This chapter is all about the tiny building blocks of the universe — particles smaller than atoms — and what happens when we smash them together at incredible speeds. Think of it as the universe's ultimate Lego set.
🗺️ Big Picture: You will learn about particle accelerators, antimatter, how mass turns into energy and back again, quarks, and the four fundamental forces of nature.
Key Formulas You Must Know
⭐ Einstein's Mass-Energy Equation
E = mc²
E = Energy (in Joules, J)
m = mass (in kg)
c = speed of light = 3 × 10⁸ m/s
💡 This equation tells us that mass and energy are interchangeable. A tiny bit of mass produces an enormous amount of energy!
m = mass (in kg)
c = speed of light = 3 × 10⁸ m/s
💡 This equation tells us that mass and energy are interchangeable. A tiny bit of mass produces an enormous amount of energy!
⭐ Energy of a Photon
E = hf
E = Energy of photon (J)
h = Planck's constant = 6.6 × 10⁻³⁴ J·s
f = frequency of the photon (Hz)
💡 Used in pair production and pair annihilation calculations.
h = Planck's constant = 6.6 × 10⁻³⁴ J·s
f = frequency of the photon (Hz)
💡 Used in pair production and pair annihilation calculations.
⭐ Kinetic Energy from Electric Field (Accelerator)
QV = ½mv²
Q = charge (in Coulombs)
V = potential difference (in Volts)
m = mass of particle (kg)
v = speed of particle (m/s)
💡 Used when a particle is accelerated through a voltage. The electrical potential energy becomes kinetic energy.
V = potential difference (in Volts)
m = mass of particle (kg)
v = speed of particle (m/s)
💡 Used when a particle is accelerated through a voltage. The electrical potential energy becomes kinetic energy.
Essential Data (Memorise These!)
| Quantity | Symbol | Value |
|---|---|---|
| Speed of light | c | 3.0 × 10⁸ m/s |
| Planck's constant | h | 6.6 × 10⁻³⁴ J·s |
| Mass of electron | mₑ | 9.1 × 10⁻³¹ kg |
| Mass of proton | mₚ | 1.67 × 10⁻²⁷ kg |
| Mass of neutron | mₙ | 1.67 × 10⁻²⁷ kg |
| Charge of electron | e | 1.6 × 10⁻¹⁹ C |
| 1 eV in Joules | — | 1.6 × 10⁻¹⁹ J |
⚠️ Exam Tip
In the exam you'll have the Formulae & Tables book. But knowing these values saves time — and some questions give slightly different values so pay attention to what's given!
Experiments
⚡ Cockcroft & Walton
The first artificial splitting of the atom — and the first proof of E = mc²
In 1932, the Irish physicist Ernest Walton (from Dungarvan!) and English physicist John Cockcroft built the world's first particle accelerator. They shared the Nobel Prize in Physics (1951) for this work.
📖 Definition — Cockcroft & Walton Experiment
Cockcroft and Walton used a high-voltage linear accelerator to accelerate protons and fire them at a lithium target. The protons split the lithium nucleus, producing two alpha particles. This was the first artificial splitting of the nucleus and the first experimental verification of E = mc².
How the Experiment Worked
1
Proton production: A hydrogen gas discharge tube releases protons (hydrogen nuclei = just a proton) at the top of the apparatus.
2
Acceleration: The protons are accelerated downwards across a potential difference of 700,000 volts (70 kV in some versions). The electric field gives the protons kinetic energy.
3
Collision: The high-speed protons hit a lithium target. A proton collides with a lithium-7 nucleus.
4
Result: The collision produces two alpha particles (helium-4 nuclei) which fly off in opposite directions at high speed.
5
Detection: The alpha particles hit a zinc sulphide screen, causing tiny flashes of light (scintillations) which are observed through microscopes.
The Nuclear Equation
¹₁p + ⁷₃Li → ⁴₂He + ⁴₂He + K.E.
A proton (¹₁p) hits a lithium-7 (⁷₃Li) nucleus and produces two alpha particles (⁴₂He) plus kinetic energy.
🧠 The Mass Mystery: If you add up the mass of the proton + lithium, it's more than the mass of the two alpha particles. Mass has vanished! But the alpha particles fly off with much more kinetic energy than the proton had going in. Cockcroft and Walton proved that the "missing mass" had been converted into kinetic energy using E = mc².
Why Was This Experiment Significant?
