Senior 6 practice book · Unit 6 of 10

Nature of Particles and their Interactions

50 questions that complete the Senior 6 quiz for this unit: 24 core and 26 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

A particle with zero charge, such as the neutron, cannot contain any charged parts.The neutron (udd) is built from charged quarks whose charges (+2/3, −1/3, −1/3) add up to zero.
In beta-minus decay the electron was already sitting inside the nucleus and simply escapes.The electron is created at the moment of decay, when a down quark changes into an up quark through the weak interaction.
Antimatter has negative mass or is "anti-gravity" material.Antiparticles have exactly the same mass as their particles; only quantities such as charge, baryon number and lepton number are reversed.
Neutral particles have no antiparticle.The neutron has an antineutron (ūd̄d̄), with opposite baryon number; only a few particles, such as the photon, are their own antiparticles.
In annihilation, matter is destroyed and energy is lost.Mass is converted into an equal amount of energy (E = mc²) carried by photons; total energy, momentum and charge are all conserved.

What this unit covers

Topics marked new are not tested much in the quiz, so this book gives them extra questions.

Elementary particles and the Standard Model: quarks, leptons and bosons in three generations
Quark composition and charge of baryons and mesons
Antiparticles and antimatter
Annihilation and pair production (E = mc², photon energy)
The four fundamental interactions: relative strength and range
Exchange particles: photon, gluon, W and Z bosons, graviton
Feynman diagrams: drawing and reading particle interactions
Conservation of charge, baryon number and lepton number in reactions
Beta decay at the quark level and the neutrino
The six quark flavours, strange particles and strangeness
Particle detectors: cloud and bubble chambers, tracks in a magnetic field (r = p/Bq)
Particle accelerators: linear accelerator, cyclotron and synchrotron
Rest energy and particle masses in MeV/c²; energy released in decays
The Higgs boson and the limits of the Standard Model

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 26 harder ones are marked ★ Challenge.

1True or false
At every vertex of a Feynman diagram, electric charge must be conserved.
Show answer
Answer: True
Each vertex is a single interaction point, so the charge going in equals the charge coming out, including the charge of any W boson.
Common mistakeLearners sometimes check conservation only for the whole reaction; it must also hold at each vertex separately.
2True or false · ★ Challenge
A photon is its own antiparticle.
Show answer
Answer: True
The photon has zero charge, zero baryon number and zero lepton number, so reversing them changes nothing; the photon and the antiphoton are the same particle.
Common mistakeLearners may think every particle needs a different antiparticle; particles with all such numbers equal to zero, like the photon and π⁰, are their own antiparticles.
3True or false
A neutron leaves a clear track in a cloud chamber because it is a heavy particle.
Show answer
Answer: False
Tracks come from ionisation, which needs a charge; the neutral neutron ionises almost nothing, so it leaves no track.
Common mistakeLearners link heavy with visible; it is charge, not mass, that makes a particle ionise and show a track.
4True or false · ★ Challenge
Strangeness is conserved in strong interactions but can change in weak interactions.
Show answer
Answer: True
Strong interactions cannot change quark flavour, so S is conserved; the weak interaction can change s → u, so S can change by 1.
Common mistakeLearners often treat strangeness like charge, which is always conserved; strangeness is broken by the weak interaction.
5True or false
The graviton, the proposed exchange particle of gravity, has already been detected in experiments.
Show answer
Answer: False
The graviton is predicted but has never been detected; gravity is far too weak for single gravitons to be observed.
Common mistakeLearners may mix up gravitons with gravitational waves; gravitational waves were detected in 2015, but no individual graviton has been.
6True or false · ★ Challenge
Since a proton inside some nuclei can change into a neutron by β⁺ decay, an isolated proton in empty space can also decay into a neutron.
Show answer
Answer: False
A neutron is heavier than a proton, so an isolated proton has too little energy to become a neutron; inside a nucleus the extra energy comes from the change in nuclear binding energy.
Common mistakeLearners assume a process that happens in a nucleus can happen anywhere; energy conservation forbids it for a lone proton.
7True or false
There are three generations of leptons, each made of a charged lepton and its own type of neutrino.
