AQA A-Level Physics Revision PDF

CGP CGP P...

CGP CGP P G C CGP — a force for good in AQA A-Level Physics revision! A-Level We’ve packed this stunning all-in-one book with New-tons of helpful features... Physics Unbeatably clear CGP study notes... You bet — that’s what we’re famous for Exam Board: AQA Plenty of essential exam-style questions... Yep, including a section of synoptic practice Perfectly tailored to the AQA course... All the Core Content and Options 9-12... covered! So buy this CGP book on impulse — it’ll change your revision momentum! ☻ P.S. For even more amazing AQA A-Level Physics exam prep, don’t miss CGP’s matching Exam Practice Workbook! Complete Revision & Practice Everything you need to pass the exams! P G C www.cgpbooks.co.uk  P CGP G C CGP books — they might Meet CGP’s unbeatable double act just save your life... for A-Level Physics revision! OK, maybe not your life. But when it comes to exam revision, CGP are the undisputed champions. You can order any of our books (with next-day delivery!) from us, online or by phone: Like equal and opposite forces, our Complete Revision & Practice guide and Exam Practice Workbook for AQA are perfectly matched. www.cgpbooks.co.uk 0800 1712 712 Order now at cgpbooks.co.uk Or you’ll find our range in any good bookshop, including: 0418 - 17298  A-Level Physics Exam Board: AQA Physics is a big subject — it covers everything. Minuscule subatomic particles? Check. Mind-bendingly enormous astronomical phenomena? Check. The broader socio-historical significance of heroic archetypes in classical Greek mythology? Oh. But even without that last one, there are still plenty of challenging topics to tackle in the AQA A-Level Physics exams. Which is why you’ll need this amazing CGP book. It’s packed with crystal-clear study notes, realistic exam questions and much more... P G C A-Level revision? It has to be CGP! Published by CGP Editors: Emily Garrett, Sharon Keeley-Holden, Andy Park, Ethan Starmer-Jones, Hannah Taylor and Charlotte Whiteley. Contributors: Tony Alldridge, Jane Cartwright, Peter Cecil, Peter Clarke, Mark Edwards, Duncan Kamya, Barbara Mascetti, John Myers, Zoe Nye, Oliver Rigg, Frances Rooney, Moira Steven, Andy Williams and Tony Winzor. PAR73DK With thanks to Matthew Benyohai, Mark Edwards and Duncan Lindsay for the proofreading. With thanks to Jan Greenway for the copyright research. Clipart from Corel® Printed by Elanders Ltd, Newcastle upon Tyne. Based on the classic CGP style created by Richard Parsons. Text, design, layout and original illustrations © Coordination Group Publications Ltd. (CGP) 2018 All rights reserved. 0800 1712 712 www.cgpbooks.co.uk  Contents If you’re revising for the AS exams, you’ll need to revise Sections 1-6, and the Practical and Investigative Skills section at the back. If you’re revising for the A-level exams, you’ll need to revise the whole book — but only the option you’ve studied from Section 13. Option 13: “Electronics” isn’t covered in this book. Specification Map i Section 4 — Mechanics AS Scalars and Vectors 42 Section 1 — Particles AS Forces 44 Moments 46 Atomic Structure 2 Mass, Weight and Centre of Mass 48 Stable and Unstable Nuclei 4 Displacement-Time Graphs 50 Particles and Antiparticles 6 Velocity-Time and Forces and Exchange Particles 8 Acceleration-Time Graphs 52 Classification of Particles 10 Motion With Uniform Acceleration 54 Quarks 13 Acceleration Due to Gravity 56 Projectile Motion 58 Newton’s Laws of Motion 60 Section 2 — Electromagnetic AS Drag, Lift and Terminal Speed 62 Radiation and Quantum Phenomena Momentum and Impulse 64 The Photoelectric Effect 16 Work and Power 66 Energy Levels and Photon Emission 18 Conservation of Energy and Efficiency 68 Wave-Particle Duality 20 Extra Exam Practice for Sections 1 and 2 22 Section 5 — Materials AS Properties of Materials 70 Section 3 — Waves AS Stress and Strain 72 Progressive Waves 24 The Young Modulus 74 Longitudinal and Transverse Waves 26 Stress-Strain and Force-Extension Graphs 76 Superposition and Coherence 28 Extra Exam Practice for Sections 4 and 5 78 Stationary Waves 30 Diffraction 32 Two-Source Interference 34 Section 6 — Electricity AS Diffraction Gratings 36 Current, Potential Difference and Resistance 82 Refractive Index 38 I/V Characteristics 84 Extra Exam Practice for Section 3 40 Resistivity and Superconductivity 86 Electrical Energy and Power 88 E.m.f. and Internal Resistance 90 Conservation of Energy and Charge 92 The Potential Divider 94 Extra Exam Practice for Section 6 96 Section 7 — Further Mechanics Section 11 — Magnetic Fields Circular Motion 98 Magnetic Fields 140 Simple Harmonic Motion 100 Charged Particles in a Magnetic Field 142 Simple Harmonic Oscillators 102 Electromagnetic Induction 144 Free and Forced Vibrations 104 Induction Laws and Alternators 146 Extra Exam Practice for Section 7 106 Alternating Currents 148 Transformers 150 Extra Exam Practice for Section 11 152 Section 8 — Thermal Physics Thermal Energy Transfer 108 Gas Laws 110 Section 12 — Nuclear Physics Ideal Gas Equation 112 Rutherford Scattering and Atomic Structure 154 The Pressure of an Ideal Gas 114 Nuclear Radius and Density 156 Kinetic Energy and the Development of Theories 116 Radioactive