Physics 11. Unit 10 Nuclear Physics

Transcription

1 Physics 11 Unit 10 Nuclear Physics

2 1. Review of atomic structure From chemistry we have learned that all matters in this world are made of tiny particles called atoms. Atoms are made of three smaller particles: protons, neutrons, and electrons. These particles possess the following properties: Unit 10 - Nuclear Physics 2

3 The number of protons of an atom is called the atomic number Z, and it determines the type of the element the atom belongs to. The number of neutrons of an atom is called the neutron number N. It tells which isotope of the element the atom is. The sum of these values is called the atomic mass number A, or sometimes called nucleon number. A = Z + N If the element the atom belongs to has a chemical symbol X (which can be found out from the periodic table), the atom will be represented by the following symbol: Unit 10 - Nuclear Physics 3

4 Example: Give specification of Al. The number of protons: 13 The number of neutrons: = 14 The number of electrons: 13 Example: An nucleus has 7 protons and 8 neutrons. Identify what element it is, and write out its symbol. Z = 7 A = Z + N = = 15 X = "N" Hence, the symbol of the nucleus is 15 7N Unit 10 - Nuclear Physics 4

5 In nature, we can find atoms of the same element that have the same number of protons but different numbers of neutrons in the nucleus. These atoms are called the isotopes of the element. Isotopes of an element have almost identical chemical properties but different physical properties. Each isotope of an element has its own natural abundance which indicates how much it can be found from an average sample of the element. Unit 10 - Nuclear Physics 5

6 Using the natural abundance of different isotopes, we can calculate the average atomic mass of the element. For example, the average atomic mass of carbon is given by Mass = (0.00) = Recall that this value can be interpreted in units of u (atomic mass unit) or g/mol; that is, grams per mole of atoms. The atomic mass unit is the scale defined based on the neutral carbon-12 atom which is given exactly a mass of u. Equivalently, 1u = kg Unit 10 - Nuclear Physics 6

7 Using this conversion factor, the masses of proton, neutron and electron can be given in amu: Subatomic particles Mass in kg Mass in amu Proton Neutron Electron The mass of electron is approximately 3 orders of magnitude (~2000 times) smaller than that of proton and neutron. Therefore, in calculations the mass of electrons is usually ignored. Unit 10 - Nuclear Physics 7

8 2. Radioactivity and radioactive decays (a) Radioactivity The phenomenon of radioactivity was discovered accidentally by Henri Becquerel (Nobel prize winner in 1903) in 1896 when he performed experiments involving uranium samples. He found that photographic plates placed nearby the uranium sample became fogged up, suggesting that the sample had emitted some sort of radiation similar to UV light. After the monumental work by Marie and Pierre Curie (Nobel prize winners in 1903 and 1911), it has been realized that the radiation arises from radioactivity which is the emission of radiation due to transmutation of a nucleus. Unit 10 - Nuclear Physics 8

9 Ernest Rutherford (1899) and Paul Villard (1900) later on analyzed the radiation discovered by Becquerel (so called Becquerel rays) and identified the three components (α, β, and γ rays, respectively) which can be distinguished by their penetrating power: Radiation α β γ Maximum penetrating distance in Lead cm 0.01 cm 10 cm Unit 10 - Nuclear Physics 9

10 A lot of work has been done by many scientists to figure out what these radiations are. Experiment that provides useful information regarding these rays are shown below. A beam of Becquerel rays is split into three beams when it is passed through an electromagnetic field. Unit 10 - Nuclear Physics 10

11 The illustrations of the experimental observations: Unit 10 - Nuclear Physics 11

12 What do these observation tell us? (1) The α and β radiations are made of charged species since they are deflected by the electric and magnetic fields. (2) The γ radiation, on the other hand, should be neutral. (3) Based upon the sizes of the deflected paths of the α and β rays, the α particles are much heavier than the β particles. Unit 10 - Nuclear Physics 12

13 Rutherford and Royd using a smart experimental approach verified that the α particles are made of particles with two positive charges. These particles are helium ions with a double positive charge, He 2+. Unit 10 - Nuclear Physics 13