- ✅ First artificial splitting of the atomic nucleus
- ✅ First transmutation using artificially accelerated particles
- ✅ First experimental verification of Einstein's E = mc²
- ✅ First particle accelerator ever built
Why Did Most Protons Miss?
📖 Key Exam Question
Most protons passed through without hitting a lithium nucleus because the atom is mostly empty space. (This was proven earlier by Rutherford's gold foil experiment.) Only the occasional proton came close enough to a nucleus to cause a reaction.
Diagram — What to Draw in the Exam
Your diagram needs to show these 4 labelled parts:
- Hydrogen discharge tube (produces protons) — at the top
- Linear accelerator / high voltage supply — connected correctly
- Lithium target — at 45° angle
- Zinc sulphide screen + microscope — for detection
⚡ Worked Calculation — Proton Speed
📐 Exam Example [2007]
What is the velocity of a proton accelerated through a potential difference of 700 kV?
What's happening: The proton starts at rest. The electric field (voltage) gives it kinetic energy. All the electrical potential energy becomes kinetic energy.
Step 1 — Write the energy equation
QV = ½mv²Step 2 — Rearrange for v
v² = 2QV ÷ mStep 3 — Substitute values
Q = 1.6022 × 10⁻¹⁹ C (charge of proton)V = 700,000 V = 7 × 10⁵ V
m = 1.6726 × 10⁻²⁷ kg
Step 4 — Calculate
v² = (2)(1.6022 × 10⁻¹⁹)(7 × 10⁵) ÷ (1.6726 × 10⁻²⁷)v² = 1.342 × 10¹⁴
v = 1.16 × 10⁷ m/s
💡 That's about 4% of the speed of light — very fast, but not fast enough for relativistic effects to matter much here.
⚡ Worked Calculation — Energy Released in Cockcroft-Walton
📐 Exam Example [2002, 2007]
When a lithium nucleus is bombarded with a proton, two alpha-particles are produced. Calculate the energy released.
Strategy: Find the total mass before, find the total mass after. The difference in mass has been converted to energy using E = mc².
Step 1 — Mass BEFORE
Mass of proton + mass of lithium nucleus= (1.6726 × 10⁻²⁷) + (1.1646 × 10⁻²⁶)
= 1.33186 × 10⁻²⁶ kg
Step 2 — Mass AFTER
Mass of 2 alpha particles= 2 × (6.6443 × 10⁻²⁷)
= 1.32886 × 10⁻²⁶ kg
Step 3 — Mass LOST (this became energy)
Δm = 1.33186 × 10⁻²⁶ − 1.32886 × 10⁻²⁶ = 2.92 × 10⁻²⁹ kgStep 4 — Energy released
E = mc²E = (2.92 × 10⁻²⁹) × (3.0 × 10⁸)²
E = 2.6 × 10⁻¹² J
⚠️ Exam Tip — Naming the Force
Always write "strong nuclear force" not just "strong force". Always write "gravitational force" not just "gravity". The examiners are strict on this!
Particle Accelerators
🔄 Modern Particle Accelerators
How physicists convert kinetic energy into brand new particles
The Cockcroft-Walton experiment used a linear accelerator. Modern accelerators like CERN's Large Hadron Collider (LHC) are circular, much bigger, and far more powerful.
Linear vs Circular Accelerators
| Feature | Linear Accelerator | Circular Accelerator |
|---|---|---|
| Direction of travel | Straight line | Around a circle/ring |
| Energy | One acceleration | Continuously accelerated (gains energy each loop) |
| Size | Very long for high energies | Compact — same track reused |
| Uses magnets? | No | Yes — to bend path |
| Examples | Cockcroft-Walton | LHC at CERN, Fermilab |
📖 Advantages of Circular Accelerators
1. They result in progressively increasing speed/energy — particles gain energy every time they go around.
2. They occupy much less space than an equivalent linear accelerator.
2. They occupy much less space than an equivalent linear accelerator.
Why Are the Tubes Evacuated?
📖 Key Answer
The tube is evacuated (emptied of air) so that the accelerated particles don't collide with air molecules and lose their energy before reaching the target.
What Do the Magnets Do?
📖 Key Answer
The magnets bend the path of the charged particles, keeping them moving in a circle. Without the magnets, the particles would fly off in a straight line.
Can You Accelerate Neutrons?
📖 Key Answer
No. Neutrons have no charge. Accelerators work by using electric fields to push charged particles. Since neutrons are neutral, an electric field has no effect on them.