Emissions 158 Extra Exam Practice for Section 8 118 Investigations of Radioactive Emissions 160 Exponential Law of Decay 162 Nuclear Decay 164 Section 9 — Gravitational Nuclear Fission and Fusion 166 and Electric Fields Binding Energy 168 Gravitational Fields 120 Extra Exam Practice for Section 12 170 Gravitational Potential 122 Orbits and Gravity 124 Electric Fields 126 Section 13: Option A — Astrophysics Electric Potential and Work Done 128 Optical Telescopes 172 Comparing Electric and Non-Optical Telescopes 175 Gravitational Fields 130 Distances and Magnitude 178 Stars as Black Bodies 180 Spectral Classes and the H-R Diagram 182 Section 10 — Capacitors Stellar Evolution 184 Capacitors 132 The Doppler Effect and Red Shift 188 Charging and Discharging 134 Quasars and Exoplanets 190 More Charging and Discharging 136 The Big Bang Model of the Universe 192 Extra Exam Practice for Sections 9 and 10 138 Section 13: Option B — Section 13: Option D — Medical Physics Turning Points in Physics Physics of the Eye 194 Specific Charge of the Electron 240 Defects of Vision 196 Millikan’s Oil-Drop Experiment 242 Physics of the Ear 198 Light — Particles vs Waves 244 Intensity and Loudness 200 The Photoelectric Effect and the Photon Model 247 Electrocardiography (ECG) 202 Wave-Particle Duality 250 Ultrasound Imaging 204 The Speed of Light and Relativity 252 Endoscopy 206 Special Relativity 254 X-Ray Production 208 Extra Exam Practice for Section 13 256 X-Ray Imaging Techniques 210 Magnetic Resonance (MR) Imaging 212 Medical Uses of Radiation 214 Practical and Investigative Skills Experiment Design 258 Section 13: Option C — Uncertainty and Errors 260 Engineering Physics Presenting and Evaluating Data 262 Inertia and Kinetic Energy 216 Rotational Motion 218 Torque, Work and Power 220 Do Well In Your Exams Flywheels 222 Exam Structure and Technique 264 Angular Momentum 224 Working with Exponentials and Logarithms 266 The First Law of Thermodynamics 226 p-V Diagrams 229 Four-Stroke Engines 232 Synoptic Practice 268 Using Indicator Diagrams 234 Engine Efficiency 236 Answers 276 Reversed Heat Engines 238 Index 310 i Specification Map This specification map tells you where each bit of the AQA specification is covered in the book. 3.1 — Measurements and their errors 3.1.1 — Use of SI units and their prefixes 3.1.3 — Estimation of physical quantities covered throughout the book covered throughout the book 3.1.2 — Limitation of physical measurements p.259­-261, p.263 3.2 — Particles and radiation 3.2.1 — Particles 3.2.1.7   p.14 AS 3.2.1.1   p.2, p.3 3.2.2 — Electromagnetic radiation and 3.2.1.2   p.4, p.5 quantum phenomena 3.2.1.3   p.6, p.7 3.2.2.1   p.16, p.17 3.2.1.4   p.8, p.9 3.2.2.2   p.18 3.2.1.5   p.8, p.10-15 3.2.2.3   p.18, p.19 3.2.1.6   p.13, p.14 3.2.2.4   p.20, p.21 3.3 — Waves 3.3.1 — Progressive and stationary waves 3.3.2 — Refraction, diffraction AS 3.3.1.1   p.24, p.25 and interference 3.3.1.2   p.25-27 3.3.2.1   p.29, p.32, p.34, p.35 3.3.1.3   p.30, p.31 3.3.2.2   p.32, p.33, p.36, p.37 3.3.2.3   p.38, p.39 3.4 — Mechanics and materials 3.4.1 — Force, energy and momentum 3.4.1.6   p.64, p.65 AS 3.4.1.1   p.42-45 3.4.1.7   p.66-68 3.4.1.2   p.46-49 3.4.1.8   p.68, p.69 3.4.1.3   p.50-57 3.4.2 — Materials 3.4.1.4   p.58, p.59, p.62, p.63 3.4.2.1   p.68, p.70-73, p.76, p.77 3.4.1.5   p.60, p.61 3.4.2.2   p.74, p.75 3.5 — Electricity 3.5.1 — Current electricity 3.5.1.4   p.88-90, p.92, p.93 AS 3.5.1.1   p.82 3.5.1.5   p.94, p.95 3.5.1.2   p.82-85 3.5.1.6   p.90, p.91 3.5.1.3   p.85-87 3.6 — Further mechanics and thermal physics 3.6.1 — Periodic motion 3.6.2 — Thermal physics 3.6.1.1   p.98, p.99 3.6.2.1   p.108, p.109 3.6.1.2   p.100, p.101 3.6.2.2   p.110-113 3.6.1.3   p.100, p.102, p.103, p.105 3.6.2.3   p.110, p.114-117 3.6.1.4   p.104, p.105 3.7 — Fields and their consequences 3.7.1 — Fields 3.7.4 — Capacitance p.120, p.130, p.131 3.7.4.1   p.132 3.7.2 — Gravitational fields 3.7.4.2   p.132 3.7.2.1   p.120 3.7.4.3   p.133, p.134 3.7.2.2   p.120, p.121 3.7.4.4   p.134-137 3.7.2.3   p.122, p.123, p.129 3.7.5 — Magnetic fields 3.7.2.4   p.122, p.124, p.125 3.7.5.1   p.140, p.141 3.7.3 — Electric fields 3.7.5.2   p.142, p.143 3.7.3.1   p.126, p.131 3.7.5.3   p.144, p.145 3.7.3.2   p.126-128 3.7.5.4   p.146, p.147 3.7.3.3   p.128, p.129 3.7.5.5   p.148, p.149 3.7.5.6   p.150, p.151 Specification Map  ii Specification Map 3.8 — Nuclear Physics 3.8.1 — Radioactivity 3.8.1.5   p.155-157 3.8.1.1   p.154 3.8.1.6   p.166-169 3.8.1.2   p.158-161 3.8.1.7   p.166 3.8.1.3   p.162, p.163, p.266 3.8.1.8   p.166, p.167 3.8.1.4   p.164, p.165 3.9 — Astrophysics 3.9.1 — Telescopes 3.9.2.4   p.182 3.9.1.1   p.172 3.9.2.5   p.183-185 3.9.1.2   p.173 3.9.2.6   p.186, p.187, p.190, p.192 3.9.1.3   p.175-177 3.9.3 — Cosmology 3.9.1.4   p.173, p.174, p.177 3.9.3.1   p.188-190 3.9.2 — Classification of stars 3.9.3.2   p.192, p.193 3.9.2.1   p.178 3.9.3.3   p.190 3.9.2.2   p.178, p.179 3.9.3.4   p.190, p.191 3.9.2.3   p.180, p.181 3.10 — Medical Physics 3.10.1 — Physics of the eye 3.10.5 — X-ray imaging 3.10.1.1   p.194, p.195 3.10.5.1   p.208, p.209 3.10.1.2   p.194, p.196, p.197 3.10.5.2   p.210, p.211 3.10.2 — Physics of the ear 3.10.5.3   p.210 3.10.2.1   p.198, p.199 