14 On the other hand, Becquerel investigated the β particles and found that they have the same charge-to-mass ratio as electrons which were discovered by J. J. Thomson shortly beforehand. Therefore, he concluded that β particle is actually an electron. Rutherford and Andrade studied the γ radiation using diffraction technique, and realized in 1914 that it is a kind of electromagnetic radiation similar to X-ray yet having a shorter wavelength, and travels at the speed of light. In summary: Particles α β γ Nature Helium nucleus Electron High-energy electromagnetic wave Unit 10 - Nuclear Physics 14

15 (b) Radioactive decays These particles are generated by the disintegration of radioactive substances through the process of transmutation, a process in which a nucleus of one type is transformed into another type by means of emitting a particle (decay) or absorbing a particle (capture). Depending on the particles given out, radioactive decay can be classified into 3 types: (i) α-decay This is a process in which α particles are produced. Since each α-particle consists of 2 protons and 2 neutrons, the α- decay causes the change of atomic number by 2 and the change of atomic mass number by 4. It is due to the law of conservation of nucleons. Unit 10 - Nuclear Physics 15

16 In general: There are a lot of examples in nature about α-decay. Namely: Unit 10 - Nuclear Physics 16

17 More examples: Unit 10 - Nuclear Physics 17

18 Example: The iridium-168 isotope is known to go through alpha decays. Write out a decay equation that shows this process. Unit 10 - Nuclear Physics 18

19 Practice: Complete the nuclear equations: Practice: What is the name of the product isotope formed when Radon-222 decays by alpha decay? Unit 10 - Nuclear Physics 19

20 (ii) β-decays In β - decay process, electron(s) is/are emitted when the nucleus is transformed. Note that the emitted electron is not the original electrons which are surrounding the nucleus. This is the electron produced when a neutron at the nucleus decomposes to a proton. Proton has an atomic number of 1 and a mass number of 1, while neutron has an atomic number of 0 and a mass number of 1. By conservation of nucleons: 0 1 n 1 1 p e + തν e Unit 10 - Nuclear Physics 20

21 Therefore, the general nuclear equation for β - decay is: A typical example of β - decay process: Unit 10 - Nuclear Physics 21

22 Some more examples: Unit 10 - Nuclear Physics 22

23 Example: Write out the beta decay reaction for calcium-46. The complete nuclear equation for this process is Ca 0 1 β Sc + തν e The last particle, തν e, is called antineutrino which has an extremely small mass. This particle was first proposed to account for the conservation of momentum for the β-decay process. Unit 10 - Nuclear Physics 23

24 There is another type of β-decay that is observed in nature. In this process, a positive electron, called positron, is produced when a proton in a nucleus is transformed into a neutron. It is therefore also known as positron emission. Positron is the anti-particle of an electron, having exactly the same mass but opposite charge. Hence, it is denoted by 1 0 β in nuclear equation. By the conservation of nucleons, we can write the following nuclear process for the production of positron: 1 1 p 1 0 n e + ν e Unit 10 - Nuclear Physics 24

25 In general, a β + decay is described as: Note that the daughter nucleus has one proton less yet same mass number as the parent nucleus. This process is associated with the production of a neutrino ν e. Unit 10 - Nuclear Physics 25

26 Some examples: Unit 10 - Nuclear Physics 26

27 Example: Potassium-40 is known to go through beta plus decays. Write out the decay equation for this process. The nuclear equation for this process is: 40 19K Ar e + ν e Note that neutrino, but not antineutrino, is produced together with argon-40. Unit 10 - Nuclear Physics 27

28 Practice: Complete the following nuclear equations. 14 6C 0 1 e Hg e 2 6 He 0 1 e Co e 15 8O 0 1 e Ni e Unit 10 - Nuclear Physics 28

29 (iii) γ-decay The nucleus exists in discrete energy levels just like electrons. When the nucleus is transiting from a high energy level to a low energy level, the excess energy is released in form of photon radiation. The emitted photon is called a γ-particle. The general equation for γ-decay is: Note that the parent nucleus is not transformed into the daughter nucleus of a new type during this process. Unit 10 - Nuclear Physics 29

