Nuclear Physics Part 3: Nuclear Energy

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Louise Atkinson
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1 Nuclear Physics Part 3: Nuclear Energy Last modified: 24/10/2017

2 CONTENTS Fission & Fusion Definitions Binding Energy Curve Revisited Fission Spontaneous Fission Neutron-Induced Fission Controlled Fission Chain Reaction Reproduction Constant Critical Mass Moderation of Neutrons Absorption of Neutrons Nuclear Reactor Nuclear Fusion Stars Stellar Nucleosynthesis Controlled Fusion Beyond the Nucleus... (not examinable)

3 Fission & Fusion Two types of nuclear reaction are of particular interest in energy generation: Fission is the breaking up (or fissioning ) of a nucleus into smaller nuclei. Fusion is the joining together ( fusing ) of nuclei to create a new larger nucleus. To understand the energy implications of these reactions, we need to return to the binding energy curve we saw previously. Remember that larger binding energy means lower nuclear mass. If, in a reaction, binding energy in increased then energy will be released. i.e. The reaction will be exothermic.

4 Binding Energy Curve Revisited 10 8 Q R BE/A (MeV ) P P Q: fusion is exothermic (small nuclei like to undergo fusion) R Q: fission is exothermic (large nuclei like to undergo fission) A

5 Spontaneous Fission Spontaneous fission is the process where a single heavy nucleus will, without the influence of any other particle, split into (usually) two smaller nuclei and a number of neutrons. Energy is released in this process (i.e. the Q-value is positive). A Z X A1 Z 1 Y 1 + A2 Z 2 Y 2 + neutrons + Energy To understand why neutrons are emitted, we need to return to the line of stability graph seen in previous lectures. This showed that the ratio of neutrons to protons in stable nuclides is higher for heavy nuclides than for lighter nuclides, so after a fission there will be several (typically 1-5) neutrons left-over. For the same reason, it is often the case that the daughter nuclei Y 1 and Y 2 (also known as fission fragments) have too many neutrons and will be likely to β decay.

6 There will be a mixture of different fission fragments formed in a sample of a fissioning nuclide. The exact split into smaller nuclei is random. Note: α decay fits this definition of spontaneous fission, but because it is relatively common, and because the decay products are always the same, it is considered to be in a category of its own and is not referred to as fission. The only naturally occurring nuclide that is observed to spontaneously fission is U, though it does this only rarely (with a half-life of years). Some artificially produced nuclides will also spontaneously fission.

7 Neutron-Induced Fission Much more common is neutron-induced fission which requires a neutron to be absorbed by the nucleus before it can then fission. 1 0n + A ZX A1 Z 1 Y 1 + A2 Z 2 Y 2 + neutrons + Energy This can be thought of as a two-stage process, with the nucleus first absorbing a neutron to briefly form a heavier unstable nucleus which will then spontaneously fission: 1 0n + X ZX A+1 ZX A1 Z 1 Y 1 + A2 Z 2 Y 2 + neutrons + Energy Beacause the neutrons are so much lighter than the other fission products, most of the Q-value is seen as kinetic energy of these neutrons. A nuclide that can undergo neutron-induced fission is said to be fissile.

8 As with spontaneous fission, there are many possible pairs of fission fragments Y 1 and Y 2, as well as differing numbers of neutrons produced. For instance, among many other possibilities, U can fission according to: 1 0n U U Ba Kr + 3( 1 0n) + Energy and 1 0n U U Xe Sr + 2( 1 0n) + Energy The fission fragments are usually radioactive and will subsequently decay. As seen in the above examples, the split of protons into the fission fragments tends to favour a roughly 60%:40% split. The average number of neutrons released in the fission of U is about 2.5.

9 Example Calculate the Q-value for the neutron-induced fission of U into Ba and 92 36Kr. The reaction is: 1 0n U Ba Kr + 3( 1 0n) and the Q-value is calculated in the usual way: Q (in MeV) = δm(in u) = (M U + m n M Ba M Kr 3m n ) = [ ( ) ] = MeV The energy released when one molecule of octane (found in petrol) is burnt is about 200 ev - one millionth of the energy released in this fission.

