Upper 6th – Unit 5 Nuclear Physics Ideas about Atoms Timeline • 400 BC – Democritus – idea of atomism • 1803 AD – Dalton – elements made of atoms of different weights, combine to make compounds • 1827 – Brownian motion reported – supports kinetic theory and atomic model • Diffusion, also observed around this time, provides further support. • 1896 – Becquerel discovers radioactivity • 1897 – J J Thomson discovers the electron. • 1898 – Rutherford identifies alpha and beta rays. • 1899 – Thomson determines e/m for electron, develops “plum pudding” model of the atom • 1907 – Thomson identifies the Proton and Isotopes • 1909 – Geiger & Marsden find evidence for the nucleus • 1913 – Bohr proposes that electrons exist in discrete orbits around the nucleus • 1932 – Chadwick discovers neutron Rutherford’s Atomic Model • The familiar model we have was devised by Rutherford in 1910, working from evidence collected by Geiger and Marsden. Geiger & Marsden’s experiment • a particles of fixed energy were fired at a thin gold foil and their paths measured. • Most passed straight through the foil or were only slightly deflected, but a few (~1 in 10,000) bounced back. • • • • Alpha scattering Rutherford scattering G-M experiment simulation Force on alpha particles The Geiger-Marsden experiment • Why is it important that all a particles have the same KE? • Why do you think they used a thin foil? Why gold? • Why did the container need to be evacuated? Ernest Rutherford • “It was quite the most incredible event that has ever happened to me. It was almost as incredible as if you fired a 15 inch shell at a piece of tissue paper and it came back and hit you” Rutherford’s Interpretation • Rutherford couldn’t explain these results using Thomson’s “Plum pudding model” of the atom. • He concluded that atoms are mostly empty space, with all the + charge and almost all mass concentrated in a small nucleus. Estimating the size of the nucleus • Only a particles passing close to the nucleus experience a significant deflection Estimating the size of the nucleus • Geiger & Marsden found about 1 in 10,000 a particles were deflected by more than 90°. • The foil used was a few 1000s of atoms thick (say n=104) • So the chance of an a particle being deflected by a single atom must be 1 in 10,000n. – This must depend on the ratio of the area of the nucleus compared to the area of the atom • If D=atomic diameter and d=nuclear diameter, 1 d 2 1 D 4 ,d 2 10000n 1 D 10000n 4 • So d≈1/10,000. Alpha particle (+2e) Gold nucleus (+79e) d Estimating Size of the Nucleus (KE converted to PE) Size of the nucleus Relative scales of atom and solar system (Or a ball in a football stadium) Structure of the atom • Nucleus of protons and neutrons (“nucleons”), surrounded by electrons • Helium atom • Mostly empty space! • Electrons “orbit” ~105 nuclear radii away from centre Seeing atoms • A scanning tunnelling electron microscope image of the surface of a gold sample, with individual atoms visible. – “Stripes” caused by surface crystalline detail • Atoms of silicon Size of nucleus by electron diffraction • Remember that electrons can behave like waves? – They can be diffracted by objects of a similar scale to their wavelength, just like light Size of nucleus by electron diffraction – more accurate • de Broglie wavelength: l=hc/E • Diffraction pattern is superimposed on the normal scattering pattern • First diffraction minimum is at an angle q, where sinq =0.61l/R (R is radius of nucleus) How nuclear radius depends on A • Using electron diffraction with samples of different elements we can measure R and A for different nuclides. • By plotting a suitable graph it is possible to show 1 that R r0 A 3 – r0 is a constant, 1.05 fm • Given data for R & A, what graph might you plot to find the above relationship? – See p. 177 Volume proportional to mass, so nuclear density is constant. V 4 3 r0 A 3 Constant nucleon spacing – suggests strong force is same for all nucleons Nuclear Radiation a – Helium nuclei (2 neutrons and 2 protons) b – electrons (from the nucleus) (or positrons) g – photons (energy) Nuclear Radiation Properties of nuclear radiation Cloud chamber observations • Ionising radiation triggers the formation of droplets in a supersaturated vapour • a particles – Straight, radiate from source – Same length (energy) • b particles – Easily deflected (light) – Less distinct (less ionising) • video Inverse Square Law • Intensity is energy per second passing through unit area. • For a point source, the Intensity is inversely proportional to the square of the distance from the source • If the source radiates energy nhf per second, nhf I 2 4r 1 I 2 r Isotopes • Different isotopes of a given element have different numbers of neutrons. • So they have the same atomic number (Z) but different mass numbers (A). • The chemical properties of the different isotopes of an element are identical, but they will often have great differences in nuclear stability Isotopes • For stable isotopes of light elements, the number of neutrons will be almost equal to the number of protons • A growing neutron excess is characteristic of stable heavy elements. • The element tin (Sn) has the most stable isotopes with 10 Nuclear Notation Practice • How many protons and neutrons is the following? 