Standard Model of Particle Physics
Quantum and Nuclear

Particles and antiparticles

Lesson for 16-19

It is important to avoid turning this entire topic into ‘stamp collecting’. The underlying themes to develop here are that discoveries in nuclear physics, accelerating during the middle of the twentieth century, resulted in a need to classify the particles discovered. The key to this classification was the application of conservation laws, some of quantities already well established (charge, baryon number), some modified from earlier versions (mass/energy) and some new (lepton number) or even bizarre (strangeness is the one met here, but there are also parity, isospin and hypercharge). The other aspects developed are: antiparticles, the explanation of particle interactions in terms of exchange particles (vector bosons), and the development of the standard model of three generations of quarks and leptons to explain and simplify the 'particle zoo.'

    Up next

    Preparation for particle physics topic

    Electron
    Quantum and Nuclear

    Episode 532: Preparation for particle physics topic

    Teaching Guidance for 16-19

    The first topic makes use of activities based on card sorting and arranging. The baryon, meson and lepton cards suggested here have been constructed for this project, but other excellent examples have been published, and it is well worth your considering the following:

    • A resource for particle physics teaching in schools, Physics Education, March 2003, 38, p 107 with sets of online resources
    • Playing with Particles – a teaching approach for A-level (post-16) particle physics, School Science Review, December 2002, 84 (307), pp 118-123

    Main aims of this topic

    Particles and antiparticles


    Students will:

    • use the terms baryon, meson, hadron and lepton
    • know that, for each particle, there exists an antiparticle
    • apply conservation rules to particle interactions, including particle annihilation and creation
    • know that interactions between fundamental particles (quarks and leptons) are due to the exchange of other particles (vector bosons), and that these are (virtual) photons for the electromagnetic interaction and W+, W- and Z0 particles for the weak interaction
    • construct and interpret Feynman diagrams showing interactions

    Prior knowledge

    Students should know about the constituent particles of the atom (protons, neutrons, electrons). They should be familiar with the ideas of conservation of mass, energy and electric charge.

    Where this leads

    The first topic deals with the fundamental particles that students have already met, and how their number proliferated in the second half of the twentieth century. Classification of the different sorts of fundamental particles then leads to use of conserved quantities (some rather bizarre) to establish rules for particle reactions.

    Students will learn that particles can be classified as hadrons – baryons and mesons – and leptons, each with its anti-particle, and they should know that interactions between these particles can be described in terms of transfer of other particles known as vector bosons.

    Once the ground rules for particle interactions have been established, students can go on to learn that there is a finer level of structure to mesons and baryons.

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    The particle zoo

    Electron
    Quantum and Nuclear

    Episode 533: The particle zoo

    Lesson for 16-19

    Protons, neutrons and electrons are familiar particles of matter. However, students are likely to have heard of other particles, and this episode introduces some of these.

    Lesson Summary

    • Discussion: Establishing prior knowledge (15 minutes)
    • Discussion: Conservation of charge and mass (20 minutes)
    • Discussion: Units of mass (10 minutes)
    • Student activity: Classification of hadrons (30 minutes)
    • Student activity: Research task (30 minutes)

    Discussion: Establishing prior knowledge

    Brainstorm to review prior knowledge. What’s in an atom, and how do we know?

    Establish with the students that the atom contains:

    • electrons (discovered by J J Thomson in 1897, Cavendish Lab, Cambridge, though he called them negative corpuscles, the name electron was coined by G Johnstone Stoney in 1891)
    • nuclei (Rutherford, Geiger and Marsden, 1911)
    • it was soon realised that nuclei contained multiples of the nuclei of hydrogen atoms (i.e. protons; Rutherford suggested the name proton in 1920)
    • that the simple picture was completed with Chadwick’s discovery of the neutron (predicted by Rutherford) in 1932.