30 Often γ-decay occurs following other decay processes because in these processes the daughter nuclei acquire extra energy and become excited. For example, the protactinium-234 nucleus resulted from the α-decay of thorium-234 is in the excited state, and decays to the stable form by γ radiation. Unit 10 - Nuclear Physics 30

31 Example: The argon-40 produced in the β+ decay of potassium-40 is in an excited state, so it releases a burst of gamma radiation. Write the equation for this. Since only gamma radiation is produced, there exists no change in the identity of the nucleus. Hence, Ar Ar + γ Usually, an excited nucleus is denoted by an asterisk *. Either γ or 0 0 γ is used to represent a gamma particle. Unit 10 - Nuclear Physics 31

32 In addition to the decay processes described above, there exists a common process in which an electron is absorbed into the nucleus. It is called electron capture, and is the reverse of the β - decay. In an electron capture, a proton is combined with an electron to form a neutron plus a neutrino: 1 1 p e 1 0 n + ν e Example: Unit 10 - Nuclear Physics 32

33 More examples of electron captures: Unit 10 - Nuclear Physics 33

34 Example: Rubidium-83 is known to go through electron captures. Write the corresponding decay equation. Electron capture requires both the parent nucleus and an electron. Therefore, Rb e Kr + ν e Remember that the daughter nucleus has one less proton than the parent. Unit 10 - Nuclear Physics 34

35 (c) Decay chain When an unstable parent nucleus decays, the resulting daughter nucleus is also unstable sometimes, and it decays subsequently to produce its daughter. This process goes on and on until the daughter nucleus is completely stable (or at least stable enough with respect to the lifespan of the Earth, for example). Such a sequence of decay processes forms a radioactive decay series or decay chain. For example, thorium-226 is unstable and undergoes α-decay to form radium-222: Th 4 2 He Ra Radium-222 is however unstable too, and decays to actinium-222: Ra 0 1 e Ac + തν e Unit 10 - Nuclear Physics 35

36 The resulting actinium-222 undergoes three consecutive α-decays to form bismuth-210: Ac 4 2 He Fr Fr 4 2 He At At 4 2 He Bi Bismuth-210, since unstable, is gradually transformed into polonium- 210 and eventually stable lead Bi 0 1 e Po + തν e Po 4 2 He Pb Unit 10 - Nuclear Physics 36

37 Since we can deduce what kind of process a parent nucleus has undergone by checking the daughter nucleus, the series of decay equations mentioned above can be condensed into a single decay series: Th Ra Ac Fr At Bi Po Pb It is not necessary to indicate the type of decay for each step, and no need to include the particles emitted (i.e., 2 4 He, 1 0 e, or γ). Unit 10 - Nuclear Physics 37

38 Another way of expressing a decay series is a graphical representation. There are several popular designs of such graph; the majority of them consists of atomic number (Z) / mass number (A) plots. Each isotope is specified by its (Z, A). Unit 10 - Nuclear Physics 38

39 An example of decay series: U Pb Unit 10 - Nuclear Physics 39

40 There exists four naturally occurring decay series, all of which start with a radioactive actinide element: U, and Th, U, Np. Unit 10 - Nuclear Physics 40

41 These series converge to the stable isotopes of lead (206, 207 and 208) or bismuth-209. Unit 10 - Nuclear Physics 41

42 Practice: Complete the following series. Unit 10 - Nuclear Physics 42

43 3. Half-life The previous section discussed the different types of decays through which a radioactive nucleus disintegrates. However, how often does the decay process occur? The period of time for decay is measured in terms of half-life, t 1/2, which is defined as the time taken for half of the amount of a radioactive sample to decay. Please remember that half-life is a statistical quantity; it is measured as an average over a large number of nuclei. The time actually taken for an individual nucleus to decay is purely random, and cannot be predicted. Unit 10 - Nuclear Physics 43