Show answer
Answer: True
The three pairs are (e⁻, ν_e), (μ⁻, ν_μ) and (τ⁻, ν_τ).
Common mistakeSome learners think there is only one neutrino; each charged lepton has its own neutrino flavour.
8Multiple choice · ★ Challenge
In a collider the reaction e⁻ + e⁺ → μ⁻ + μ⁺ is observed. A learner says it breaks lepton number because electrons turn into muons. Which evaluation is correct?
1. AForbidden: lepton number changes from 2 to 0
2. BForbidden: electrons can never become muons
3. CAllowed only if a photon is also produced
4. DAllowed: electron number 0 → 0 and muon number 0 → 0
Show answer
Answer: D. Allowed: electron number 0 → 0 and muon number 0 → 0
Before: e⁻ (+1) + e⁺ (−1) gives electron number 0. After: μ⁻ (+1) + μ⁺ (−1) gives muon number 0. Each lepton family is balanced.
Common mistakeChoosing "changes from 2 to 0" comes from giving the positron +1; antileptons have lepton number −1.
9Multiple choice · ★ Challenge
In a bubble chamber inside a magnetic field, two tracks start at the same point and curve in opposite directions with equal radii. No track leads to that point. What most likely happened?
1. AA neutron split into two protons
2. BAn electron changed into a positron
3. CTwo electrons were knocked out of the same atom at once
4. DA photon produced an electron–positron pair
Show answer
Answer: D. A photon produced an electron–positron pair
A neutral particle leaves no track, opposite curvature means opposite charges, and equal radii mean equal momenta: this is pair production by a gamma photon.
Common mistakeChoosing "two electrons knocked out" ignores the curvature: two electrons have the same charge and would curve the same way.
10True or false
A gamma photon of energy 0.80 MeV can produce an electron–positron pair.
Show answer
Answer: False
The pair needs at least 2 × 0.511 = 1.022 MeV, so a 0.80 MeV photon has too little energy.
Common mistakeComparing 0.80 MeV with the rest energy of one electron (0.511 MeV) forgets that two particles must be made.
11Fill in the blank · ★ Challenge
In the decay τ⁻ → π⁻ + X, particle X has zero charge and is needed to keep the tau-lepton number at +1. X is a tau ______.
Show answer
Answer: neutrino
Charge: −1 = −1 + 0. The τ⁻ has tau-lepton number +1 and the pion 0, so X must be a tau neutrino ν_τ (L_τ = +1).
Common mistakeWriting "antineutrino" gives tau-lepton number −1, so the total would change from +1 to −1.
12Fill in the blank
The weak interaction acts only over distances of about ______ m, about a thousandth of the size of a proton.
Show answer
Answer: 10⁻¹⁸
A proton is about 10⁻¹⁵ m across, and the weak interaction reaches only about 10⁻¹⁸ m.
Common mistakeGiving 10⁻¹⁵ m confuses the range of the weak interaction with that of the strong nuclear force.
13Multiple choice · ★ Challenge
A strange quark has strangeness −1. The K⁺ meson is made of an up quark and an anti-strange quark (us̄). What is its strangeness?
1. A−1
2. B0
3. C+1
4. D+1/3
Show answer
Answer: C. +1
An antiquark has the opposite strangeness to its quark, so s̄ has +1; the up quark has 0, so S = +1.
Common mistakeChoosing −1 forgets that the K⁺ contains an anti-strange quark, not a strange quark.
14Multiple choice
Which list contains all six quark flavours?
1. Aup, down, strange, charm, bottom, top
2. Bup, down, strange, charm, top, gluon
3. Cup, down, electron, muon, tau, neutrino
4. Dup, down, strange, charm, bottom, Higgs
Show answer
Answer: A. up, down, strange, charm, bottom, top
The six flavours come in three generations: (up, down), (charm, strange), (top, bottom).
Common mistakeLists with the gluon or Higgs mix quarks with bosons; those carry forces or give mass and are not quarks.
15Fill in the blank · ★ Challenge
A charged pion has a rest energy of 140 MeV and an electron 0.511 MeV. So the pion mass is about ______ times the electron mass.
Show answer
Answer: 274
Mass ratio = rest energy ratio = 140 ÷ 0.511 ≈ 274.