    At this point, you may find it useful to ask how students think how a neutral particle such as a neutron may be detected. You can tell them that sub atomic particle detection in 1932 relied on ionisation (as in a GM tube, or in a photographic film), and that this only detects charged particles. They should realise that the neutron must do something to some other matter that then produces some ionising radiation. (For Chadwick, the ionising radiation consisted of protons emitted from paraffin wax when neutrons hit the nuclei of hydrogen atoms. The neutrons came from beryllium that had been bombarded with alpha particles. (J Chadwick, The Existence of a Neuron, Proceedings Royal Society of London, 1932)

    Discussion: Conservation of charge and mass

    Use alpha and beta decay to show conservation of charge and baryon number (see below).

    Use the equations for one example of each, e.g.:

    22086Rn  →  21684Po + 42He

    146C  →  147N + 0-1e

    To show conservation rules in action: the fact that the bottom numbers add to give the same total each side shows conservation of charge, while the fact that the top numbers do likewise shows that the number of nucleons (neutrons and protons) is also conserved. Introduce the term baryon (heavy particle) for these two particles, so that these processes also conserve baryon number. It is worthwhile giving each student an example to do, as this is confidence building, and it is a simple skill that is often examined.

    Discussion: Units of mass

    It may help your students, before embarking on a discussion of the various families of particles, if they have an idea of the different units used for mass. All those powers of 10 are very inconvenient; hence, it is easier to work in energy units, particularly the MeV (mega electron volt).

    Although it is useful to have met E = m × c 2 , this is not essential. All that is needed here is that students appreciate that mass and energy can be inter-converted in nuclear reactions (such as fission and fusion, which students should be familiar with), and that the energy that would be released if the entire mass of a particle were transferred into energy is used as a measure of its mass in particle physics. Rather than define an electron-volt in terms of charge and pd, you may prefer to state that it is a convenient atomic size energy unit where 1 MeV = 1.6 × 10-13 J equivalent to 1.783 × 10-30 kg. It is useful to have a poster in your lab/ teaching room with different mass units on it. Students who have met the equation can see that there is a c 2 involved in the inter-conversion.

    Episode 533-1: Mass units for particle physics (Word, 26 KB)


    Student activity: Classification of hadrons

    Hadrons

    Hadrons is a collective term for both mesons and baryons ; mesons are less massive than baryons.

    This activity is a card-sorting exercise. Helpfully, this slows down the pace compared with teacher exposition or question and answer. Introduce the activity by explaining that, following the discovery of the neutron, many other particles were discovered, including some strange ones: these seemed to be created in pairs, encouraging the physicist Murray Gell-Mann to allocate strangeness numbers to some of these particles. In these reactions, strangeness was conserved.

    This is a kinaesthetic exercise using cards for a collection of hadrons. It is best to print up several sets of the two hadron card sheets, on card rather than paper. There is a similar sheet of lepton cards – they can be added to or simplified as you wish. It is best to use a different colour for the lepton cards. You may consider laminating them.

    For the first exercise, use the first sheet of hadron cards (omitting some mesons and all anti-baryons), cut into individual cards.

    Ask your students to sort particles by mass and to note the charge and baryon number. Mesons are those hadrons, mostly of lower mass, which have baryon number of 0.

    Later, the cards can be used, together with genuine particle reactions, to check on conserved quantities.

    Episode 533-2: Hadron cards (Word, 146 KB)


    Episode 533-3: Lepton cards (Word, 44 KB)


    Student activity: Research task

    Conclude this episode with some questions for students to research, leading to the next episode:

    • What is a positron?
    • Who suggested it must exist?
    • Who discovered it?
    • What is a muon?
    • When was it discovered?
    • Who said, Who ordered that?
    • What is a neutrino?
    • Who suggested it must exist?
    • Who discovered it?

    Episode 533-4: Positron, muon, neutrino (Word, 34 KB)


    Up next

    Antiparticles and the lepton family

    Electron
    Quantum and Nuclear

    Episode 534: Antiparticles and the lepton family

    Lesson for 16-19

    The purpose of this episode is to introduce the lepton family, and also to bring in the idea of anti-particles, which annihilate when they meet particles.

    If you have had students research the questions at the end of episode 533, time must now be allowed for them to feed back what they have found. You may need to supplement their finding with some of the details mentioned below.