Why Are Particles Accelerated to High Speeds?
The more kinetic energy the protons have before they collide, the more new, exotic particles can be created from that energy. It's E = mc² working in reverse: kinetic energy → mass of new particles.
Proton-Proton Collisions — Creating New Particles
p⁺ + p⁺ + K.E. → p⁺ + p⁺ + new particles (+ K.E.)
When two protons collide at enormous speeds, their kinetic energy is converted into the mass of brand new particles. The greater the kinetic energy going in, the more massive (and exotic!) the particles that come out.
⚡ Worked Calculation — Maximum Mass of New Particles
📐 Exam Example [2009 — LHC question]
Each proton in the LHC has kinetic energy of 2.0 GeV. What is the maximum net mass of new particles created per collision?
Strategy: Maximum mass is created when ALL kinetic energy is converted to mass. Two protons collide so total kinetic energy = 2 × 2 GeV = 4 GeV.
Step 1 — Convert GeV to Joules
1 eV = 1.6 × 10⁻¹⁹ J4 GeV = 4 × 10⁹ eV
= (4 × 10⁹) × (1.6 × 10⁻¹⁹) = 6.4 × 10⁻¹⁰ J
Step 2 — Use E = mc² to find mass
m = E ÷ c²m = (6.4 × 10⁻¹⁰) ÷ (3.0 × 10⁸)²
m = 7.12 × 10⁻²⁷ kg
📐 Exam Example [2020 — Fermilab]
Two protons, each with kinetic energy 29 GeV, collide. Afterwards the total kinetic energy of all particles is 16 GeV. Calculate the total mass of new particles created.
Strategy: Energy "missing" from kinetic energy was used to create mass.
Step 1 — Find energy used to create mass
KE before = 29 + 29 = 58 GeVKE after = 16 GeV
Energy → mass = 58 − 16 = 42 GeV
Step 2 — Convert to Joules
42 GeV = (42 × 10⁹)(1.6 × 10⁻¹⁹) = 6.72 × 10⁻⁹ JStep 3 — Use E = mc²
m = E ÷ c² = (6.72 × 10⁻⁹) ÷ (3 × 10⁸)²m = 7.47 × 10⁻²⁶ kg
💡 Unit Conversion — Super Important!
The exam loves GeV and MeV. Always convert to Joules first!• 1 eV = 1.6 × 10⁻¹⁹ J
• 1 MeV = 1.6 × 10⁻¹³ J (×10⁶)
• 1 GeV = 1.6 × 10⁻¹⁰ J (×10⁹)
Particle Classification
🦁 The Particle Zoo
Hundreds of new particles were discovered — and physicists needed a system to organise them
When physicists started smashing protons together at high speeds, they discovered hundreds of new, previously unknown particles. The collection became so large it was nicknamed the particle zoo.
To make sense of this zoo, physicists grouped particles by their properties — especially by which forces they experience and what they're made of.
📖 The Particle Zoo
The "particle zoo" refers to the large number of subatomic particles discovered in particle accelerator experiments in the 20th century. The quark model was proposed to bring order to this zoo.
The Big Picture: Particle Family Tree
ALL PARTICLES
├── LEPTONS (not made of quarks)
│ └── electron, muon, tau, neutrinos, positron...
└── HADRONS (made of quarks)
├── BARYONS (3 quarks)
│ └── proton, neutron...
└── MESONS (1 quark + 1 antiquark)
└── pion, kaon...
├── LEPTONS (not made of quarks)
│ └── electron, muon, tau, neutrinos, positron...
└── HADRONS (made of quarks)
├── BARYONS (3 quarks)
│ └── proton, neutron...
└── MESONS (1 quark + 1 antiquark)
└── pion, kaon...
Key Definitions
📖 Leptons
Leptons are fundamental particles that are not subject to the strong nuclear force. They are not made of quarks. Examples: electron, muon, tau (and their neutrinos), positron.
📖 Hadrons
Hadrons are particles made up of quarks. They experience all four fundamental forces, including the strong nuclear force. Hadrons are divided into baryons and mesons.
📖 Baryons
Baryons are hadrons made of three quarks (or three antiquarks). Examples: proton (uud) and neutron (udd).
📖 Mesons
Mesons are hadrons made of one quark and one antiquark. They have a mass between the electron and proton. Examples: pion, kaon. Because they contain both matter and antimatter, they are very unstable and annihilate almost immediately.