3.10.5.4   p.210 3.10.2.2   p.200, p.201 3.10.6 — Radionuclide imaging and therapy 3.10.2.3   p.201 3.10.6.1   p.214, p.215 3.10.3 — Biological measurement 3.10.6.2   p.214 3.10.3.1   p.202, p.203 3.10.6.3   p.214 3.10.6.4   p.215 3.10.4 — Non-ionising imaging 3.10.6.5   p.215 3.10.4.1   p.204, p.205 3.10.6.6   p.213 3.10.4.2   p.206, p.207 3.10.4.3   p.212 3.11 — Engineering Physics 3.11.1 — Rotational dynamics 3.11.2 — Thermodynamics and engines 3.11.1.1   p.216 3.11.2.1   p.226 3.11.1.2   p.217, p.222, p.223 3.11.2.2   p.226-228 3.11.1.3   p.218, p.219 3.11.2.3   p.229-231 3.11.1.4   p.220 3.11.2.4   p.232-236 3.11.1.5   p.224, p.225 3.11.2.5   p.236, p.237 3.11.1.6   p.220, p.221 3.11.2.6   p.238, p.239 3.12 — Turning points in physics 3.12.1 — The discovery of the electron 3.12.2.4   p.247-249 3.12.1.1   p.240 3.12.2.5   p.250 3.12.1.2   p.240 3.12.2.6   p.251 3.12.1.3   p.240, p.241 3.12.3 — Special relativity 3.12.1.4   p.242, p.243 3.12.3.1   p.252 3.12.2 — Wave-particle duality 3.12.3.2   p.253 3.12.2.1   p.244 3.12.3.3   p.254 3.12.2.2   p.245 3.12.3.4   p.254 3.12.2.3   p.245, p.246 3.12.3.5   p.255 Option 13: “Electronics” isn’t covered in this book. Specification Map 2 Section 1 — Particles Atomic Structure “So what did you do today, Johnny?” “Particle physics, Mum.” “How nice dear — done with times tables then?” Yeah, well, it’s not exactly the easiest topic in the world, but it’s a darn sight more interesting than biology. Atoms are made up of Protons, Neutrons and Electrons Inside every atom, there’s a nucleus containing protons and neutrons. Protons and neutrons are both known as nucleons. Orbiting this core are the electrons. This is the nuclear model of the atom. The diagram shows neutral oxygen, with eight protons and eight electrons. Tom dreamt of The nucleus — containing becoming a nuclear protons and neutrons model when he grew up. The electrons in orbit | || | | | | | | | | | | | | | | | | | You need to le | | around the nucleus arn | | | | | | | | | | | | | | | | | | | | | | | the values in the orange colum ns you won’t be — The particles in an atom have different properties. Their charges and masses are so tiny given them in the ex that it’s often easier to talk about their relative charge and relative mass. am. | | | | | | | | | | || | | | | | | | | | | Particle Charge (coulombs, C) Mass (kg) Relative Charge Relative Mass Proton +1.60 × 10–19 1.67 × 10–27 +1 1 Neutron 0 1.67 × 10–27 0 1 Electron –1.60 × 10–19 9.11 × 10–31 –1 0.0005 The Proton Number is the Number of Protons in the Nucleus No... really. The proton number is sometimes called the atomic number, and has the symbol Z (I’m sure it makes sense to someone). Z is just the number of protons in the nucleus. It’s the proton number that defines the element — no two elements will have the same number of protons. || | | | | | | | | In a neutral atom, the number of electrons equals the number of protons. || | | | | | | | | | | | | | A particle with a different | | | | | || The element’s reactions and chemical behaviour depend on the number of electrons. number of electrons to | | | | | || So the proton number tells you a lot about its chemical properties. protons is called an ion. || | | || | | | | | | | | | | | | | | | | | | | | | | The Nucleon Number is the Total Number of Protons and Neutrons The nucleon number is also called the mass number, and has the symbol A (*shrug*). It tells you how many protons and neutrons are in the nucleus. Since each proton or neutron has a relative mass of (approximately) 1 and the electrons weigh virtually nothing, the number of nucleons is the same as the atom’s relative mass. The nuclide notation of an element summarises information about its atomic structure: The nucleon number — there are a total of 12 protons and neutrons in a carbon-12 atom. C 12 The proton number — there are The symbol for the element carbon. six protons in a carbon atom. 6 Section 1 — Particles  3 Atomic Structure Isotopes have the Same Proton Number, but Different Nucleon Numbers Atoms with the same number of protons but different numbers of neutrons are called isotopes. Changing the number of neutrons doesn’t Example: Hydrogen has three natural isotopes affect the atom’s chemical properties. — hydrogen, deuterium and tritium. Hydrogen has 1 proton and 0 neutrons. The number of neutrons affects the stability of the nucleus though. Deuterium has 1 proton and 1 neutron. Unstable nuclei may be radioactive and decay over Tritium has 1 proton and 2 neutrons. time into different nuclei that are more stable (see p.5). Radioactive Isotopes Can be Used to Find Out How Old Stuff Is 1) All living things contain the same percentage of radioactive carbon-14 taken in from the atmosphere. 2) After they die, the amount of carbon-14 inside them decreases over time as it decays to stable elements. 