    Lesson Summary

    • Student presentations: Information about leptons (15 minutes)
    • Discussion: PET scans (10 minutes)
    • Student activity: Examining particle tracks (10 minutes)
    • Discussion: Summarising the main points (5 minutes)
    • Student activities: Readings (20 minutes)

    Student presentations: Information about leptons

    Your students should present their findings in response to the questions posed at the end of

    episode 533


    Important points to establish:

    Positron, e+

    Dirac’s theoretical prediction of the antiparticle to the electron is too difficult to elaborate here, but Carl Anderson’s discovery of it in cosmic rays – he discovered the muon a few years later in the same way – is worth describing.

    The original cloud chamber track of Carl Anderson’s positron is shown in this famous photograph (Projecting this using a digital projector makes for more dramatic discussion.):

    Episode 534-1: Anderson’s positron photograph (Word, 63 KB)


    The particle is moving up the photograph. It has been slowed down by passing through the lead plate across the centre, and the curvature of the path is caused by a magnetic field. At this stage, it’s enough to say that the particle is curved more when it is slower because the particle spends longer in the magnetic field.

    Anderson could deduce, from the direction and magnitude of the curvature and the length of the particle track, that the particle was positive and had a mass not more than twice that of an electron.

    The positron was the first anti-particle discovered: since then it has been found that every particle has its antiparticle.

    Muon, μ

    The muon quote (Who ordered that?) was from physicist Isadore Rabi – it’s whimsically supposed to be the sort of thing you say in a Chinese restaurant when you get some strange dish you don’t recognize. The muon was a problem because it had exactly the mass predicted for Yukawa’s meson, but it didn’t undergo strong nuclear interactions at all, which the meson had to do (that was its job, after all!). It turned out to be a heavy type of electron. Like the electron, it has an anti-particle (the anti-muon, μ+ ) which is positively charged.

    Neutrinos, ν

    The problems with beta decay are worth describing in detail. Reactions such as carbon-14  →  nitrogen-14  +  β - were expected to produce beta particles with identical kinetic energy: this is what happens in alpha decay. This does not happen in beta decay; sometimes a lot of the energy seems to be missing.

    In 1930 Wolfgang Pauli suggested, in a famous letter to fellow physicists starting Dear Radioactive Ladies and Gentlemen, in which he wrote Ive done something terrible: I have predicted an undetectable particle’. He suggested that the lost energy was carried away by a new particle, which must be chargeless and have virtually no mass. Enrico Fermi developed the theory of this new particle, which he called a neutrino, but it wasn’t until 1951 that Reines and Cowan discovered it at the Savannah River nuclear reactor. Current (2005) thought is that the mass of the electron neutrino is in the range

    0 < mass < 3 eVc 2

    (compare with the electron, me = 0.511 MeVc 2 ).

    Like the electron and the muon, neutrinos have antiparticles. Furthermore, there are different neutrinos associated with the electron and the muon.

    Because these light particles do not experience the strong force of hadrons, they form a different category of particle and given the name leptons .

    There are now a total of 12 leptons: the electron, the muon, and a super-heavy version called the tau (t); a neutrino for each of these three; and six antiparticles for these six particles. The six leptons each have a lepton number of +1, while the six anti-leptons each have a lepton number of -1.

    Discussion: PET scans

    Take a look at PET scans and how they are made.

    When a positron meets an electron, they annihilate to produce a pair of gamma ray photons, each of energy 511 keV. (Both the electron and the positron have a mass of 511 keVc 2 .) This principle is used in medicine, in Positron-Electron Tomography (PET) scans. A radiochemical emitting positrons is injected into the body. When the chemical reaches the organ of interest, positrons emitted very soon meet electrons and annihilate. The scan reveals exactly where the radiochemical is by looking for a pair of gamma photons travelling in opposite directions.

    You may like to ask students how they think radiochemicals which emit positrons are made: they can be led to realize that the unstable nuclei lose positive charge when a positron is emitted, and so have too many protons. This suggests that you have to fire protons into the nucleus, which is one way this is actually done.