📐 2011 Exam — Pion Creation
Two protons and two charged pi mesons are produced in a collision. Show that the kinetic energy of each proton must be at least 140 MeV.
Strategy: Find the energy needed to create 2 pions (from the Formulae & Tables: mass of pion = 273 × mass of electron).
Step 1 — Find mass of one pion
mπ = 273 × mₑ = 273 × (9.109 × 10⁻³¹) = 2.487 × 10⁻²⁸ kgStep 2 — Energy to create 2 pions
E = 2mπc² = 2 × (2.487 × 10⁻²⁸) × (3 × 10⁸)²= 4.476 × 10⁻¹¹ J
Step 3 — Convert to eV
E = (4.476 × 10⁻¹¹) ÷ (1.602 × 10⁻¹⁹) = 279.4 × 10⁶ eV ≈ 280 MeVStep 4 — Per proton
280 MeV comes from two protons, so each needs at least 140 MeV. ✓Antimatter
🔄 Antimatter
Same mass, opposite charge — and it annihilates on contact with regular matter
Every particle of ordinary matter has a corresponding antiparticle. When a particle meets its antiparticle, they destroy each other in a burst of energy — this is called pair annihilation.
📖 Definition — Antimatter
Antimatter has the same mass as ordinary matter but opposite charge. Each particle has a corresponding antiparticle.
Key Antiparticles to Know
| Particle | Charge | Antiparticle | Charge |
|---|---|---|---|
| Electron (e⁻) | −1 | Positron (e⁺) | +1 |
| Proton (p⁺) | +1 | Antiproton | −1 |
| Up quark (u) | +2/3 | Anti-up quark (ū) | −2/3 |
| Down quark (d) | −1/3 | Anti-down quark (d̄) | +1/3 |
📖 The Positron
The positron (or anti-electron) is the antiparticle of the electron. It has the same mass as an electron but a positive charge. Symbol: e⁺ or β⁺.
Who Predicted Antimatter?
The English physicist Paul Dirac mathematically predicted the existence of antimatter before it was experimentally detected. He was working on combining quantum mechanics with special relativity.
The positron was first discovered experimentally by Carl Anderson in 1932 during the study of cosmic rays.
📝 Exam Points About Dirac
The exam may ask: "Give one contribution made to physics by Paul Dirac."Answer: Dirac predicted the existence of antimatter (antiparticles).
Comparing Electron and Positron
📖 Exam Answer — Electron vs Positron
✅ Same: mass, magnitude of charge
❌ Different: sign of charge (electron is negative, positron is positive)
❌ Different: sign of charge (electron is negative, positron is positive)
Beta-Positive Decay (Bonus Topic)
In ordinary beta decay, a neutron → proton + electron. But there is also beta-positive decay, where a proton → neutron + positron.
📐 2014 Exam — Carbon-11 Decay
A carbon-11 nucleus decays with the emission of a positron. Write a nuclear equation.
Answer
¹¹₆C → ¹¹₅B + ⁰₊₁e (positron)The carbon-11 nucleus has 6 protons. One proton "turns into" a neutron + positron. So afterwards we have 5 protons, 6 neutrons = Boron-11.
Pair Production
✨ Pair Production
Energy turns into matter — a gamma ray photon creates a particle and its antiparticle
📖 Definition — Pair Production
Pair production occurs when a high-energy gamma ray photon spontaneously creates a particle and its antiparticle (most commonly an electron and a positron). The photon disappears and two particles appear in its place.
The Equation
γ → e⁻ + e⁺ + K.E.
A gamma ray photon (γ) produces an electron (e⁻) and a positron (e⁺), which may also carry kinetic energy.
The Energy Equation
📐 Pair Production Energy Equation
hf = 2mₑc² + K.E.
Energy of photon = energy to create both particles + kinetic energy of the particles
For minimum frequency, we assume the particles are created with zero kinetic energy:
hf = 2mₑc²
For minimum frequency, we assume the particles are created with zero kinetic energy:
hf = 2mₑc²
Conservation Laws in Pair Production
✅ Conservation of Charge:
A photon has zero charge. The electron has charge −1, the positron has charge +1. Net charge = −1 + 1 = 0. ✓ Charge is conserved.
✅ Conservation of Momentum:
A photon carries momentum (even though it has no rest mass!). So there must be momentum after too. This means the electron and positron cannot travel in opposite directions — they must move off at angles to conserve momentum.