3) Scientists can calculate the approximate age of archaeological finds made from dead organic matter (e.g. wood, bone) by using the isotopic data (amount of each isotope present) to find the percentage of radioactive carbon-14 that’s left in the object. The Specific Charge of a Particle is Equal to its Charge Over its Mass The specific charge of a particle is the ratio of its charge to its mass, given in coulombs per kilogram (C kg–1). To calculate specific charge Specific charge = mass charge, you just divide the charge in C by the mass in kg. You could be asked to find the specific charge of any particle, from a | || | | | | | | | | | | | | | | | | | | | | | fundamental particle like an electron, to the nucleus of an atom or an ion. A fundamental particle is | | | | | | | || || | | | | | | | one that you can’t break Example: Calculate the specific charge of a proton. up into anything smaller. || | | | | | | || | | | | | | | | | | | | | | | A proton has a charge of +1.60 × 10–19 C and a mass of 1.67 × 10–27 kg (see p.2). So specific charge = (+1.60 × 10–19) ÷ (1.67 × 10–27) = 9.580... × 107 = 9.58 × 107 C kg–1 (to 3 s.f.) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | || In calculations, always give your answer | | | | | | | || | | | | | | | to the smallest number of significant Warm-Up Questions || figures used in the question. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | || Q1 List the particles that make up the atom and give their relative charges and relative masses. PRA Q2 Define the proton number and nucleon number. QUE CTICE STI ON Q3 Explain how the amount of carbon-14 in dead organic matter can tell scientists how old it is. S Q4 How could you calculate the specific charge of a particle? Exam Questions Q1 Describe the nuclear model of the atom. [2 marks] Q2 Write down the numbers of protons, neutrons and electrons in a neutral atom of oxygen, 168 O. [2 marks] Q3 a) State what is meant by an ‘isotope’. [1 mark] b) State the similarities and differences between the properties of two isotopes of the same element. [2 marks] Q4 An alpha particle is the nucleus of a 24 He atom. Calculate the specific charge of an alpha particle. [4 marks] “Proton no. = no. of protons” — hardly nuclear physics is it... oh wait... Physics is the science of all things great and small — on these pages you saw the small (like, really really small). That’s why it’s useful to know about things like relative charge and relative mass — ‘one point six seven times ten to the power of negative twenty-seven’ is a bit more of a mouthful than ‘one’. It all makes perfect sense. Section 1 — Particles 4 Stable and Unstable Nuclei Keeping the nucleus stable requires a lot of effort — a bit like Physics then... The Strong Nuclear Force Binds Nucleons Together There are several different forces acting on the nucleons in a nucleus. The two you already know about are electrostatic forces from the protons’ electric charges, and gravitational forces due to the masses of the particles. If you do the calculations (don’t worry, you don’t have to) you find the repulsion from the electrostatic force is much, much bigger than the gravitational attraction. If these were the only forces acting in the nucleus, the nucleons would fly apart. So there must be another attractive force that holds the nucleus together — called the strong nuclear force. (The gravitational force is so small, you can just ignore it.) The strong nuclear force is quite complicated: 1) To hold the nucleus together, it must be an attractive force that’s stronger than the electrostatic force. 2) Experiments have shown that the strong nuclear force has a very short range. It can only hold nucleons together when they’re separated by up to a few femtometres (1 fm = 1 × 10–15 m) — the size of a nucleus. 3) The strength of the strong nuclear force quickly falls beyond this distance (see the graph below). 4) Experiments also show that the strong nuclear force works equally between all nucleons. This means that the size of the force is the same whether it’s proton-proton, neutron-neutron or proton-neutron. 5) At very small separations, the strong nuclear force must be repulsive or it would crush the nucleus to a point. The Size of the Strong Nuclear Force Varies with Nucleon Separation The strong nuclear force can be plotted on a graph to show how it changes with the distance of separation between nucleons. If the electrostatic force is also plotted, you can see the relationship between these two forces. 3) The electrostatic repulsive force extends over a much larger range (indefinitely, actually). 1) The strong Repulsion nuclear force is Electrostatic force repulsive for very Nucleon small separations separation of nucleons. Strong nuclear force 3 fm || || | | | | | | | | | Attraction You might | | | | | 2) As nucleon separation increases past about 0.5 fm, || | | | | | | | | | | | hea | || nuclear fo r the strong the strong nuclear force becomes attractive. || | | | | | || rce called strong inte the It reaches a maximum attractive value and then | raction. | | | | | | | 0.5 fm || | | | | | | | | | | | | | | | | falls rapidly towards zero after about 3 fm. a Emission Happens in Very Big Nuclei nucleon number decreases by 4 1) Alpha emission only happens in very big nuclei, like uranium and radium. U 238 92 234 90 Th + 42 α 2) The nuclei of these atoms are just too massive for the strong nuclear force to keep them stable. proton number decreases by 2 3) When an alpha particle is emitted: The proton number decreases by two, and the nucleon number decreases by four. Alpha particles have a very short range — only a few cm in air. This can be seen by observing the tracks left by alpha particles in a cloud chamber. The thin line is a cosmic You could also use a Geiger counter (a device that measures the ray particle amount of ionising radiation). Bring it up close to the alpha source, then move it away slowly and observe how the count rate drops. Section 1 — Particles  5 Stable and Unstable Nuclei b – Emission Happens in Neutron-Rich Nuclei 1) Beta-minus (usually just called beta) decay is the emission of an electron from the nucleus along with an antineutrino. nucleon number 2) Beta decay happens in isotopes that are unstable due to being ‘neutron rich’ stays the same (i.e. they have too many more neutrons than protons in their nucleus). 