    Episode 534-2: Making PET scans (Word, 4 MB)


    Student activity: Examining particle tracks

    Examining particle tracks: This can be done as class discussion with a digital projector, as suggested for the Anderson photograph of the positron track shown above, or students can work individually or in pairs, using printed copies of the images or looking at them on computer screens. If you adopt the latter approach, give a little more time for the activity: it could be a homework activity. The questions are intended for students late in the post-16 level course, so you should concentrate on simple patterns:

    Gamma photons are not very ionising, so tend not to leave tracks in bubble chambers or cloud chambers.

    Gamma photons of enough energy (2  ×  511 keV) can produce an electron-positron pair (provided they are near nuclei at the time: don’t emphasize this point.)

    Particles and anti-particles – protons and antiprotons in this case – can annihilate with production of radiation, or new mass in the case of big particles.

    In a magnetic field, charged particles follow curved paths, with opposite charges curving in opposite directions.

    Episode 519-3: Particle tracks (Word, 612 KB)


    Episode 534-3: Annihilation and pair production: Bubble chamber pictures (Word, 5 MB)


    Discussion: Summarising the main points

    Establish the main points of this episode:

    The electron is one of a small family of fundamental particles called leptons, which are quite different from the nuclear particles (hadrons) of

    episode 533


    Particle have anti-particles, with opposite value of charge, lepton number and (by implication) baryon number and strangeness as well).

    Student activities: Readings

    Here are a number of supplementary readings that you may care to use to broaden students’ background knowledge:

    Episode 534-5: The discovery of beta decay (Word, 35 KB)


    Episode 534-6: Three poems about particles (Word, 29 KB)


    Episode 519-3: Particle tracks (Word, 613 KB)


    Up next

    Particle reactions

    Electron
    Quantum and Nuclear

    Episode 535: Particle reactions

    Lesson for 16-19

    This episode considers both hadrons and leptons in particle reactions. Students must take account of both conservation of lepton number and conservation of baryon number.

    Lesson Summary

    • Student activity: Applying conservation rules (20 minutes)
    • Discussion: Identifying conservation rules (10 minutes)
    • Student questions: Questions on conservation rules (30 minutes)

    Student activity: Applying conservation rules

    Students should first check on the conservation of (electric) charge, baryon number, lepton number and strangeness in real reactions. They should also note that the mass/energy of products should be less/equal to the mass/energy of reactants.

    Use the first sheet of hadron cards from the previous episode and the four leptons from the lepton cards document to decide which particle is needed to complete several reactions.

    Episode 535-1: Applying conservation of baryon and lepton number (Word, 27 KB)


    You should expect some ambiguity as to which neutrino or antineutrino is involved: after all, this ambiguity was not resolved until recently. Ask students what they would expect, from symmetry, in each case.

    Now add the second sheet of cards from the hadron cards document, containing all the anti-baryons and some more mesons.

    Episode 535-2: Particle card student activities (Word, 28 KB)


    A quick sort of all cards should reveal that all baryons and leptons have their anti-particles, all with obvious names except electron/positron. Tell students that all mesons – those with baryon number and lepton number of zero – have antiparticles, but that some are their own anti-particles; they can then sort out which is which.

    Students are now able to check whether reactions can proceed according to the conservation rules met so far.

    Discussion: Identifying conservation rules

    Invite students to sum up what they now know about particles and particle reactions. Look for the following points:

    • Baryon number is always conserved
    • (Electric) charge is always conserved
    • Lepton number is always conserved
    • Mass on the left hand side of the equation must be bigger than the mass on the right hand side
    • Strangeness may be conserved, but not always. (In weak interactions it can change by 1)

    Student questions: Questions on conservation rules

    Here are some suggestions for questions that could be given as student exercises at this point.

    Episode 535-3: Things that don’t change (Word, 33 KB)


    Questions about creation and annihilation (but note that this question uses Δ E =  Δ m × c 2 ; however, you may find that more mathematical students will accept mass values quoted as e.g. 939.6 MeVc 2 once they have done a calculation of this sort.

    Episode 535-4: Creation and annihilation (Word, 28 KB)


    Questions about creation from annihilation. (To reduce the demand, you may wish to delete all the text from Exotic forms of matter can occur fleetingly … and dropping questions 7 to 11.)