44 To understand the meaning of t 1/2, we look at the following example: Given the half-life of 14 6C is 5730 years. Imagine that there are C atoms in the sample originally. 6 t 1/2 t 1/2 100 atoms 50 atoms 25 atoms t 1/2 3 or 4 atoms t 1/2 6 or 7 atoms t 1/2 12 or 13 atoms Unit 10 - Nuclear Physics 44

45 This change can be represented graphically. In general, if it starts with a sample having N 0 nuclei, the number of the radioactive nuclei remaining in the sample, N, at any given time t can be deduced from the decay curve: Unit 10 - Nuclear Physics 45

46 The curve is described mathematically by an exponential function N = N 0 e λt The term λ is called a decay constant, and N 0 is the number of nuclei at t = 0. The average or mean lifetime of a radioactive particle is related to the decay constant by a reciprocal relationship: τ = 1 λ That means, it takes time τ for a sample of radioactive nuclei to decrease to 37% of its original amount. Unit 10 - Nuclear Physics 46

47 It can be shown that the half-life which is the time it takes for the number of nuclei to decrease by half is given be t 1/2 = λ = 0.693τ Using t 1/2 the decay equation can be rewritten as 0.693t N = N 0 e λt t 1 = N 0 e 1/2 = N 0 2 t t 1/2 Unit 10 - Nuclear Physics 47

48 Example: Marie Curie had a 765 g sample of polonium-210 (half-life = 138 days) in a box. After 3.8 years of refining radium, she goes to the box to get her polonium. Determine how much polonium-210 is in the box? Using the decay formula, 0.693t t N = N 0 e 1/2 = 765 e 0.693( ) 138 = g Therefore she could only find g of polonium-210 in the box. The rest has been decayed into some other elements. Unit 10 - Nuclear Physics 48

49 Example: You have 75 g of lead-212. If it has a half life of 10.6 hours, determine how long it will take until only 9.3 g remains. The decay formula yields: 0.693t t N = N 0 e 1/2 9.3 = 75e 0.693t 10.6 t = ln = 31.9 It will take 31.9 hours for the sample to reduce to 9.3 g. Unit 10 - Nuclear Physics 49

50 Example: After 26 days, the number of radioactive cobalt-60 atoms in a sample is reduced to 1/32 of the initial count. What is the half-life of the isotope? Using the decay formula: If N = N 0 /32 when t = 26, 0.693t t N = N 0 e 1/2 N 0 32 = N 0e The half-life of cobalt-60 is 5.20 days (26) t 1/2 t 1/2 = 0.693(26) ln 1/32 = 5.20 Unit 10 - Nuclear Physics 50

51 4. Activity and carbon dating A quantity activity is defined as the number of disintegrations that occur per second in a radioactive sample. When a decay happens, the number of nuclei in the sample decreases; therefore, activity can be written as the ratio of the change of the number of nuclei to the time interval; i.e., N/ t. Decay is a random process; so its rate is proportional to the total number of available nuclei in the sample. Mathematically, N t = λn The factor λ is the decay constant as defined previously. Unit 10 - Nuclear Physics 51

52 The SI unit of activity is called becquerel (Bq) which is defined as 1 disintegration per second. Another unit called curie (Ci) is also employed which is approximately equal to the activity of 1 g of pure radium. These two units can be interconverted through the following relationship: 1 Ci = Bq Unit 10 - Nuclear Physics 52

53 To have a sense of what these units are about, see the following: A radium watch Activity: Bq Or Ci A radiotherapy device Activity: Bq Or Ci Unit 10 - Nuclear Physics 53

54 Example: Suppose that radon atoms are trapped in a basement at the time the basement is sealed against further entry of the gas. The half-life of radon is 3.83 days. (a) How many radon atoms remain after 31 days? (b) Find the activity just after the basement is sealed against further entry of radon. (c) Find the activity after 31 days. (a) The number of radon atoms remains is: N = e 3.83 = atoms Unit 10 - Nuclear Physics 54