187 3) When a nucleus ejects a beta particle, one of the Re 75 187 76 Os +–10  + e neutrons in the nucleus is changed into a proton. | | | | | | | | | | | | | | | | | | | | | Beta particles have a proton number | | | | | | | | | | | | | | | | | | much greater range increases by 1 The proton number increases by one, than alpha particles. and the nucleon number stays the same. | | | | | | | | | | | | | | | | | | | | | In beta decay, you get a tiny neutral particle called an antineutrino released. This antineutrino carries away some energy and momentum. Neutrinos Were First Hypothesised Due to Observations of Beta Decay 1) Scientists originally thought that the only particle emitted from the nucleus during beta decay was an electron. 2) However, observations showed that the energy of the particles after the beta decay was less than it was before, which didn’t fit with the principle of conservation of energy (p. 68). 3) In 1930 Wolfgang Pauli suggested another particle was being emitted too, and it carried away the missing energy. This particle had to be neutral (or charge wouldn’t be conserved in beta decay) and had to have zero or almost zero mass (as it had never been detected). 4) Other discoveries led to Pauli’s theory becoming accepted and the particle was named the neutrino. (We now know this particle was an antineutrino — p. 6). 5) The neutrino was eventually observed 25 years later, providing evidence for Pauli’s hypothesis. Warm-Up Questions Q1 What causes an electrostatic force inside the nucleus? PRA QUE CTICE Q2 What evidence suggests the existence of a strong nuclear force? STI ON S Q3 Is the strong interaction attractive or repulsive at a nucleon separation of 2 fm? Q4 Describe the changes that happen in the nucleus during alpha and beta-minus decay. Q5 What observations led to the hypothesis of the existence of the neutrino? Exam Questions Q1 The strong nuclear force binds the nucleus together. a) Explain why the force must be repulsive at very short distances. [1 mark] b) Explain why a nucleus containing two protons in unstable, but one containing two protons and two neutrons is stable. [2 marks] Q2 Radium-226 and potassium-40 are both unstable isotopes. a) Radium-226 undergoes alpha decay to radon. Complete the balanced nuclear equation for this reaction: Ra Rn + 226  88 [3 marks] b) Potassium-40 (Z = 19, A = 40) undergoes beta decay to calcium. Write a balanced nuclear equation for this reaction. [4 marks] The strong interaction’s like nuclear glue... Energy, momentum, charge and nucleon number (and several other things that you’ll find out about in this section) are conserved in every nuclear reaction. That’s why the antineutrino in beta decay has to be there. Section 1 — Particles 6 Particles and Antiparticles “I cannae do it Cap’n — their electron-antineutrino ray gun’s interfering with my antineutron positron reading...” Photons are Packets of Electromagnetic Radiation Visible light is just one type of Increasing wavelength electromagnetic radiation. The Increasing frequency electromagnetic spectrum is RADIO MICRO– INFRA– VISIBLE ULTRA– GAMMA a continuous spectrum of all WAVES WAVES RED LIGHT VIOLET X-RAYS RAYS the possible frequencies of electromagnetic radiation. c The frequency f and wavelength l are linked by f = l , where c = 3.00 × 108 ms–1 is the speed of light in a vacuum (sometimes called the speed of light in vacuo). | || | | | | | | | | | | | | | | | | | | h is the Planck | | | | | | | || | | | | | | | || Electromagnetic radiation exists as photons of energy (page 16). constant, equal to The energy of a photon depends on the frequency of the radiation: E = hf = hc 6.63 × 10–34 Js. l | | | | | | | | | | | | | | | | | | | | | Every Particle has an Antiparticle 1) Each particle has a matching antiparticle with the same mass and rest energy (more later), but with opposite charge (amongst other things). 