📖 Why Is a Nucleus Needed?
Pair production usually occurs near an atomic nucleus. The nucleus can absorb some recoil momentum, which is needed for both conservation of energy and momentum to be satisfied simultaneously in free space.
⚡ Worked Calculations
📐 Exam Example [2003, 2013] — Minimum Frequency
Calculate the minimum frequency of a gamma-ray photon required for pair production (creating an electron and positron).
Step 1 — Write the energy equation (minimum = no K.E.)
hf = 2mₑc²Step 2 — Rearrange for f
f = 2mₑc² ÷ hStep 3 — Substitute values
f = 2 × (9.1 × 10⁻³¹) × (3.0 × 10⁸)² ÷ (6.6 × 10⁻³⁴)f = 2.48 × 10²⁰ Hz
💡 What if the frequency is greater than the minimum? The newly created particles will move off with kinetic energy.
📐 Exam Example [2010] — Kinetic Energy of Particles
A photon of frequency 3.6 × 10²⁰ Hz causes pair production. Calculate the kinetic energy of one of the particles produced.
Step 1 — Energy of the photon
E = hf = (6.6 × 10⁻³⁴)(3.6 × 10²⁰) = 2.376 × 10⁻¹³ JStep 2 — Energy used to create 2 particles
E = 2mₑc² = 2(9.1 × 10⁻³¹)(3.0 × 10⁸)² = 1.638 × 10⁻¹³ JStep 3 — Total kinetic energy of both particles
K.E. total = 2.376 × 10⁻¹³ − 1.638 × 10⁻¹³ = 7.38 × 10⁻¹⁴ JStep 4 — K.E. of ONE particle (divide by 2)
K.E. per particle = 3.69 × 10⁻¹⁴ J📐 Exam Example [2021 HL] — Muon-Antimuon Pair
A photon produces a muon–antimuon pair. Calculate the minimum energy of the photon in electronvolts.
Step 1 — Find mass of a muon (from Formulae & Tables: muon mass = 207 × mₑ)
mμ = 207 × (9.109 × 10⁻³¹) = 1.886 × 10⁻²⁸ kgStep 2 — Energy = 2mμc² (two muons created)
E = 2 × (1.886 × 10⁻²⁸) × (3.0 × 10⁸)²= 3.39 × 10⁻¹¹ J
Step 3 — Convert to eV
E = (3.39 × 10⁻¹¹) ÷ (1.602 × 10⁻¹⁹) = 2.12 × 10⁸ eV = 212 MeVPair Annihilation
💥 Pair Annihilation
Matter meets antimatter — and they convert entirely into energy
📖 Definition — Pair Annihilation
Pair annihilation occurs when a particle meets its antiparticle. Both particles are destroyed and their combined mass is converted entirely into energy in the form of two gamma-ray photons.
The Equation
e⁺ + e⁻ + K.E. → 2γ
An electron and positron annihilate, producing two gamma-ray photons.
⚠️ Always say "gamma-ray photons"! Not just "photons". The examiners want you to emphasise the very high energy level — gamma rays are the highest-energy photons.
The Energy Equation
📐 Pair Annihilation Energy Equation
2mₑc² = 2hf
Mass of electron + mass of positron → energy of two photons
Simplify: mₑc² = hf (for each photon)
For minimum frequency, no kinetic energy beforehand.
Simplify: mₑc² = hf (for each photon)
For minimum frequency, no kinetic energy beforehand.
Conservation Laws in Pair Annihilation
✅ Conservation of Charge:
Electron (−1) + Positron (+1) = 0. Two gamma photons have zero charge. ✓
✅ Conservation of Momentum:
The electron and positron travel toward each other (opposite momenta). Their total momentum sums to approximately zero. So the two photons must fly off in opposite directions to ensure net momentum remains zero. This is why we must get two photons, not one!
⚡ Worked Calculation
📐 Exam Example [2012, 2014]
Calculate the minimum frequency of the photons produced in pair annihilation of an electron and positron.
Step 1 — Write energy equation (minimum → no K.E.)
2mₑc² = 2hf → mₑc² = hfStep 2 — Solve for f
f = mₑc² ÷ hStep 3 — Substitute values
f = (9.109 × 10⁻³¹) × (3 × 10⁸)² ÷ (6.626 × 10⁻³⁴)f = 1.237 × 10²⁰ Hz
💡 Why do photons usually have a higher frequency than this minimum? Because in reality, the electron and positron usually have kinetic energy before they meet. That extra energy also gets converted into photon energy, increasing the frequency.