10 Chain Reaction The fission of U releases large amounts of energy, and since it occurs naturally, it offers the possibility of large scale power generation. The key to this is the emission of neutrons in the fission. An average of 2.5 neutrons are emitted per fission of U. These neutrons can induce more fissions, and the neutrons then released can induce more etc. This continuing series of fissions is known as a chain reaction. Not every neutron will induce a fission: Some will be absorbed by other, non-fissile nuclei. Some will escape from the surface of our fissile sample.

11 Reproduction Constant Whether or not a chain reaction will occur in a particular object depends on a number of factors, including the size and shape of the object, and its exact chemical composition. The reproduction constant K for a particular object is the average number of neutrons from each fission that induce another fission. If K < 1 the reaction will quickly die out. If K > 1 the reaction rate will increase to be rapidly out of control, and in extreme cases will lead to a nuclear explosion. If K = 1 then the reaction will sustain itself at a constant rate Controlled fission suitable for power generation requires careful management of neutrons to obtain K = 1.

12 Critical Mass For simplicity, let s consider a spherical (radius = R) mass of fissile material. The production rate of neutrons is proportional to the number of nuclei present, which depends on the volume. i.e. it scales as R 3. The rate of loss of neutrons is proportional to the surface area of the mass. i.e. it scales as R 2. As the size R is increased, the rate of production increases faster than the rate of loss, so more neutrons will induce fission. The reproduction constant K is increasing. The mass where K = 1 is known as the critical mass. Above this mass the fission reaction will run out of control. A nuclear bomb works by suddenly combining two sub-critical masses into one with K > 1.

13 Moderation of Neutrons The neutrons released in a fission process generally have very high energy. Fast neutrons will tend to bounce off (in an approximately elastic collision) a heavy nucleus, with little loss of energy. The probability of a fission occuring increases for slower neutrons. We need to slow our neutrons down, or moderate them. The loss of energy in collisions will be greatest when the neutrons are colliding with nuclei closer to their own mass. We need to use a material (a moderator) containing light nuclei that do not absorb neutrons. Some commonly used moderators are deuterium ( 2 1H or D, usually in the form of heavy water D 2 O), beryllium or 12 6C (usually in the form of graphite).

14 Absorption of Neutrons Part of the process of managing neutrons in a reactor involves the absorption of extra neutrons. In the extreme case, we want to be able to completely stop the chain reaction to shut down the reactor. For this we need material thet will absorb neutrons without fissioning, and ideally without producing large numbers of radioactive products. This process is known as neutron radiative capture, where the energy of the captured neutron leaves the nucleus in an excited state which then emits a gamma ray: 1 0n + A ZX A+1 ZX A+1 ZX + γ Most commonly used is Cadmium, which has an unusually large number of stable isotopes, so for example: 1 0n Cd Cd + γ and 1 0n Cd Cd + γ etc

15 Nuclear Reactor There are a variety of designs of nuclear reactors which all have the same basic components. The reactor of course contains fissile material, usually in the shape of cylindrical fuel rods, surrounded by a moderator (almost always heavy water). fuel rods Naturally occuring uranium is a mixture of U (99.3%) and U (0.7%). Only U is fissile and in this natural ratio a chain reaction isn t possible. The fuel rods need to be made of enriched uranium, where using chemical processes, the fraction of U is increased up to a few percent. moderator This enrichment of uranium is a complicated industrial process.

16 The reactor is designed to have an average reproduction constant of slightly more than 1. This value fluctuates randomly with time. control rods Cadmium control rods are inserted into the reactor to absorb neutrons and via constant adjustments to maintain the value of K = 1. By fully inserting these rods the reaction can be stopped completely and the reactor can be refueled/maintained etc. The energy released in the fission process will heat up the reactor, and this heat can be used to heat a coolant such as water, which in turn is then used to turn a turbine and generate power. coolant

17 Finally there are some important safety considerations in the reactor design. As we have seen, the absorption of neutrons in the control rods causes gamma emission. Additionally, many of the fission products in the fuel rods will also emit dangerous radiation. containment dome The reactor must be surrounded by radiation shielding - usually thick concrete - to protect people working close by. In the event of an accident, it is possible dangerous radioactive material can escape in the form of smoke. so the reactor is usually located within a protective dome, intended to contain any such leaks. radiation shielding

18 Nuclear Fusion in Stars Nuclear fusion is the source of energy in the Sun and other stars. Most of the Sun s energy is produced by fusing 1 1H to form 4 2He in what is called the p-p cycle: 1 1H + 1 1H 2 1H + 0 1β + + ν 1 1H + 2 1H 3 2He + γ 3 2He + 3 2He 4 2He + 2( 1 1H) The combined Q-value of these reactions is about 25 MeV. The net reaction is: 4( 1 1H) 4 2He + 2( 0 1β + ) + 2γ + 2ν Most of the positrons produced will annihilate with an electron, while the photons and neutrinos are mostly emitted from the Sun, and can be observed on Earth (though with great difficulty in the case of the neutrinos).