Common mistakeSome learners convert both values to kilograms first; this is not needed, because the ratio of rest energies equals the ratio of masses.
16Multiple choice
Which TWO interactions have an infinite range?
1. AStrong nuclear and weak nuclear forces
2. BElectromagnetic and weak
3. CGravitational and strong
4. DGravitational and electromagnetic
Show answer
Answer: D. Gravitational and electromagnetic
Gravity and electromagnetism weaken as 1/r² but never become exactly zero. The strong force acts over about 10⁻¹⁵ m and the weak force over about 10⁻¹⁸ m.
Common mistakeChoosing "gravitational and strong" links "strong" with "long reach"; in fact the strong force is the strongest but has a very short range.
17Multiple choice · ★ Challenge
Gravity is by far the weakest interaction, yet it controls the motion of planets and galaxies. Why?
1. AIt becomes stronger than the strong force when the masses are large
2. BThe strong and weak forces cancel each other between planets
3. CIt always attracts and has infinite range, while large bodies are electrically neutral
4. DPlanets carry large net charges, and gravity cancels their effect
Show answer
Answer: C. It always attracts and has infinite range, while large bodies are electrically neutral
Electric forces cancel because large bodies contain equal positive and negative charge; the strong and weak forces act only inside nuclei. Gravity only adds up, so it wins on large scales.
Common mistakeChoosing "becomes stronger than the strong force" mixes up total effect with strength: gravity is still weak per particle, but its effects all add up while the others cancel or do not reach.
18Multiple choice
Which pair of exchange particles are both massless?
1. APhoton and Z boson
2. BPhoton and gluon
3. CW boson and gluon
4. DZ boson and W boson
Show answer
Answer: B. Photon and gluon
The photon (electromagnetic) and the gluon (strong) have no mass; the W and Z bosons are very heavy, about 86 and 97 times the mass of a proton.
Common mistakeChoosing "photon and Z boson" is tempting because both are neutral, but being neutral is not the same as being massless: the Z is very heavy.
19Multiple choice · ★ Challenge
A Feynman diagram shows two electron lines. Each electron line has one vertex, and the two vertices are joined by a wavy line labelled γ. What does the diagram describe?
1. ATwo electrons repel by exchanging a virtual photon
2. BTwo electrons repel by exchanging a W⁻ boson
3. CAn electron and a positron annihilate into a photon
4. DTwo electrons attract by exchanging a gluon
Show answer
Answer: A. Two electrons repel by exchanging a virtual photon
γ is the photon, the carrier of the electromagnetic force; two electrons, both negative, repel.
Common mistakeChoosing "annihilate" mixes this up with an electron–positron annihilation diagram, where the two incoming lines meet at one vertex and no electrons leave.
20Fill in the blank
The heaviest quark, with a mass about 180 times that of a proton, is the ______ quark.
Show answer
Answer: top
The top quark (about 173 GeV/c²) is the heaviest known elementary particle; it was discovered in 1995.
Common mistakeLearners may answer "bottom" because bottom and top come as a pair; the bottom quark is much lighter, about 4.2 GeV/c².
21Fill in the blank · ★ Challenge
In a Feynman diagram where time runs upwards, the line of an antiparticle is drawn with its arrow pointing ______ in time.
Show answer
Answer: backwards (downwards)
By convention an antiparticle moving forward in time is drawn with its arrow pointing against the time direction.
Common mistakeLearners often think the arrow shows the direction of travel; for antiparticles the arrow is drawn reversed.
22Multiple choice
Which property is the SAME for a neutron and an antineutron?
1. ATheir mass
2. BTheir baryon number
3. CTheir quark content
4. DThe charge of their up (or anti-up) quark
Show answer
Answer: A. Their mass
A particle and its antiparticle always have equal mass. The antineutron has baryon number −1 and contains ūd̄d̄ instead of udd.
Common mistakeChoosing baryon number is tempting because both are neutral, but antiparticles reverse baryon number as well as charge: n has B = +1, n̄ has B = −1.
23Short answer · ★ Challenge
Quarks have never been seen on their own. Explain why pulling two quarks apart does not give two free quarks.