    Episode 535-5: Creation from annihilation (Word, 32 KB)


    Up next

    Vector bosons and Feynman diagrams

    Electron
    Quantum and Nuclear

    Episode 536: Vector bosons and Feynman diagrams

    Lesson for 16-19

    You need to check your own specification here for details of what students will need to do in examinations, and to look at past papers: although Feynman diagrams give clarity to particle interactions, they are not required by all specifications.

    Lesson Summary

    • Demonstration: Exchange particles (5 minutes)
    • Discussion: Interactions of different types (15 minutes)
    • Demonstration: Model Feynman diagrams (15 minutes)
    • Discussion: Rules for Feynman diagrams (10 minutes)
    • Student activity: Constructing Feynman diagrams (20 minutes)

    Demonstration: Exchange particles

    Yukawa’s theory of an exchange particle to explain repulsive and attractive forces in nuclei is worth demonstrating with two students and a football or other large object.

    If two students throw (gently) a heavy object such as a schoolbag or football to each other, each will report feeling an outwards force both on throwing and on catching (Why? Conservation of momentum). If the rules are changed so that, instead of throwing, each student pulls the object from the other’s hands in turn, then each will report feeling an inwards force both on gaining and on losing the particle.

    Discussion: Interactions of different types

    This crude model in the demonstration above will illustrate the idea of an exchange particle originated by Yukawa, who suggested that a nuclear exchange particle (it turned out to be the pion) could explain the strong interaction between protons and neutrons. In the last episode, it will be clear that a similar fundamental exchange works at a level that is more fundamental than mesons and baryons.

    The electromagnetic interaction, which consists of just the well-known attractions and repulsions of static electricity (pre-16 level), is a different interaction, much weaker than the strong interaction. Here the exchange particle is the photon.

    The weak interactions, which are harder to classify, and are similar in strength to the electromagnetic interactions, are associated with changes in the nature of particles.

    Demonstration: Model Feynman diagrams

    Feynman diagrams can be introduced via a physical model that can be twisted to show different interactions. The key aspects – direction of time, transfer of the force-carrying boson, difference between particles and anti-particles – can be quickly illustrated for an electromagnetic interaction.

    As an example of these points (including the last), you may wish to use a simple physical model. It is quick and easy to use cheap coat hangers linked by their hooks, with triangles of card attached midway across the shoulder of each. The supporting shoulders of the coat hangers are the interacting particles, while the interlocked hooks constitute the vector boson. With one twist each time, it is possible to go from electron-electron interaction to electron positron interaction to positron-positron interaction to electron-positron annihilation.

    For these electromagnetic interactions, the particle exchanged is a photon. For the weak interaction, there are three particles, depending on the changes in charge taking place. If you deal with quark interactions later, the exchange particle is the gluon.

    Some teacher notes:

    Episode 536-1: Feynman diagrams (Word, 53 KB)


    Episode 536-2: Coat-hanger Feynman diagrams (Word, 37 KB)


    Discussion: Rules for Feynman diagrams

    If your specification requires Feynman diagrams, you will need to emphasise the rules for drawing them. These are not consistent from source to source! In this episode, the following conventions are followed.

    Time goes vertically up the diagram (many sources have time horizontal).

    Side-to-side displacement in the diagrams has no meaning other than to show separate particles. If two paths are heading outwards, it does not imply that particles are repelling each other.

    Particles are shown by normal arrow-heads, while anti-particles are shown by reversed arrow-heads (remember that the direction of time is upwards), so a collision between a proton and an anti-proton can be represented as:

    From any vertex, such as the collision point of the proton and anti-proton, a boson can be drawn. This can be a photon (wavy line), a weak interaction boson (a dotted line).

    A Feynman diagram – certainly the simple ones in this episode – can be pivoted about any of the vertices to produce another valid diagram.

    Student activity: Constructing Feynman diagrams

    Students are supplied with cards from which they can construct Feynman diagrams. They use the different left-hand sides of the diagrams with the single vector boson and the appropriate right-hand side to produce the different possible weak interactions, and then to label the boson with W+, W- or Z0 as appropriate.

    Episode 536-3: Feynman diagram student activities (Word, 49 KB)


    Episode 536-4: Feynman weak interaction cards (Word, 32 KB)


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