19 Stellar Nucleosynthesis Many other fusion reactions occur less frequently in the Sun. Fusions forming nuclei up to the peak of the average binding energy curve at about 56 26Fe, are mostly exothermic and will occur regularly, while heavier nuclides are produced only rarely. The table at right illustrates that apart from Helium, only very small amounts of even the lighter nuclides are produced by fusion in the Sun. Composition of Sun by Mass H 71.0% He 27.1% O 1.0% C 0.4% Fe 0.1% N 0.1%.. Larger stars (greater than about 1.5 times the Sun s mass) have higher temperatures and pressures and produce a wider range of heavy nuclides. As these stars age, they run out of hydrogen to fuse, at which point gravitational forces cause the star to rapidly collapse. In this collapse, medium sized nuclides will be forced together to form large nuclides such as Lead, Uranium etc. After the initial collapse, the star s material will then explode outward in a supernova, spreading out through space.

20 Smaller stars, including the Sun, will also eventually run out of hydrogen, but will just quietly shrink and gradually fizzle out, rather than exploding. Planets such as the Earth have formed from the products of earlier supernovas. Earth s core is believed to be mostly composed of iron (88.8%), with smaller amounts of nickel (5.8%) and sulphur (4.5%) with less than 1% other elements. The crust of the Earth has a wider variety of mostly lighter (i.e. up to iron) elements, shown in the table at right. Even in a supernova explosion, only very small quantities of the heavy elements like Gold, Platinum, Lead, Uranium etc are produced, and are thus only found on Earth in small amounts. Composition of Earth s Crust by Mass O 46.6% Si 27.7% Al 8.1% Fe 5.0% Ca 3.6% Na 2.8% K 2.6% Mg 2.1%.. Au 10 7 %..

21 Controlled Fusion Nuclear fusion potentially has many advantages over fission as a source of energy. The biggest is the relatively safer waste produced. Fission will produce a random mix of medium-size nuclei, some of them with very long half-lives, and some of them toxic. Handling and storing this waste safely is a major problem. Fusion on the other hand tends to produce smaller, shorter-lived nuclides which are easier to handle safely. In addition, the fuel for a fusion reactor - typically hydrogen - is abundant and cheap in comparison to uranium or other fissionable elements. The big challenge in producing fusion reactions is overcoming the Coulomb repulsion between nuclei. The nuclei require large kinetic energy, which means very high temperatures (millions of degrees). Containing such high temperatiures is technically challenging and most efforts have used magnetic fields to hold the plasma (ionized gas) in a toroid.

22 The Sun solves this problem by being so big - its gravity holds the gas together. Achieving fusion in the lab is actually relatively easy, but to date all experiments have required more energy input (to heat and contain the gas) than is produced by the fusion. The best results have achieved output energy of about 95% the energy input. A viable energy source will require more energy output than input. A large international facility called ITER, located in France, is due to start operating soon and it is hoped that this will achieve surplus output energy. ITER will attempt to fuse deuterium and tritium: which has a Q-value of 17.6 MeV. 2 1H + 3 1H 4 2He + 1 0n

23 Beyond the Nucleus... The history of our understanding of matter has involved the progressive discovery of new components that clarify the structure of a much larger number of particles. 19th century Chemistry saw the development of the Periodic Table and the understanding of 1000 s of different molecules as being made up of just 100 types of atom. These 100 elements are in Nuclear Physics explained as being made up of protons, neutrons and electrons - which is a dramatic simplification! But... Beta decay adds the neutrino and the concept of anti-particles, so our neat picture of only three fundamental particles has sudddenly become eight!. And during the 1940 s and 1950 s, this situation became dramatically more complicated....