Pair Production vs Pair Annihilation — Quick Comparison
| Feature | Pair Production | Pair Annihilation |
|---|---|---|
| What goes in? | 1 gamma-ray photon | Electron + Positron |
| What comes out? | Electron + Positron | 2 gamma-ray photons |
| Conversion | Energy → Mass | Mass → Energy |
| Number of photons | 1 in | 2 out |
| Equation | γ → e⁻ + e⁺ | e⁺ + e⁻ → 2γ |
The Neutrino
👻 The Neutrino
The particle that shouldn't exist — predicted before it could be detected
Right now, approximately 10 trillion neutrinos from the Sun are passing through your hand every second. They pass through the entire Earth as if it's not even there!
📖 Definition — Neutrino
The neutrino is an extremely small, nearly massless, chargeless particle. It travels at close to the speed of light and barely interacts with ordinary matter. The symbol is ν (Greek letter "nu"). Its name means "little neutral one" in Italian.
Why Was the Neutrino Proposed?
The neutrino was first proposed by Wolfgang Pauli (Austrian physicist) to solve a problem with beta decay.
In beta decay, a neutron decays into a proton and an electron:
n⁰ → p⁺ + e⁻
When scientists measured the momentum before and after this decay, they found the momentum afterwards was always slightly less than before. This violated the law of conservation of momentum — which should be impossible!
📖 Pauli's Solution
Pauli suggested that a third particle must also be produced in beta decay — one that carried away the "missing" momentum. Because it was never detected, it had to have no charge and almost no mass. He called it the neutrino.
The Full Beta Decay Equation (with Neutrino)
⁰₁n → ¹₁p + ⁰₋₁e + ν + K.E.
⚠️ Always include the neutrino (ν) in beta decay equations! If you leave it out, you'll lose marks.
Who Named It?
The term "neutrino" was coined by Italian physicist Enrico Fermi, meaning "little neutral one" in Italian. Fermi is the same person who developed the theory of radioactive decay (called Fermi's theory).
📝 Know Your People!
• Pauli — proposed the neutrino existed• Fermi — named it "neutrino" and developed the theory of beta decay
• The neutrino was finally detected experimentally in 1956 — 26 years after Pauli predicted it!
Why Is It Hard to Detect?
📖 Exam Answer — Two Reasons It's Hard to Detect
1. The neutrino has no charge — it doesn't interact electromagnetically, so it doesn't leave a track or cause ionisation.
2. The neutrino has very small (nearly zero) mass — and barely interacts with matter at all through the weak nuclear force.
2. The neutrino has very small (nearly zero) mass — and barely interacts with matter at all through the weak nuclear force.
⚡ Worked Calculation — Energy Released in Beta Decay
📐 Exam Example [2015] — Energy from Beta Decay
Calculate the energy released, in MeV, during beta decay.
Step 1 — Mass BEFORE: mass of neutron
mₙ = 1.674927 × 10⁻²⁷ kgStep 2 — Mass AFTER: proton + electron + neutrino
mₚ = 1.672622 × 10⁻²⁷ kgmₑ = 9.109 × 10⁻³¹ kg
mᵥ = 4.305 × 10⁻⁶ × mₑ ≈ negligible
Total ≈ 1.673533 × 10⁻²⁷ kg
Step 3 — Mass lost
Δm = 1.674927 × 10⁻²⁷ − 1.673533 × 10⁻²⁷ = 1.394 × 10⁻³⁰ kgStep 4 — Energy released
E = mc² = (1.394 × 10⁻³⁰)(3 × 10⁸)² = 1.25 × 10⁻¹³ JStep 5 — Convert to MeV
E = (1.25 × 10⁻¹³) ÷ (1.6 × 10⁻¹³) ≈ 0.78 MeVHow Did Fermi's Theory Resolve the Momentum Problem?
📖 Exam Answer
Fermi's theory of radioactive decay proposed that a third particle (the neutrino) must be emitted during beta decay. This neutrino carries away the "missing" momentum, thereby restoring conservation of momentum.
Quarks
🔬 Quarks & Anti-Quarks
The true building blocks of protons and neutrons
For a long time, protons and neutrons were thought to be the smallest particles. But in the 1960s, physicists discovered that they are made of even smaller particles called quarks.