4 2 He 14 6 C 40 19 K 238 92 U Alpha emission • An alpha particle consists of 2 protons and 2 neutrons 4 – Like a helium nucleus 2 a • So when an atom undergoes a decay it loses 2 protons and 2 neutrons • e.g., Mass numbers Th Ra a 228 90 224 88 4 2 balance Charge numbers balance Beta– emission • A b- particle is an electron which comes 0 from a neutron-rich nucleus – A neutron changes into a proton, and an electron and an antineutrino are emitted 1 b • So when an atom undergoes b– decay it gains 1 proton and loses 1 neutron • e.g., 40 19 K Ca b e 40 20 0 1 Mass numbers balance Charge numbers balance Beta+ emission • A b+ particle is a positron (anti-electron) 0 which comes from a proton nucleus – A proton changes into a neutron, and a positron and an neutrino are emitted 1 b • So when an atom undergoes b+ decay it gains 1 neutron and loses 1 proton • eg: C B b e 11 6 11 5 0 1 Mass numbers balance Charge numbers balance Electron capture • Some proton-rich nuclei can capture an inner shell electron, causing a proton to change into a neutron, with a neutrino emitted. • An outer shell electron drops down to fill the lower shell, emitting an x-ray photon as it does. 40 19 K e Ar e 40 18 Mass numbers balance Charge numbers balance g radiation produced by “rearrangement” of nucleus Energy released Same components Unstable Stable • So no change to the nuclear composition Now do some practice… • Fill in the missing parts: ? ? ? ? a ? ? ? ? • So how do you know what kind of radioactive decay an unstable nucleus will undergo? The N–Z graph • Provides a survey of nuclear stability – For light nuclei (Z<20) N=Z for stable isotopes – As Z increases, stable nuclei have increasing proportion of neutrons providing strong force ‘glue’ – Away from the stability curve, unstable nuclei decay to move closer to the stability curve What does what? • a emitters occur for Z>60 or so. – They have more neutrons than protons, but just not enough to overcome Coulomb repulsion. • b- emitters are on the left of the stability belt. – Neutron-rich nuclei can redress the balance by converting neutrons to protons • b+ emitters are on the right of the stability belt. – proton-rich nuclei can redress the balance by converting protons to neutrons Changes on the N-Z graph • As shown opposite… • Many radioactive isotopes decay to produce further unstable isotopes. • It is possible for whole series of decays to be undergone before a stable daughter isotope is reached. – Such a series can be represented on the N-Z graph by a series of arrows (see p. 173) N b a b Z Natural radioactive series U238 Th232 • figures in red are half-lives. Figures in boxes are averages for multiple paths. So when do you get g? • Similar to electrons, nucleons only exist in allowed energy levels. • Following the emission of an a of b particle the daughter nucleus may be formed in an excited state. • This will be short-lived and the nucleus will move to its ground state, releasing the energy as a gamma ray (like photons produced when electrons de-excite). Technetium – a pure g emitter • For medical imaging applications we want an isotope which – Has a reasonably short half-life – Only emits g rays • Technetium is formed in an excited state from the beta decay of molybdenum. • The excited state is long lived (“metastable”, T1/2~ 6 h), so Tc can be separated from Mo to give the tracer required. • See p.174 for more details Activity • The activity, A, of a radioactive isotope is the number of nuclei that decay per second. – Unit – becquerel (Bq) – 1 Bq = 1 decay per second. • Radioactive decay is random, all undecayed nuclei have an equal probability of decaying at any time. • The activity is proportional to the mass of undecayed isotope present. • This mass decreases with time, due to decays, so the activity decreases with time too. Activity gradually decreases • Over time the activity of a sample will decrease Half-life • Half-life (T1/2) is the time taken for half the radioactive atoms in a sample to decay – or the time for the activity to drop to a half • Activity after n half-lives is 1/2n times the original 1/2 1/2 1/2 1/2 1/2 1/2 Varying half-lives • Half-lives for different substances range from seconds to many millions of years • The most abundant isotopes are the most stable Activity and Power • A radioactive source of activity A emitting radiation of energy E is releasing energy at a rate AE per second. • Power transferred = AE • If such a source is sealed into a container, the container will gain thermal energy. • This can be converted to electrical power in a Radioisotope thermoelectric generator, as used on many spacecraft. Radioisotope thermoelectric generator • Typically use plutonium-238 dioxide pellets: – best enegy/mass ratio – mostly useful a radiation – longish half-life (87 yrs) • An array of thermocouples convert the heat energy to electricity via the Seebeck effect. • Units typically produce a few 100 s of watts for 25 years. • Used for remote, unmanned installations – Spacecraft, satellites, polar lighthouses, navigation beacons, pacemakers (in the past) Radioactive decay • Every unstable nucleus has an equal probability of decaying in a second, l (the ‘decay constant’) • Consider a sample containing N0 nuclei at time t=0: – N is the number of undecayed nuclei remaining after a time t – Dt is a time interval • The number of nuclei decaying in a time Dt is given by: DN lNDt Radioactive decay 1100 1000 900 DN lNDt 800 700 N 600 500 DN so lN , and A lN Dt lt solving this for N gives N N 0e 400 300 200 100 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 time (s) • Exponential decay, like capacitor discharge, water running out of a hole, etc… • Number of unstable nuclei falls by a fixed proportion in a fixed time period • Animation here 5000 Radioactive decay N N 0e lt , so : lt A A0e , where A0 lN 0 • Example: – The decay constant for caesium-137 is 7.3x10-10 s–1. Calculate: • The number of atoms present in a sample with an activity of 2.0 × 105 Bq 2.7 × 1014 • The activity of the sample after 30 years 1.0 × 105 Bq The decay constant l • l is the probability of an individual nucleus decaying per second. • When t = 1/l, the activity has fallen to 1/e (~37%) of its initial value. N N 0 e l t , so N e lt and 0.5 e lT1 / 2 N0 ln 0.5 ln 2 lT1/ 2 so T1/ 2 ln 2 l 0.693 l Decay graphs 1100 1000 N N 0e ln N ln N 0 lt 800 700 N 600 500 400 300 200 100 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 4500 5000 time (s) 7.0 6.5 Gradient = -l Intercept = ln N0 6.0 5.5 ln N • Half-life can be read off a graph as the time when N=N0/2 • 1/l can be read off a graph as the time when N=N0/e • l and N0 can also be determined from a ln graph lt 900 5.0 4.5 4.0 3.5 3.0 0 500 1000 1500 2000 2500 time (s) 3000 3500 4000 Dangers of radiation • Ionising radiation is hazardous to living cells. It can: – Destroy cell membranes, killing cells – Damage vital molecules such as DNA, possibly leading to: • Uncontrolled cell division (cancer) • Genetic mutation in sex cells • These can impact the health of the affected organism and its offspring. • There is no “safe” dose of radiation – But the higher the exposure the greater the risk Radiation dose • Radiation dose is measured in Sieverts (or milliSieverts) – Unit accounts for type and amount of radiation given • UK average annual dose 2.6 mSv • The higher the dose, the higher the chances of harm (but there are no guarantees!) – up to 500 mSv: no noticeable symptoms – 500–1000 mSv: light radiation poisoning – 3000 mSv: severe radiation poisoning – > 6000 mSv: always fatal People at risk from radiation • • • • • Hospital radiologists Nuclear workers Pilots and flight crew Some miners Industrial radiation workers • Exposure is regularly monitored • Exposure is kept as low as reasonably achievable (ALARA) • Exposure time is adjusted to ensure annual dose is within accepted levels Background Radiation Background radiation – (mostly) harmless! Correcting for background radiation • A radiation detector does not distinguish between background and other radiation. • The background count rate can be measured by simply leaving the detector running for some time away from any obvious sources. • Any experimental measurement of activity for a source then needs to have this background count rate subtracted to calculate the “true” count rate from the source. Safety precautions • Radioactive materials should be: – Stored in lead-lined containers. • Thick enough to reduce g radiation to background levels • Gases, Liquids and powders should be in sealed containers to avoid ingestion, inhalation or skin contact – Kept as far from the body as possible • Use tongs, gloves or handling robots to stay out of range of a and b and