2) For instance, an antiproton is a negatively-charged particle with the same mass as the proton, and the antineutrino is the antiparticle of the neutrino — it doesn’t do much either. Particle/Antiparticle Symbol Relative Charge Mass (kg) Rest Energy (MeV) proton p +1 1.67(3) × 10–27 938(.3) antiproton p –1 neutron n 0 1.67(5) × 10–27 939(.6) antineutron n electron e– –1 9.11 × 10–31 0.51(1) positron e+ +1 neutrino ne | || | | | | | | | | | | | | | | | | || These are actually | | | | | | | | | | || | | | | | | | | | | | 0 0 0 an electron-neutrino antineutrino ne and an electron- antineutrino (p. 12). Luckily, in the exam you’ll be given all the masses in kg and rest energies || | | | | | | | | | | | | | || | | | | | | | | | | | | | | | | | | | in MeV of each of these particles and their antiparticles. You just need 1 MeV = 1 × 106 | | | | | | | | | || | | | | | | | eV. || | | | | | || to remember that the mass and rest energy are the same for a particle There’s more on eV and its antiparticle. Neutrinos and antineutrinos are incredibly tiny (electron volts) on p. 18. | | || — you can assume they have zero mass and zero rest energy. || | | | | | | | | | | | | | | | | | | You can Create Matter and Antimatter from Energy You’ve probably heard about the equivalence of energy and mass. It all comes out of Einstein’s Special Theory of Relativity. Energy can turn into mass and mass can turn into energy if you know how. The rest energy of a particle is just the ‘energy equivalent’ of the particle’s mass, measured in MeV. You can work it all out using the formula E = mc2, but you won’t be expected to do the calculations for AS. When energy is converted into mass you get equal amounts of matter and antimatter. Fire two protons at each other at high speed and you’ll p p end up with a lot of energy at the point of impact. p p This energy might be converted into more particles. p p If an extra proton is formed then there will always be an antiproton to go with it. It’s called pair production. Section 1 — Particles  7 Particles and Antiparticles Each Particle-Antiparticle Pair is Produced from a Single Photon Energy that gets converted into matter and antimatter || || | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | is in the form of a photon (p.16). Pair production e – The particle tracks are curved | | | | | | | | | | | | | | | | || | | | | | | | | | | | | | || only happens if one photon has enough energy to because there’s usually a magnetic produce that much mass — only gamma ray photons field present in particle physics γ experiments. They curve in opposite have enough energy. It also tends to happen near + directions because of the opposite a nucleus, which helps conserve momentum. e charges on the electron and positron. You usually get electron-positron pairs produced | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | || (rather than any other pair) — because they have a relatively low mass. The minimum energy for a photon to undergo pair production is the total rest energy of the particles produced. Emin = hfmin = 2E0 The particle and antiparticle each have a rest energy of E0, so: The Opposite of Pair-Production is Annihilation  When a particle meets its antiparticle the result e+ is annihilation. All the mass of the particle and e– e + antiparticle gets converted back to energy. Antiparticles OR e–  can usually only exist for a fraction of a second before BANG this happens, so you don’t get them in ordinary matter. | | | | | | | | | | | | | | | | | | | | An annihilation is between a particle-antiparticle pair, which both have a rest The electron and | | | | | | | || | | | | | | | | | | | | | positron || | | | | | | | | | | | | energy E0. Both photons need to have a minimum energy, Emin, which when annihilate and th eir mass is added together equals at least 2E0 for energy to be converted into th e energy of a conserved in this interaction. So 2Emin = 2E0 and: Emin = hfmin = E0 pair of gamma ray photons to conserve momen tum. | | | | | | | | | | | | | | | | | | | | | | | | | | | | Example: Calculate the maximum wavelength of one of the photons produced when an electron and positron annihilate each other. For annihilation, minimum photon energy Emin = hfmin = E0. Remember f = c , so hc = E0. λ lmax ^6.63 × 10 –34h × ^3.00 × 108h So lmax = hc = = 2.432... × 10–12 = 2.43 × 10–12 m (to 3 s.f.) E0 ^0.511 ×106h × ^1.60 × 10 –19h | | | | | | | | | | || | | | | | | | | | | | | | | || | | | | | | | | | | | | | | || The Planck constant is in J, so you need | | | | | || to convert E0 from MeV to J. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | || Warm-Up Questions Q1 Describe the properties of an electron-antineutrino. PRA QUE CTICE Q2 Give one similarity and one difference between a proton and an antiproton. STI ON S Q3 What is pair production? Q4 What happens when a proton collides with an antiproton? Exam Questions Q1 Write down an equation for the reaction between a positron and an electron and state the name for this type of reaction. [2 marks] Q2 Explain what causes extra particles to be created when two particles collide. [2 marks] Q3 Give a reason why the reaction: p + p " p + p + n is not possible. [1 mark] Q4 A photon produces an electron-positron pair, each with 9.84 × 10–14 J of energy. Calculate the frequency of the photon. [2 marks] This really is Physics at its hardest grooviest... Inertial dampers are off-line Captain………oops, no — it’s just these false ears making me feel dizzy. Anyway — you’d need to carry an awful lot of antimatter to provide enough energy to run a spaceship. Plus, it’s not the easiest to store... Section 1 — Particles 8 Forces and Exchange Particles Having learnt about all those lovely particles and antiparticles, you now have the esteemed privilege of learning about yet another weirdy thing called a gauge boson. To the casual observer this might not seem entirely fair. And I have to say, I’d be with them. Forces are Caused by Particle Exchange You can’t have instantaneous action at a distance (according to Einstein, anyway). So, when two particles interact, something must happen to let one particle know that the other one’s there. That’s the idea behind exchange particles. 