📖 Definition — Quark
Quarks are fundamental particles that make up hadrons (baryons and mesons). They carry fractional electric charges (fractions of the electron charge) and always come in groups of two or three — they are never found alone.
Who Named Quarks?
The American physicist Murray Gell-Mann proposed the quark model and gave quarks their name. He found the word "quark" in a novel by Irish writer James Joyce — specifically in Finnegans Wake. You need to know this!
The Six Flavours of Quark
| Name | Symbol | Charge (×e) | Type |
|---|---|---|---|
| Up | u | +2/3 | Positive |
| Down | d | −1/3 | Negative |
| Charm | c | +2/3 | Positive |
| Strange | s | −1/3 | Negative |
| Top | t | +2/3 | Positive |
| Bottom | b | −1/3 | Negative |
💡 Memory Trick for the 6 Flavours
"Uncle Dave Can Sometimes Take Breaks"
Up, Down, Charm, Strange, Top, Bottom
💡 Which Quarks Are Positively Charged?
Up, Charm, Top = +2/3 charge
Down, Strange, Bottom = −1/3 charge
Anti-Quarks
📖 Definition — Anti-Quark
An anti-quark has the same mass as its corresponding quark, but opposite charge. For example, the anti-up quark (ū) has a charge of −2/3.
Quark Compositions — Must Know!
| Particle | Quarks | Charge Calculation | Classification |
|---|---|---|---|
| Proton | uud | +2/3 + 2/3 − 1/3 = +1 | Baryon |
| Neutron | udd | +2/3 − 1/3 − 1/3 = 0 | Baryon |
| π⁺ (positive pion) | ud̄ (up + anti-down) | +2/3 + 1/3 = +1 | Meson |
| π⁻ (negative pion) | dū (down + anti-up) | −1/3 − 2/3 = −1 | Meson |
| Anti-neutron | ūd̄d̄ | −2/3 + 1/3 + 1/3 = 0 | Baryon |
📝 Exam Tip — Kaon Classification
A kaon consists of a strange quark and an up anti-quark (sū). Because it's made of one quark and one antiquark, it is a MESON.
Quark vs Anti-Quark — Comparing Properties
📖 Exam Answer [2018]
Same: mass AND the magnitude (size) of the charge
Different: the sign of the charge (one is positive, the other is negative)
Different: the sign of the charge (one is positive, the other is negative)
Possible Meson Combinations from up/down Quarks
| Composition | Charge | Name |
|---|---|---|
| uū | +2/3 − 2/3 = 0 | Pi-zero (π⁰) |
| ud̄ | +2/3 + 1/3 = +1 | Pi-plus (π⁺) |
| dū | −1/3 − 2/3 = −1 | Pi-minus (π⁻) |
| dd̄ | −1/3 + 1/3 = 0 | Pi-zero (π⁰) |
Fundamental Forces
💪 The Four Fundamental Forces
Every force in the universe is one of just four fundamental forces
No matter how complex a force seems — magnetism, friction, pressure — it all boils down to one of just four fundamental forces.
💡 Mnemonic — Order from strongest to weakest
"Steady Effort Wins Games"
Strong nuclear → Electromagnetic → Weak nuclear → Gravitational
⚠️ Exam Language Warning!
Always write "strong nuclear force" (not "strong force") and "gravitational force" (not "gravity"). The examiners dock marks for these!
The Four Forces
Quick Summary Table
| Force | Relative Strength | Range | Acts On | Role |
|---|---|---|---|---|
| Strong nuclear | 1 (strongest) | Very short (nuclear scale) | Quarks, hadrons | Binds nucleus |
| Electromagnetic | ~10⁻² | Infinite (inverse square) | Charged particles | Atom structure, chemistry |
| Weak nuclear | ~10⁻⁶ | Very short (sub-nuclear) | Quarks, leptons | Beta decay |
| Gravitational | ~10⁻³⁹ (weakest) | Infinite (inverse square) | All masses | Planetary orbits |
Which Forces Act on Which Particles?
🎯 Leptons (e.g. electron, muon, neutrino): experience electromagnetic, weak nuclear, gravitational forces — but NOT the strong nuclear force
🎯 Hadrons (e.g. proton, neutron, pion): experience all four fundamental forces
🎯 Pions specifically: experience all four forces — strong, electromagnetic, weak, gravitational
📐 Exam Example [2009]
Arrange the fundamental forces of nature in increasing order of strength.
