directed at this mass and this initiated the uncontrolled chain reaction leading to the explosion. A barometric-pressure sensor was used to determine the optimum detonation altitude and so ensure maximum destruction.

9 9 ENVIRONMENTAL EFFECTS OF NUCLEAR WASTE The nuclear industry, and nuclear reactors in particular produce large quantities of hazardous material. The management of nuclear waste is one of the most controversial issues surrounding the production of electrical energy from nuclear power. Intermediate-level waste consists mainly of empty fuel rods, contaminated reactor components and chemical sludges used in the treatment of nuclear fuel. After some years in the reactor, the proportion of U-235 in the fuel rods will have decreased to the point at which a chain reaction can no longer be sustained. The fuel is removed and must be re-processed, a hazardous operation in which plutonium-239 and other useful isotopes are extracted. The remaining radioactive material must be stored for later disposal Radioactive waste is categorised according to its activity as high, medium or low level waste. This type of nuclear waste is very much less radioactive than the spent fuel rods. This waste is encased in cement inside stainless steel drums which are then stored in concrete vaults or underground. High-level radioactive waste (such as spent fuel rods) contains many different radioisotopes, including fission fragments as well as unused U-235, U-238 and Pu-239. Low-level waste is only slightly radioactive and includes items such as packaging, laboratory instruments and protective clothing. The spent fuel rods are handled remotely and stored in cooling ponds (because they continue to release heat as a result of radioactive decay) for up to a year. The unused U and Pu is then removed and stored for further possible use. It is disposed of by compacting, placing in steel containers and either given a shallow land burial or dumped at sea. Liquid wastes, such as cooling pond water, are cleaned and then discharged into the sea.. The high-level radioactve waste is sealed inside glass blocks which are placed in thick, steel containers, encased in concrete and buried underground. Although this packaging of the nuclear waste is both safe and effective, the problem is that the radioisotopes contained have long half-lives and remain hazardous for thousands of years. We don t know for how long the packaging will remain intact.

10 10 NUCLEAR FUSION If you look back to the binding energy per nucleon versus nucleon number graph shown on page 4, you will see that the binding energy per nucleon of light nuclei (such as hydrogen, deuterium, tritium and helium-3) is much less than that of larger nuclei. Thus, if two light nuclei could be forced to fuse into a single larger nucleus, the difference in the binding energy could be released. This forms the basis of the process of nuclear fusion. In nuclear fusion, the mass of the resulting larger nucleus < the sum of the masses of the fusing nuclei and it is this mass difference which is Converted into energy. This is exactly the case in the Sun s core and that of all stars, where the temperature is in excess of 20 million ºC and matter exists as a soup of free nuclei and negatively charged electrons. This mixture is called a plasma. The density of this plasma is greater than kg m -3 (due to compression by the enormous gravitational forces produced by Such massive bodies), and under these conditions, the nuclei collide with enough kinetic energy to fuse, releasing more energy to sustain the reaction. In order for two light nuclei to fuse, they must be brought close enough for the strong force to come into action and overcome the electrostatic repulsion force due to the positive charges of the nuclei. F F F F F F The two main series of fusion reactions occurring in the Sun are : 1. THE HYDROGEN CYCLE The problem is that the repulsion force increases dramatically as the two nuclei come closer. For two hydrogen nuclei to have enough Kinetic energy to overcome the electrostatic repulsion forces and so fuse, the hydrogen needs to be at an enormously high temperature.