reduce g intensity – Used as quickly as possible • Minimising dose Uses of radioisotopes • The usual GCSE ones: – Thickness monitoring – Imaging (gamma camera) – Treating cancer • irradiation and contamination – Sterilisation (seal then irradiate, g) • Food • Surgical instruments Carbon dating • Half-life of C-14 is 5570 yrs Argon dating • Radioactive potassium, “frozen” into rocks when they cool, decays: 40 0 40 K b 19 1 20 Ca e 40 0 40 19 K 1 e18 Ar e • The decay producing Ca is 8 times more likely than the decay producing Ar • There is no Ar in the rocks when they solidify • The effective half-life is 1250 My. Argon dating 40 19 40 K 10b 20 Ca e 8 times more likely 40 K 10e18 Ar e • For every N atoms of K-40 now present, if there is 1 Ar atom present there must have been N+9 K-40 atoms originally. • Knowing N0, N and T1/2 (or l), we can calculate t using N N 0 e lt 40 19 Radioactive tracers • Radioactive isotopes are chemically identical to their stable cousins, but can be detected. • A radioactive tracer is introduced to the system of interest and allowed to circulate. • Information is revealed by where the radioactive isotopes end up. • Generally want g (or b) emitters • See table on p.170 Mass and Energy • Mass and energy are related: E mc 2 • According to Einstein, mass is just another form of energy. • Principle of conservation of mass is therefore just an extension of the principle of conservation of energy. Energy changes in reactions • Nuclear reactions involve significant changes in mass • This “lost” mass is transferred to the products as kinetic energy • Energy released Q=Dmc2 – In a decay, energy shared between nucleus and a particle in inverse proportion to their masses Proof? – In b decay, energy is shared between b particle and neutrino in varying proportions • If Dm=1u, E=931.3 MeV (see worked eg p. 183) • Now try SQs p. 184 Binding Energy • Unified atomic mass constant, u – u=1.66x10-27 kg (12C has mass 12u, by definition) • • • • • • Mass of a proton=1.0073u Mass of a neutron=1.0087u Calculate the mass of an atom of 24 He Measured mass of He is 4.0026u So where is the “missing mass”? What is the binding energy released when a He atom forms? Binding Energy • “The binding energy of the nucleus is the work that must be done to separate it into its constituent protons and neutrons”. – i.e. equal to the energy released when the strong nuclear force did work forming the nucleus • The release of binding energy on nuclear formation results in a mass defect. – Dm=Zmp+(A-Z)mn-Mnuc – Binding energy=Dmc2 – Hint: if you are given the mass of an atom, don’t forget to subtract Zme Element Mass of nucleons Deuterium Helium 4 Lithium 7 Beryllium 9 Iron 56 Silver 107 Iodine 127 Lead 206 Polonium 210 Uranium 235 Uranium 238 2.01594 4.03188 7.05649 9.07243 56.44913 107.86187 128.02684 207.67109 211.70297 236.90849 239.93448 Nuclear Mass (u) 2.01355 4.00151 7.01336 9.00999 55.92069 106.87934 126.87544 205.92952 209.93683 234.99351 238.00037 Binding Energy (u) 2.23 28.29 40.15 58.13 492.24 915.23 1072.53 1622.27 1645.16 1783.80 1801.63 Binding Energy per Nucleon (MeV) (MeV) 1.12 7.07 5.74 6.46 8.79 8.55 8.45 7.88 7.83 7.59 7.57 proton mass = 1.67262158 × 10–27 kg neutron mass = 1.67492729(28) × 10–27 kg 1 amu = 1 u = 1.66053873 × 10–27 kg c = 2.99792458 × 108 ms–1 element deuterium helium 4 lithium 7 beryllium 9 iron 56 silver 107 iodine 127 lead 206 polonium 210 uranium 235 uranium 238 BE/nucleon nuclear mass (u) 2.01355 4.00151 7.01336 9.00999 55.92069 106.87934 126.87544 205.92952 209.93683 234.99351 238.00037 Z 1 2 3 4 26 47 53 82 84 92 92 = c2Dm/A = c2(Zmp+(A–Z)mn–Mnuc)/A Binding energy/nucleon curve Increasing stability • binding energy/nucleon is the average work done per nucleon to break up a nucleus into constituent particles – A measure of nuclear stability fusion fission Binding energy/nucleon curve • From the curve, estimate the energy released when: – 235U splits in two – Two 3He fuse fusion fission Nuclear fission • From the binding energy curve, we can see that energy can be released if heavy nuclei split into lighter ones. • This can be induced by the absorption of a neutron. – If fast neutrons are needed to provide extra energy the material is said to be fissionable – If slow neutrons can induce fission the material is said to be fissile • U-235 and Pu-239 are the only fissile nuclei, according to your text book (not actually true) Uranium 235 fission • Can fission spontaneously, but this is rare. • Usually induced by the absorption of a neutron • The nucleus splits into two large particles (see graph) and 2 or 3 neutrons • ~200 MeV of energy released per fission Chain reaction applet • The fission neutrons released can collide with other fissile nuclei and trigger further fission – a chain reaction • If, on average, each fission triggers one further fission we have a self-sustaining chain reaction • If each fission triggers more than one further fission we have a runaway chain reaction Controlled chain reaction • Uncontrolled chain reaction – explosion • Controlled chain reaction – each fission causes one more fission. – Steady release of energy. To control the rate of energy release we need to control how many neutrons there are Uncontrolled chain reaction Uranium Fission product neutron Controlled chain reaction Uranium Fission product Neutron Control rod An electricity generation station The Chimney has gone – no CO2! But nuclear waste is generated... • In a conventional power station water is heated by burning fossil fuel • In a nuclear power station water is heated by energy released during nuclear fission Nuclear Reactor • Pressurised water reactor (PWR) – What does pressure do to the water? – Increase the boiling point • The water circulating through the reactor core is bombarded with neutrons and becomes radioactive. It is kept in a closed circuit. • The water to which the energy is transferred in the heat exchanger may be irradiated as it passes through, but it does not become radioactive and is safe. Nuclear fuels • Natural uranium contains <1% U-235 • To make a viable fuel it must be enriched to ~3% • Plutonium-239 is a by-product of Uranium fission. It can be obtained by re-processing spent nuclear fuel. • Pu-239 can be used as a nuclear fuel, but not in a conventional reactor. Reactor components • Fuel rods – Contain pellets of Uranium oxide – U-235 content has been enriched from ~0.7% to ~3% – Rods made of zirconium alloy • Resistant to corrosion • “transparent” to neutrons – Core may contain up to 8,000 fuel rods Reactor components • Control rods – Made of silver-indium-cadmium alloys, or boron – Have a high neutron capture cross-section – Are moved in and out of the core to absorb more or fewer neutrons and hence control the rate of the chain reaction Neutron Moderator • Fast neutrons from fission are not readily absorbed by U-235, but slower neutrons are • A moderator reduces the KE of fast neutrons through multiple collisions – A good moderator should be of comparable mass to a neutron for efficient energy transfer – It should also be a poor absorber of neutrons • Water and graphite are the most common Radioactive waste • Nuclear power produces radioactive waste, some with extremely long half-lives – High, intermediate and low level Three categories of waste Category (quantity /m3/yr worldwide) Typical composition Storage method Low level (150,000) negligible Protective clothing, medical Compacted in drums and waste, building materials stored securely on surface Intermediate level (75,000) 10% of total radioactivity Fuel cladding, filter materials, decommissioned reactor parts, decayed high level waste Cut up, packed in cement-filled drums and stored securely in surface buildings High level (2,000)* 90% of total radioactivity Spent fuel rods Vitrified and stored securely underwater (to cool) in stainless steel cylinders * A nuclear reactor produces about 3m3 of HLW per year Nuclear fusion • If two small nuclei collide with enough energy they fuse, to produce a new nucleus • When this happens a large amount of energy is released – This is what makes stars (including our Sun) shine • For this to happen the nuclei must be moving very fast – High temperature (~15 million K) • plasma – High density (~10,000 x air) Hydrogen Fusion •Proton-Proton Process 0 1 1 1 H H H e ν 1 1 H H He g 3 2 He He He H H 1 1 2 1 2 1 3 2 3 2 4 2 1 1 1 1 Hydrogen Fusion 0 1 H H H e ν 1 1 1 1 2 1 •Step 1: Deuterium formation Hydrogen Fusion H H He g 1 1 2 1 3 2 •Step 2: Deuterium/proton fusion Hydrogen Fusion 3 2 He He He H H 3 2 •Step3: Helium fusion 4 2 1 1 1 1 The fusion chain Fusion reactors • Mostly try to fuse 2H and 3H • The light nuclei must be very hot before fusion can take place. – This is done with a very high electric current • The plasma must be contained so it doesn’t touch the reactor walls – This is done with magnetic fields • So far a commercial fusion reactor has not been built. Practical fusion • It is very difficult to recreate the conditions necessary to sustain fusion reactions on Earth, but it would be great if we could! – Potentially huge amounts of energy available – Plentiful supply of fuel (from sea water) – Non-radioactive waste products – No greenhouse gases – No chain reaction (so no danger of runaway) • Research continues… • Now do the end-of-chapter questions