Show answer
Model answer: The strong force between quarks does not weaken as they separate, so the energy stored between them keeps growing. Before they come apart, this energy is enough to create a new quark–antiquark pair, so the result is new hadrons (for example mesons), never a single free quark. This is called quark confinement.
Common mistakeLearners often picture the strong force as weakening with distance like gravity; between quarks it stays strong, which is why quarks are always confined in hadrons.
24Multiple choice
In a Feynman diagram, what does a wavy line usually represent?
1. AAn exchange particle such as a photon
2. BThe exact path of a particle through space
3. CA neutrino moving at nearly the speed of light
4. DThe time axis of the diagram
Show answer
Answer: A. An exchange particle such as a photon
Straight lines with arrows show matter particles; wavy lines show exchange (gauge) bosons such as the photon or W and Z bosons.
Common mistakeChoosing "exact path through space" treats a Feynman diagram like a photograph of tracks; it only shows which particles meet at each vertex, not their real paths.
25Multiple choice · ★ Challenge
A proton crosses 50 gaps in a linear accelerator and gains energy from a 200 kV potential difference at each gap. What is its final kinetic energy?
1. A0.20 MeV
2. B5.0 MeV
3. C250 MeV
4. D10.0 MeV
Show answer
Answer: D. 10.0 MeV
Energy per gap = eV = 0.20 MeV for a proton; total = 50 × 0.20 = 10 MeV.
Common mistakeChoosing 0.20 MeV counts only one gap; the energy is gained at every gap, so it is multiplied by 50.
26Short answer · ★ Challenge
The Standard Model is very successful, but physicists know it is not complete. State two observations or questions that it cannot yet explain.
Show answer
Model answer: Any two of: gravity (no graviton in the model); dark matter (no Standard Model particle fits it); neutrinos have small masses, which the original model did not include; why the universe contains much more matter than antimatter; dark energy.
Common mistakeA common error is to list things the model does explain, such as beta decay or the quark content of hadrons.
27Fill in the blank
A circular accelerator in which the magnetic field is increased as the particles speed up, so that they stay on a ring of fixed radius, is called a ______.
Show answer
Answer: synchrotron
In a synchrotron the field and the accelerating frequency are synchronised with the rising energy; the LHC at CERN is one.
Common mistakeAnswering "cyclotron" is wrong: in a cyclotron the field is fixed and the radius of the path grows as the particle speeds up.
28True or false
The Standard Model explains all four fundamental interactions, including gravity.
Show answer
Answer: False
The Standard Model describes the strong, weak and electromagnetic interactions; gravity is described separately by general relativity.
Common mistakeLearners assume the "standard" model covers everything; joining gravity to it is still an open problem.
29Short answer · ★ Challenge
A neutrino can scatter off an electron: ν_e + e⁻ → ν_e + e⁻. Describe the Feynman diagram for this process and explain why the exchange particle cannot be a photon.
Show answer
Model answer: Two vertices: at one, the neutrino line comes in and goes out; at the other, the electron line comes in and goes out. A wavy line joins the vertices, labelled Z⁰ (a neutral weak boson; for this pair a W-exchange diagram is also possible). It cannot be a photon, because photons interact only with charged particles and the neutrino has no charge; only the weak interaction (and gravity) acts on neutrinos.
Common mistakeLearners often put a photon in every scattering diagram; a photon can only couple to charged particles, so neutrino diagrams always use W or Z bosons.
30Short answer · ★ Challenge
Two people on skates throw a heavy ball back and forth. Explain how this models a repulsive force carried by an exchange particle, and state one way in which the model fails.
Show answer
Model answer: Each throw pushes the thrower backwards and each catch pushes the catcher backwards, so the two move apart, as if they repelled: momentum is carried by the ball, like a photon between two electrons. The model fails for attractive forces (throwing a ball cannot pull people together), and real exchange particles are virtual particles that cannot be observed in flight.
Common mistakeA common error is to take the model literally; it only illustrates momentum transfer and cannot explain attraction.