1) Repulsion — Each time the ball is thrown or caught the people get pushed apart. It happens because the ball carries momentum. Particle exchange also explains attraction, but you need a bit more imagination. REPULSION 2) Attraction — Each time the boomerang is thrown or caught the people ATTRACTION get pushed together. (In real life, you’d probably fall in first.) These exchange particles are called gauge bosons. The repulsion between two protons is caused by the exchange of virtual photons, which are the gauge bosons of the electromagnetic force. Gauge bosons are virtual particles — they only exist for a very short time. There are Four Fundamental Forces All forces in nature are caused by four fundamental forces — the strong nuclear force, the weak nuclear force, the electromagnetic force and gravity. Each one has its own gauge boson and these are the ones you have to learn: Type of Particle physicists never bother about gravity Gauge Boson Particles Affected Interaction because it’s so incredibly feeble compared with the other types of interaction. Gravity only virtual photon charged particles really matters when you’ve got big masses like electromagnetic stars and planets. (symbol, g) only In the strong nuclear force, pions are described weak W+, W– all types as being exchanged between nucleons. You might also see it described as gluons strong pions (p+, p–, p0) hadrons only being exchanged between quarks (p. 13). The Larger the Mass of the Gauge Boson, the Shorter the Range of the Force 1) The W bosons have a mass of about 100 times that of a proton, which gives the weak force a very short range. Creating a virtual W particle uses so much energy that it can only exist for a very short time and it can’t travel far. 2) On the other hand, the photon has zero mass, which gives you a force with infinite range. You can use Diagrams to Show What’s Going In and What’s Coming Out Particle interactions can be hard to get your head around. A neat way of solving problems is by drawing simple diagrams of particle proton proton 1 out p p 2 out interactions rather than doing calculations. virtual photon 1) Gauge bosons are represented by wiggly lines (technical term). γ 2) Other particles are represented by straight lines. proton p proton p 2 in 1 in Section 1 — Particles  9 Forces and Exchange Particles You can draw simple diagrams of loads of interactions, but you only need to learn these ones for your exams. You Need to Be Able to Draw Diagrams of these Interactions Electromagnetic Repulsion RULES FOR DRAWING PARTICLE This is the easiest of the lot. When two particles with INTERACTION DIAGRAMS: equal charges get close to each other, they repel. 1) Incoming particles start at the bottom of the diagram and move upwards. virtual virtual photon photon 2) The baryons (p.10) and leptons (p.12) can’t e– e– e+ e+ cross from one side to the other.   3) Make sure the charges on both sides balance. The W bosons carry charge from one side of the diagram to the other. e– e– e+ e+ 4) A W– particle going to the left has the same effect as a W+ particle going to the right. two electrons two positrons repelling each other repelling each other Beta-plus and Beta-minus Decay Electron Capture and Electron-proton Collisions e e+ p e n e + W W Electrons and protons are of course attracted by the electromagnetic interaction between them, but if a proton captures an electron, the n p weak interaction can make this interaction happen. decay  + decay p + e– ® n + ne n ® p + e– + ne p ® n + e+ + ne You also need to know about You get an antineutrino in b – decay and electron-proton collisions, where an electron collides with a neutrino in b + decay so that lepton a proton. The equation is just the same as electron capture number (p.12) is conserved. | | | | | | | | | | | but in the diagram a W– boson goes from the electron to the | | | | | | | | | | | | | | | | when a proton | | | | | | | | | || at proton instead of a W+ travelling the other way. You’ll see on p.14 th | | | | | | n or vice versa, it | | | | | | changes to a neutro interaction. has to be the weak || | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Warm-Up Questions | Q1 List the four fundamental forces in nature. PRA QUE CTICE Q2 Explain what a virtual particle is. STI ON S Q3 Draw a simple diagram to show the particles involved in a beta-minus decay interaction. Q4 Which gauge bosons are exchanged in weak interactions? Exam Questions Q1 Describe how the force of electromagnetic repulsion between two protons is explained by particle exchange. [2 marks] Q2 Draw a diagram to show the particle interaction when an electron and a proton collide. Label all the particles involved and state clearly which type of interaction is involved. [3 marks] I need a drink... Urrrgghhhh... eyes... glazed... brain... melting... ears... bleeding... help