24 Baryons & Mesons Technological advances in the 1940 s (particularly the cyclotron) enabled for the first time investigations of high energy nuclear collisions. The of these experiments results were startling. Literally of dozens of new sub-atomic particles were discovered over a decade or so - completely upsetting the simple picture of everything being made up just protons, neutrons and electrons. These new particles are unstable, with quite short lifetimes and are classified into two categories: Baryons and Mesons. Baryons (from Greek baryos : heavy) are heavier than protons/neutrons, and are mostly given the names of Greek letters. The table at right shows some of the lightest baryons. Baryon mass/m proton Λ 0 (*) 1.19 Σ +,Σ 0, Σ , +, 0, 1.31 (*) discovered 1950 at Melbourne Uni

25 Mesons (from Greek mesos : in between) are lighter than protons/neutrons, but heavier than electrons and are also given letter names. The table at right shows some the lightest mesons. A heavier version of the electron was also discovered - the muon (originally classified as the mu meson ). Together with the electron and neutrino, these particles are classified as leptons (from Greek leptos : small). Meson mass/m proton π +,π 0, π 0.15 K +,K 0,K 0.50 η 0.58 ρ +, ρ 0, ρ 0.78 Lepton mass/m proton e µ 0.11 This situation was a return to situation of the 100 elements of the periodic table. Perhaps the solution is the same? Are all of these observed particles made up of something smaller?

26 Quarks This is indeed the solution. Baryons and Mesons (collectively called hadrons) are made of smaller particles called quarks. All of the observed particles as of 1960 could be explained as a combination of three types of quark: up (u), down (d) and strange (s). The u quark has a charge = + 2 3e and the d and s both have a charge of 1 3 e. These fractional charges are peculiar, and we would expect that they would be easy to detect, but it turns out that we cannot have an isolated individual quark. Quarks can only appear in groups of three (baryons) or as part of a quark-antiquark pair (mesons). This behaviour is explained in terms of the so-called colour of the quarks. Only colour-less combinations are observed, so a combination of a red, a green and a blue quark in a baryon or a red and anti-red in a meson. Baryon q q q Meson q q Obviously this use of colour is metaphorical.

27 The quark compositions of some of the hadrons listed earlier: Baryon quarks Meson quarks p uud π +, π u d,dū n udd K +,K u s,sū Λ 0 uds ρ +,ρ u d,dū Σ +,Σ 0, Σ uus,uds,dds ++, +, 0, uuu, uud,udd,ddd In the case where two particles include the same quarks - for example p and + - the heavier particle is essentially an excited state of the lighter one, typically with extra angular momentum. Remember these heavier baryons and mesons are unstable and will decay to some combination of our familiar light particles. For instance: ++ p + π + and π + e + + ν

28 The Standard Model This system of three types (or flavours ) of quark, takes us back to a relatively simple system similar to the proton,neutron and electron but again there were problems. Heavier quarks: charm (c), bottom (b) and top (t) have been discovered, as well as an extra lepton, the tauon τ. Each of the extra charged leptons has its own associated neutrino. The known quarks and leptons are grouped into three generations : ( ) ( ) ( ) u c t charge = e d s b charge = 1 3 e ( ) ( ) ( ) e µ τ charge = e νe νµ ντ charge = 0 These particles and the theory of the forces acting between them: (i) the Coulomb force, (ii) the strong nuclear force and (iii) the weak nuclear force (responsible for beta decay), are together known as the Standard Model.

29 Is That it Then? There are strong reasons to believe that there are no more than three generations of quarks and leptons, but three generations already means 12 particles + 12 anti-particles, which seems a lot for a basic theory of nature (Even more if we count different colours of quarks). A bigger problem is that the Standard Model does not include gravity. Including it in the same way as the other forces has enormous difficulties. For these reasons, it is generally believed that the Standard Model is incomplete, and trying to improve it is a very active area of research. One idea is string theory, where (very simplistically) the different quarks and leptons are different modes of vibration of a tiny string.

NUCLEI. Atomic mass unit

NUCLEI. Atomic mass unit 13 NUCLEI Atomic mass unit It is a unit used to express the mass of atoms and particles inside it. One atomic mass unit is the mass of atom. 1u = 1.660539 10. Chadwick discovered neutron. The sum of number