55 (b) The decay constant is λ = (3.83)(24)(60)(60) = s 1 Therefore, the activity at the beginning is: N t = λn = = 63 Bq (c) The activity after 31 days is: N t = λn = = 0.23 Bq Unit 10 - Nuclear Physics 55

56 An important application of the activity of radioactive substances is radioactive dating, a method which is used to determine the age of archeological or geological samples. The physics behind radioactive dating is the comparison of activity of the radioactive isotopes in the sample at present and when it was made initially. Assume that the initial amount of a type of radioactive isotopes in the sample, N 0, is estimated, and the present amount of these isotopes, N, is measured accurately. Since the half-life of the isotope is known, by fitting these data into the decay equation: 0.693t t 1 N = N 0 e 1/2 = N 0 2 the age of the sample, t, can be determined. t t 1/2 Unit 10 - Nuclear Physics 56

57 Since the activity of a radioactive substance is directly proportional to its amount, the radioactive dating formula can also be written in terms of activities: 0.693t t 1 λn = λn 0 e 1/2 = λn 0 2 N t = N 0 t 0.693t t e 1/2 = N 0 t t t 1/2 1 2 t t 1/2 Present activity Initial activity Unit 10 - Nuclear Physics 57

58 Example: It has been observed that the carbon-14 isotope undergoes β- decay with a half-life of 5730 years. This isotope is found to be present in the Earth s atmosphere at an equilibrium concentration of about one atom for every atoms of normal carbon-12. This value is assumed to be constant over the years since carbon-14 is created by cosmic rays, offsetting the loss due to the β- decay. (a) Determine the number of carbon-14 atoms present for every gram of carbon-12 in a living organism. (b) Find the decay constant. (c) Find the activity of this sample. Unit 10 - Nuclear Physics 58

59 (a) The number of carbon-14 atoms is: N = = atoms (b) The decay constant is: λ = t 1/2 = (5730)(365)(24)(60)(60) = s 1 (c) The activity is: N = λn = = 0.23 Bq t Unit 10 - Nuclear Physics 59

60 Example: A team of German tourists found a Stone-age traveler whose body had become trapped in a glacier in the Italian Alps in This Ice Man was well preserved, and was dated using the radiocarbon method. It is found that the body had a carbon-14 activity of about Bq per gram of carbon. Find the age of the Ice Man s remains. Given the activity of carbon-14 per gram of carbon in living organism is 0.23 Bq, and the half-life of carbon-14 is 5730 years. t = t 1/2 N log t N 0 t log(0.5) log = log 0.5 = 5300 years Unit 10 - Nuclear Physics 60

61 Example: An archeological specimen containing 9.2 g of carbon has an activity of 1.6 Bq. How old (in years) is the specimen? The activity of carbon-14 in 9.2 g of carbon in living organism is: N 0 = = Bq t Therefore, the age of the specimen is: 1.6 = 2.116(0.5) t 5730 t = years Unit 10 - Nuclear Physics 61

62 Example: A bone containing 200 g of carbon has a β- decay rate of 400 decays/min. How old is the bone? The decay rate of 400 decays/min is equivalent to decays/sec or Bq. Since there are 200 g of carbon in the bone, the activity is N = = Bq t 200 The age of the bone is therefore given by t = 5730 log /0.23 log(0.5) = years Unit 10 - Nuclear Physics 62

63 5. Mass defect and binding energy As described earlier, nuclei are made of protons and neutrons bounded together. Due to the conservation of mass, the nuclear mass of a nucleus is just the sum of the masses of protons and neutrons. Let s investigate the α-particle, 2 4 He: The mass of 2 protons = u = u The mass of 2 neutrons = u = u The mass of α-particle = u The difference is m = = u 0 Unit 10 - Nuclear Physics 63

64 The mass of an alpha particle is smaller than the constituents. This difference is called the mass defect. m = Zm p + A Z m n M M is the mass of the nucleus, m p the mass of a proton, and m n the mass of a neutron. Where does this extra mass go when a nucleus is formed or broken down? Unit 10 - Nuclear Physics 64