11 11 In STEP I - Two hydrogen nuclei (protons) fuse to produce a deuterium nucleus. A positron and a neutrino are emitted. In STEP II - The deuterium nucleus fuses with another proton to produce a helium-3 nucleus. In STEP III - Two helium-3 nuclei fuse to produce a helium-4 nucleus and two protons. 2. THE CARBON CYCLE The Sun consists mainly of hydrogen and helium, but about 1% of its mass is made up of heavier elements which allow the fusion of protons to helium-4 by alternative fusion reaction sequences. The most important of these sequences starts and ends with carbon-12 and is aptly named the CARBON CYCLE (shown diagrammatically below). NUCLEAR FUSION ON EARTH The conditions for fusion in the core of stars can be created on Earth, when a nuclear fission bomb is detonated. The high temperature and high pressure generated by such an explosion can be made to cause a fusion reaction in light nuclei. The resulting hydrogen bomb is a truly awesome weapon, delivering the explosive power of millions of tons of dynamite from a few kilograms of plutonium and a few grams of lithium, deuterium and tritium. Creating these conditions for a controlled fusion reaction, in order to harness the energy for peaceful purposes, is a far more difficult proposition. A major problem in controlled fusion is that of confining the extremely hot (T 10 8 to 10 9 K) deuterium-tritium plasma. This means that the plasma cannot be allowed to come into contact with the walls of the containing vessel, since this would instantly cool it and so cause the reaction to stop. One of the most promising methods for confining the plasma is the use of magnetic fields. Since the plasma consists entirely of charged particles, magnetic fields will exert forces on them and it is hoped that the field shape can be controlled to enable the plasma to be contained within a toroidal fusion chamber. The photograph below shows the plasma containing chamber of the JET prototype fusion reactor.

12 HOMEWORK QUESTIONS 12 The most promising fusion reaction is that between deuterium (D) and tritium (T). 1 (a) (i) State what is meant by nuclear binding energy. (ii) Fig 1. shows the binding energy per nucleon for five nuclides, plotted against nucleon number. DT fusion is preferred over DD fusion because : It occurs at a lower temperature. It releases a lot more energy. The reaction equation for DT fusion is : 2 H H 4 + He 1 n energy 0 Fig 1. Fe-56 has the highest binding energy per nucleon. C-12 and U-235 have less binding energy per nucleon. Explain how these values relate to the possibility of fission or fusion of the nuclides Fe-56, C-12 and U-235. (b) (i) A U U nucleus inside a nuclear reactor can absorb a thermal neutron. State what is meant by a thermal neutron. (ii) Write a nuclear equation for this reaction. (iii) The resulting nucleus undergoes fission. iodine I and yttrium Y are produced. Write a nuclear equation for this reaction. (iv) Use data from Fig 1. to deduce how much energy in MeV is released when one nucleus of U-235 undergoes these reactions. The JET prototype fusion reactor. (OCR A2 Physics - Module June 2005)

13 3 A tin-120 atom has a mass of u. It contains 50 protons This question is about nuclear fusion inside the Sun. (a) Describe the conditions inside the Sun and explain how they favour nuclear fusion. Your account should explain why the material inside the Sun is in the plasma state and how the plasma is confined. (b) One process by which hydrogen nuclei fuse is called the carbon cycle. The following equations represent the reactions which make up this cycle. (a) How many neutrons and electrons does it contain? (b) Given the masses of the constituent particles shown below, calculate the mass defect (Δm). Mass of a proton = u. Mass of a neutron = u. Mass of an electron = u. (c) Calculate the binding energy of the atom in MeV. Given that 1u = MeV. (i) Why is it called the carbon cycle? (d) Calculate the binding energy per nucleon in MeV. (ii) Summarise the carbon cycle by reducing the six equations above to a single equation, in its simplest form. (iii) The binding energy per nucleon of He-4 is 7.1 MeV. Show that the energy released in joules when one He-4 nucleus is formed is about 4.5 x J. By referring to your answer to (b) (ii), give one reason why this is only an approximation. 4 (a) Use the binding energy per nucleon against nucleon number graph shown on page 4 to show that the total binding energy of a single U-235 nucleus is 2.8 x J. (b) A typical nuclear fission reaction is shown on page 6. (i) Explain why the energy released in this reaction as kinetic energy of the fragments is only a small fraction of the energy calculated in (a). (ii) Assuming that the actual fraction is 1/6, calculate the energy released per kilogram of U-235. (c) One sequence of reactions involving isotopes of hydrogen can be summarised by the single reaction equation : 1 H He e 0 (c) It is estimated that 8 x helium nuclei are formed per second inside the Sun. Assuming that this is the only energy-generating process, calculate the total power emitted by the Sun. (OCR A2 Physics - Module June 2004) (i) Again use the graph on page 4, to find the total energy released in this reaction. (ii) Calculate the energy released per kilogram of H-1 used. (d) Comment on your answers to (b) (ii) and (c) (ii).

14 11

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