31Multiple choice
In a cloud chamber, a visible track forms behind a fast charged particle because the particle:
1. AGlows as it is heated by the cold vapour
2. BIonises the vapour, and droplets condense on the ions
3. CFreezes the alcohol vapour along its path
4. DIs attracted to the cold metal base and leaves a dark mark there
Show answer
Answer: B. Ionises the vapour, and droplets condense on the ions
The vapour is supersaturated, so droplets form on the ions left along the path, making a line of mist.
Common mistakeChoosing "glows" assumes we see the particle itself; we only see droplets formed on ions it leaves behind.
32Multiple choice
The Standard Model groups the known elementary particles into three kinds. Which list gives them?
1. AProtons, neutrons and the electrons around them
2. BBaryons, mesons and photons
3. CQuarks, leptons and force-carrying bosons
4. DAtoms, nuclei and nucleons
Show answer
Answer: C. Quarks, leptons and force-carrying bosons
Quarks and leptons make up matter and bosons carry the forces; none of them is known to have smaller parts. Protons and neutrons are made of quarks.
Common mistakeChoosing protons, neutrons and electrons is tempting because they build atoms, but protons and neutrons are composite, so they are not elementary.
33Multiple choice · ★ Challenge
A neutron has a mass of 1.675 × 10⁻²⁷ kg. Using c = 3.0 × 10⁸ m/s and 1 MeV = 1.6 × 10⁻¹³ J, its rest energy is close to:
1. A1.5 × 10⁻¹⁰ MeV
2. B9.4 × 10² MeV
3. C9.4 × 10⁸ MeV
4. D3.1 × 10⁻⁶ MeV
Show answer
Answer: B. 9.4 × 10² MeV
E = mc² = 1.675 × 10⁻²⁷ × 9.0 × 10¹⁶ = 1.51 × 10⁻¹⁰ J; ÷ 1.6 × 10⁻¹³ = 942 MeV.
Common mistakeChoosing 1.5 × 10⁻¹⁰ MeV keeps the value in joules but labels it MeV; it must be divided by 1.6 × 10⁻¹³ J per MeV (dividing by 1.6 × 10⁻¹⁹ gives eV, not MeV).
34Short answer · ★ Challenge
In films, antimatter is used as fuel for spaceships. Explain why annihilation could, in principle, release more energy per kilogram than any chemical or nuclear fuel, and give one practical reason why it is not used.
Show answer
Model answer: In annihilation all of the rest mass of the particle and antiparticle becomes energy (E = mc², 9 × 10¹⁶ J per kg of total mass), while fission or fusion convert well under 1 % of the mass. But antimatter is extremely hard to make (far more energy is used to make it than it gives back) and to store, because it annihilates as soon as it touches the walls of any container.
Common mistakeA common error is to think antimatter is a source of free energy; making antimatter costs much more energy than its annihilation releases.
35Fill in the blank
The neutral kaon K⁰ contains a down quark and an anti-strange quark (ds̄). The strange quark has the same charge as the down quark, so the charge of the K⁰ is ______.
Show answer
Answer: 0 (zero)
d has −1/3 e and s̄ has +1/3 e (opposite to s, which has −1/3 e), so the total is −1/3 + 1/3 = 0.
Common mistakeAdding −1/3 twice (giving −2/3) forgets that an antiquark has the opposite charge to its quark.
36Short answer · ★ Challenge
In proton–proton collisions, strange particles such as kaons are always produced in pairs, quickly, but each one then decays slowly (lifetime about 10⁻¹⁰ s). Use the idea of strangeness to explain both observations.
Show answer
Model answer: They are made by the strong interaction, which conserves strangeness; since the protons have S = 0, a particle with S = −1 must be made with one of S = +1, so they appear in pairs. A single strange particle can only decay by changing its strangeness, which only the weak interaction can do; the weak interaction is slow, so the lifetime is long.
Common mistakeA common mistake is to think the slow decay means a weak production process; production is strong and fast, and only the decay is weak.
37Multiple choice
The mass of a proton is often written as 938 MeV/c². This means that:
1. AIt moves with 938 MeV of kinetic energy
2. BIt needs 938 MeV to break it into quarks
3. CIts rest energy mc² is 938 MeV
4. DIts weight on Earth is 938 MeV
Show answer
Answer: C. Its rest energy mc² is 938 MeV
Mass in MeV/c² is a mass unit: multiplying by c² gives the rest energy in MeV.