me... help me... help me... Section 1 — Particles 10 Classification of Particles There are loads of different types of particle apart from the ones you get in normal matter (protons, neutrons, etc.). They only appear in cosmic rays and in particle accelerators, and they often decay very quickly so they’re difficult to get a handle on. Nonetheless, you need to learn about a load of them and their properties. Stick with it — you’ll get there. Hadrons are Particles that Feel the Strong Nuclear Force (e.g. Protons and Neutrons) 1) The nucleus of an atom is made up of protons and neutrons (déjà vu). (Leptons are an example 2) Since the protons are positively charged they need a strong force to hold them of particles that can’t. together. This is called the strong nuclear force or the strong interaction See page 12.) (who said physicists lack imagination...). See page 4 for details. 3) Not all particles can feel the strong nuclear force — the ones that can are called hadrons. 4) Hadrons aren’t fundamental particles. They’re made up of smaller particles called quarks (see pages 13–15). 5) There are two types of hadrons — baryons (and anti-baryons) and mesons. They’re classified according to the number of quarks that make them up, but don’t worry about that for now. Protons and Neutrons are Baryons 1) It’s helpful to think of protons and neutrons as two versions of the same particle — the nucleon. They just have different electric charges. 2) Protons and neutrons are both baryons. 3) There are other baryons that you don’t get in normal matter — like sigmas (S) — they're short-lived and you don’t need to know about them (woohoo!). Baryon and Meson felt the strong interaction. The Proton is the Only Stable Baryon All baryons — except the proton — are unstable. This means that they decay to become other particles. The particles a baryon ends up as depends on what it started as, but it always includes a proton. Protons are the only stable baryons — they don’t decay (as far as we know). | | | | | | | | | | | | | | | | | | | | | | || | | | | | s should edict that proton | | | | | | | | | | | | | || | | | | Some theories pr ng half-life, but there’s | | | | || All baryons except protons decay to a proton. lo decay with a very it at the moment. | | | no evid en | | | | | | ce fo r | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | || Antiprotons and Antineutrons are Antibaryons The antiparticles of protons and neutrons — antiprotons and antineutrons — are antibaryons. But, if you remember from page 7, antiparticles are annihilated when they meet the corresponding particle — which means that you don’t find antibaryons in ordinary matter. The Number of Baryons in an Interaction is called the Baryon Number The baryon number is the number of baryons. (A bit like nucleon number but including unusual baryons like S too.) The proton and the neutron each have a baryon number B = +1. Antibaryons have a baryon number B = –1. Other particles (i.e. things that aren’t baryons) are given a baryon number B = 0. Baryon number is a quantum number that must be conserved in any interaction — that means it can only take on a certain set of values (so you can’t have 2.7981 baryons, or 1.991112 baryons... you get the idea). When an interaction happens, the baryon number on either side of the interaction has to be the same. You can use this fact to predict whether an interaction will happen — if the numbers don’t match, it can’t happen. The total baryon number in any particle interaction never changes. Section 1 — Particles  11 Classification of Particles Neutrons are Baryons that Decay into Protons You saw on pages 5 and 9 that beta decay involves a neutron changing into a proton. This happens when there are many more neutrons than protons in a nucleus or when a neutron is by itself, outside of a nucleus. Beta decay is caused by the weak interaction (see page 14). When a neutron decays, it forms a proton, an electron and an antineutrino: n ® p + e– + ne Electrons and antineutrinos aren’t baryons (they’re leptons, as you’ll see on the next page), so they have a baryon number B = 0. Neutrons and protons are baryons, so have a baryon number B = 1. This means that the baryon numbers on both sides are equal (to 1), so the interaction can happen. The Mesons You Need to Know About are Pions and Kaons The second type of hadron you need to know about is the meson. 1) All mesons are unstable and have baryon number B = 0 (because they’re not baryons). 2) Pions (p-mesons) are the lightest mesons. You get three versions with different electric charges — p+, p0 and p–. You get loads of pions in high-energy particle collisions like those studied at the CERN particle accelerator. 3) Kaons (K-mesons) are heavier and more unstable than pions. You get different ones like K+ and K0. Kaons have a very short lifetime and decay into pions. 4) Pions and kaons were discovered in cosmic rays — cosmic ray showers are a source of both particles. You can observe the tracks of these particles with a cloud chamber (see p.4). 5) Mesons interact with baryons via the strong force. | || | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | || – 0 Pion interactions swap protons with