65 Recall that protons are positively charged. When two protons are placed together, electrostatic repulsion tends to push them apart. The reason why they stick together is the presence of a strong nuclear force that hold the two protons together. This kind of force not only hold protons together; indeed it holds all nucleons (i.e., protons and neutrons) together in a nucleus. Therefore, energy is required to break the nucleus apart and separate completely the protons and neutrons. The required energy is called the binding energy (BE), and it is responsible for the mass defect in the nuclear process. Unit 10 - Nuclear Physics 65

66 Einstein has derived a very famous equation in special relativity that connects energy and mass: E 0 = m 0 c 2 The rest energy E 0 represents the energy equivalent of the rest mass m 0 of an object, which is measured when it is at rest. Unit 10 - Nuclear Physics 66

67 In a nuclear process, energy applied to break the attraction between nucleons is converted to an additional mass added to the free protons and neutrons. That makes the nuclear mass smaller than the masses of the constituents. BE = E 0 = m c 2 Unit 10 - Nuclear Physics 67

68 There are two ways of calculating the binding energy. Let s consider the α-particle again. Method 1: Using SI units The mass of proton is kg and the mass of neutron is kg. Given the mass of an α-particle is kg. The mass defect is: m = = kg The binding energy is therefore: E = = J Unit 10 - Nuclear Physics 68

69 Method 2: Using atomic mass unit Since m p = u, m n = u, and m He = u, the mass defect is: m = = u The binding energy is thus: E = m c 2 = uc 2 It can be shown that 1 uc 2 = MeV, where ev is called electronvolt, being equivalent to J. Hence, E = = MeV Unit 10 - Nuclear Physics 69

70 Example: Determine how much energy is released when Uranium- 238 (mass = u) decays to Thorium-234 (mass = u) through an alpha decay. [5.30 MeV] Unit 10 - Nuclear Physics 70

71 The amount of energy released in a nuclear process is called the Q value of the reaction, and it can be either positive or negative. Positive E: energy is absorbed during the process; it is said to be endothermic. Q < 0 Negative E: energy is released during the process; it is said to be exothermic. Q > 0 That means, energy input is required to trigger endothermic nuclear reactions, while exothermic nuclear reactions are favorable from energy perspective. Unit 10 - Nuclear Physics 71

72 6. Fission, fusion and chain reactions Binding energy is positive for all nuclei because of the existence of the nuclear force that holds the nucleons together. Usually, this quantity is expressed in terms of the energy per nucleon for the comparison purpose. Mathematically: BE per nucleon = Total BE A This allows us to investigate the trend of BE over different nuclei. Unit 10 - Nuclear Physics 72

73 Unit 10 - Nuclear Physics 73

74 There are several key observations: (1) Excluding the lighter nuclei, the average binding energy per nucleon is about 8 ev. (2) The binding energy per nucleon increases rapidly for nuclei with small masses. (3) There exists a peak around A = 60. Iron-56 is among one of the most stable nuclei. (4) Nuclei with high mass numbers are less stable, and their binding energies per nucleon decrease gradually with increasing mass number. (5) Nuclei heavier than Bismuth-209 have the binding energies smaller than 8.0 ev, and are therefore unstable and undergo radioactive decays. Unit 10 - Nuclear Physics 74

75 There are two possible reactions through which nuclei can become more stable. (1) Fission For a very heavy nucleus (e.g. A 200), it may break up into two lighter nuclei. In this process, energy is released. Meanwhile, the binding energy per nucleon of the nucleus is increased; the daughter nuclei are more stable than the parent nucleus. Usually, the process is triggered by an incoming particle such as neutron. For example: The fission of Uranium U n Kr Ba n MeV Unit 10 - Nuclear Physics 75

76 The energy released per nucleon is: E A = MeV 236 = 0.76 MeV Unit 10 - Nuclear Physics 76

77 (2) Fusion Small nuclei (A 20) may combine together to make a heavier nucleus which is relatively more stable. In this process, the total mass decreases and energy is released. No incoming particle is necessary to initiate the fusion process. For example, the fusion of two hydrogen nuclei to form a helium: 1 2 H H 4 2 He n MeV Apparently the amount of energy released is much smaller than that of fission. However, the energy released per nucleon is indeed higher! Unit 10 - Nuclear Physics 77