Common mistakeChoosing "kinetic energy" confuses rest energy (present even at rest) with energy of motion.
38Multiple choice · ★ Challenge
In a cloud chamber photo, an electron and a positron appear together, made by an unseen gamma ray of 2.6 MeV. Taking the electron rest energy as 0.511 MeV, how much kinetic energy do the two new particles have between them?
1. A2.09 MeV
2. B2.60 MeV
3. C1.02 MeV
4. D1.58 MeV
Show answer
Answer: D. 1.58 MeV
Energy needed to make the pair = 2 × 0.511 = 1.022 MeV; kinetic energy = 2.6 − 1.022 = 1.58 MeV.
Common mistakeChoosing 2.09 MeV comes from subtracting the rest energy of only one particle; both the electron and the positron must be created.
39Multiple choice
The Higgs boson, discovered at CERN in 2012, is linked to which property of elementary particles?
1. AHow they gain their mass
2. BTheir electric charge
3. CThe colour charge of quarks
4. DWhy gravity is so weak
Show answer
Answer: A. How they gain their mass
The Higgs field gives mass to the W and Z bosons, quarks and charged leptons; the Higgs boson is the particle of this field.
Common mistakeChoosing "why gravity is weak" links mass with gravity; the Higgs mechanism explains particle masses but does not explain gravity.
40Short answer · ★ Challenge
A learner says: "The muon is just a heavy electron, so it must be made of an electron plus something else." Use the idea of lepton generations to judge this claim.
Show answer
Model answer: The claim is wrong. The muon is an elementary lepton of the second generation: it has the same charge as the electron but about 207 times its mass. It can decay into an electron and neutrinos, but these are created in the decay; they are not parts hidden inside the muon.
Common mistakeLearners often think that if a particle decays into others, those others were inside it; in particle decays the products are created from the energy available.
41Multiple choice
In every reaction, the number of quarks minus the number of antiquarks, divided by 3, stays the same. This rule is the conservation of:
1. ALepton number
2. BElectric charge
3. CBaryon number
4. DStrangeness
Show answer
Answer: C. Baryon number
Each quark has baryon number +1/3 and each antiquark −1/3, so (quarks − antiquarks)/3 is the total baryon number.
Common mistakeChoosing strangeness is tempting because it also counts quarks, but it counts only strange quarks and is not conserved in weak interactions.
42Multiple choice · ★ Challenge
A learner made this table of quark content and charge: uud, +1; udd, 0; ud̄, +1; ūd, 0. Which row contains an error?
1. Auud, +1
2. Būd, 0
3. Cudd, 0
4. Dud̄, +1
Show answer
Answer: B. ūd, 0
ū has charge −2/3 and d has −1/3, so ūd has charge −1, not 0. The other rows are correct: uud = +1, udd = 0, ud̄ = +2/3 + 1/3 = +1.
Common mistakeChoosing ud̄ comes from giving the anti-down quark −1/3; an antiquark has the opposite charge of its quark, so d̄ has +1/3.
43Multiple choice
In a linear accelerator, why do the drift tubes get longer further along the machine?
1. AParticles move faster, so cover more distance per half-cycle
2. BThe particles become heavier and need more room to move
3. CLonger tubes give a stronger electric field inside them
4. DLonger tubes help to keep the beam focused on the target
Show answer
Answer: A. Particles move faster, so cover more distance per half-cycle
Each tube must take the particle exactly half a cycle of the alternating voltage; as the speed rises, the distance covered in that time rises.
Common mistakeChoosing "stronger field inside" is wrong: inside a drift tube there is no field; particles are only accelerated in the gaps.
44Short answer · ★ Challenge
The lambda particle decays as Λ⁰ → p + π⁻. Rest energies: Λ⁰ 1115.7 MeV, p 938.3 MeV, π⁻ 139.6 MeV. Show that charge and baryon number are conserved, and calculate the kinetic energy released.
Show answer
Model answer: Charge: 0 = +1 + (−1). Baryon number: 1 = 1 + 0. Energy released = 1115.7 − (938.3 + 139.6) = 37.8 MeV, shared as kinetic energy of the proton and the pion.
Common mistakeLearners sometimes add the rest energies of the products to the parent; the energy released is the parent rest energy minus the products' rest energy.
45Multiple choice
In β⁻ decay the electrons come out with a whole range of energies up to a maximum value. Why?
1. ASome electrons lose energy inside the nucleus first
2. BThe released energy is shared with an antineutrino
3. CEach nucleus releases a different amount of energy
4. DThe electrons collide with the orbiting electrons
Show answer
Answer: B. The released energy is shared with an antineutrino
Each decay releases the same energy, but it is shared between the electron and the antineutrino in different proportions, so the electron energy varies.
Common mistakeChoosing "each nucleus releases a different amount" contradicts the fixed energy of a nuclear change; the varying share is due to the invisible antineutrino.
46Short answer · ★ Challenge
An electron moves at 2.0 × 10⁷ m/s at right angles to a uniform magnetic field of 5.0 mT. Calculate the radius of its circular track. (m_e = 9.11 × 10⁻³¹ kg, e = 1.6 × 10⁻¹⁹ C)
Show answer
Model answer: r = mv/(Bq) = (9.11 × 10⁻³¹ × 2.0 × 10⁷)/(5.0 × 10⁻³ × 1.6 × 10⁻¹⁹) = 1.82 × 10⁻²³/8.0 × 10⁻²² ≈ 0.023 m = 2.3 cm.
Common mistakeA common slip is using 5.0 T instead of 5.0 × 10⁻³ T, which gives a radius 1000 times too small.
47Short answer
Compare pair production with annihilation. For each, state what goes in, what comes out, and name one quantity conserved in both.
Show answer
Model answer: Pair production: a high-energy photon (near a nucleus) goes in; a particle and its antiparticle, such as an electron and a positron, come out. Annihilation: a particle and its antiparticle go in; photons (usually two) come out. In both, energy (including rest energy), momentum and charge are conserved.
Common mistakeLearners often say mass is conserved; it is not, because rest mass changes into photon energy and back. Total energy is what is conserved.
48Short answer · ★ Challenge
For the reaction p + p̄ → π⁺ + π⁻ + π⁰ a learner says: "This is impossible, because two heavy baryons cannot turn into three light mesons." Evaluate this claim using conservation laws and energy.
Show answer
Model answer: Charge: +1 − 1 = 0 before, +1 − 1 + 0 = 0 after. Baryon number: +1 − 1 = 0 before, 0 after (mesons have B = 0). Lepton number: 0 before and after. Energy: the rest energy of p + p̄ (about 1876 MeV) is far more than that of three pions (about 3 × 140 MeV), and the rest becomes kinetic energy. The reaction is allowed; the claim is wrong.
Common mistakeThe error is to think heavy particles can only turn into heavy particles; what matters is that charge, baryon and lepton numbers balance and there is enough energy.
49Short answer
Carbon-14 in a dead tree decays by β⁻ emission, which is used in carbon dating. Write the change that happens at the quark level and show that charge is conserved.
Show answer
Model answer: A down quark in one neutron changes into an up quark: d → u + e⁻ + ν̄_e (through a W⁻ boson). Charge: −1/3 = +2/3 + (−1) + 0 = −1/3, so charge is conserved.
Common mistakeA common error is to write u → d for β⁻ decay; in β⁻ decay a neutron (udd) becomes a proton (uud), so a d quark becomes a u quark.
50Short answer · ★ Challenge
In a cyclotron, the time for one orbit does not depend on the speed of the particle. Using r = mv/(Bq), show that the frequency of revolution is f = qB/(2πm), and calculate f for protons in a 1.5 T field. (m_p = 1.67 × 10⁻²⁷ kg, e = 1.6 × 10⁻¹⁹ C)
Show answer
Model answer: Period T = 2πr/v = 2π(mv/Bq)/v = 2πm/(Bq), which does not contain v; so f = 1/T = qB/(2πm). f = (1.6 × 10⁻¹⁹ × 1.5)/(2π × 1.67 × 10⁻²⁷) ≈ 2.3 × 10⁷ Hz (23 MHz).
Common mistakeLearners often expect faster particles to go round more often; they also move in bigger circles, so the period stays the same.