78 The energy released per nucleon is: E A = 17.6 MeV 5 = 3.52 MeV Unit 10 - Nuclear Physics 78

79 While unstable nuclei can be stabilized by means of fission or fusion, the disintegration of rather stable nuclei can be induced by an incident nucleus, particle or photon. This process is called an induced nuclear transmutation. For example: This equation can be simplified to be Target nucleus 14 7N α, p 17 8O Product nucleus Incident particle Emitted particle Unit 10 - Nuclear Physics 79

80 The followings are some examples of induced nuclear transmutation plus their shorthand notations: Unit 10 - Nuclear Physics 80

81 Example: Write the balanced nuclear equation for the process summarized as Al n, α Na. Example: Using a shorthand notation, write the nuclear equation 16 8O H 13 7 N He Unit 10 - Nuclear Physics 81

82 During the fission of Uranium-235, an incident neutron is absorbed by the nucleus, forming an unstable Uranium-236. It then decomposes very rapidly to lighter nuclei together with a number of neutrons. There are two possible pathways observed in experiments: U Ba Kr n U Xe Sr n These two reactions eject different numbers of neutrons. In average, the fission of U gives 2.5 neutrons. That implies that there are net increase in the number of neutrons in the process. Unit 10 - Nuclear Physics 82

83 It implies that the self-sustaining fission reactions are possible. The initial neutron causes the fission of one U to produce two or more neutrons, and each can initiate another fission, generating even more neutrons. This cycle goes on and on until all uranium nuclei are consumed. Unit 10 - Nuclear Physics 83

84 Depending on the number of neutrons that are produced in each fission step, chain reactions can be classified into 3 types: (1) Subcritical: Less than one neutron gives rise to more reactions in average. The resulting chain reaction cannot be sustained, and will eventually die out. (2) Critical: Precisely one neutron is accessible for more reactions; therefore, the chain reaction can be barely sustained. The chain reaction and the rate of energy production are controlled. Unit 10 - Nuclear Physics 84

85 (3) Supercritical: Since two or more neutrons are generated in each fission, the rate of chain reaction is increasing exponentially over time and eventually the process becomes uncontrollable. Unit 10 - Nuclear Physics 85

86 7. Nuclear reactors As we have seen earlier, nuclear reactions usually create a huge amount of energy. Under a proper control of the process, it may be possible to harness the energy released. The major concern is how to control the rate of fission reactions. If the rate of production of neutrons is equal to the rate of consumption of neutrons, then the reaction will be self-sustained. This can be controlled by means of a moderator which is usually water or heavy water. Unit 10 - Nuclear Physics 86

87 There are many designs of nuclear reactors. These reactors consist of the following parts: (1) Fuel: the materials undergoing fission; e.g. uranium oxide (2) Moderator: to slow down neutrons; e.g. water, carbon (3) Control rods: to shutdown the reaction by absorbing neutrons; e.g. cadmium, boron (4) Coolant: to transfer the heat; either liquid or gas (5) Pressure vessels: the container holding the fission reaction (6) Steam generators: to convert steam to electrical energy (7) Containment: to protect the reactor; usually 1m-thick concrete walls Unit 10 - Nuclear Physics 87

88 Some facts about nuclear reactors in the world Unit 10 - Nuclear Physics 88

89 Boiling water reactor (BWR) Unit 10 - Nuclear Physics 89

90 Pressurized water reactor (PWR) Unit 10 - Nuclear Physics 90

91 Canadian Deuterium Uranium reactor (CANDU) Unit 10 - Nuclear Physics 91

92 To generate energy by fusion, there are two approaches: (1) Magnetic confinement Unit 10 - Nuclear Physics 92

93 (2) Inertial confinement Unit 10 - Nuclear Physics 93