Answer (weakest to strongest)
Gravitational → Weak nuclear → Electromagnetic → Strong nuclearClassification
📊 Full Particle Classification
The complete map of all fundamental particles
Now let's put it all together into one big map. Every particle fits neatly into this system.
The Particle Map
| Category | Sub-type | Composition | Experiences Strong Force? | Examples |
|---|---|---|---|---|
| LEPTONS | Charged Leptons | Fundamental (no quarks) | ❌ No | electron (e⁻), muon (μ), tau (τ) |
| Neutrinos | Fundamental (no quarks) | ❌ No | νₑ, νμ, ντ | |
| HADRONS | BARYONS | 3 quarks (or 3 antiquarks) | ✅ Yes | proton (uud), neutron (udd) |
| MESONS | 1 quark + 1 antiquark | ✅ Yes | pion (π), kaon (K) |
Negatively Charged Leptons (Know All Three!)
The three negatively charged leptons are:
🔵 Electron (e) — the lightest and most familiar
🔵 Muon (μ) — 207 times heavier than an electron
🔵 Tau (τ) — the heaviest of the three
🔵 Electron (e) — the lightest and most familiar
🔵 Muon (μ) — 207 times heavier than an electron
🔵 Tau (τ) — the heaviest of the three
Positively Charged Quarks (Know These!)
The three positively charged quarks (charge = +2/3):
🔴 Up (u) 🔴 Charm (c) 🔴 Top (t)
🔴 Up (u) 🔴 Charm (c) 🔴 Top (t)
Why Are Mesons So Unstable?
📖 Explanation
A meson contains a quark and an antiquark — matter and antimatter paired together. Because they are matter-antimatter pairs, they undergo pair annihilation almost immediately. This is why mesons are very short-lived and unstable.
Classifying the Proton
A proton is a hadron because it is composed of quarks (specifically uud) and it experiences the strong nuclear force.
A proton is a baryon because it is composed of three quarks (uud). Baryons are defined as hadrons with three quarks.
A kaon (strange quark + up anti-quark) is a meson because it is composed of one quark and one antiquark. All quark-antiquark pairs are mesons.
Calculations
🔢 Energy Conversion Equations
All the maths in this chapter is about converting between mass and energy
All the calculations in this chapter involve four types of energy conversion. Learn to recognise which type a question is asking about — then apply the right formula.
The Four Energy Conversions
📐 Type 1 — Linear Accelerator (Voltage → Speed)
QV = ½mv²
Potential energy → Kinetic energy
When to use: A particle is accelerated through a voltage. Given the voltage, find the speed.
When to use: A particle is accelerated through a voltage. Given the voltage, find the speed.
📐 Type 2 — Cockcroft-Walton (Mass → Kinetic Energy)
Δm × c² = K.E. (released)
Mass disappears → Kinetic energy appears
When to use: Given masses of particles before and after a nuclear reaction, find energy released.
Strategy: mass before − mass after = Δm. Then E = Δmc².
When to use: Given masses of particles before and after a nuclear reaction, find energy released.
Strategy: mass before − mass after = Δm. Then E = Δmc².
📐 Type 3 — Proton Collisions (Kinetic Energy → Mass)
K.E. = Δm × c²
Kinetic energy disappears → New particle mass appears
When to use: Given kinetic energies of colliding protons, find mass of new particles.
When to use: Given kinetic energies of colliding protons, find mass of new particles.
📐 Type 4a — Pair Production (Photon Energy → Mass)
hf = 2mₑc² (+ K.E.)
Gamma ray energy → Mass of electron + positron
When to use: Given photon frequency, find kinetic energy of particles. Or find minimum frequency for pair production.
When to use: Given photon frequency, find kinetic energy of particles. Or find minimum frequency for pair production.
📐 Type 4b — Pair Annihilation (Mass → Photon Energy)
2mₑc² = 2hf
Electron + positron mass → Two gamma ray photons
Simplified: mₑc² = hf per photon
Simplified: mₑc² = hf per photon
Unit Conversions — Critical!
📖 Energy Unit Conversions
1 eV = 1.6 × 10⁻¹⁹ J
1 keV = 1.6 × 10⁻¹⁶ J
1 MeV = 1.6 × 10⁻¹³ J
1 GeV = 1.6 × 10⁻¹⁰ J
To convert eV → J: multiply by 1.6 × 10⁻¹⁹
To convert J → eV: divide by 1.6 × 10⁻¹⁹
1 keV = 1.6 × 10⁻¹⁶ J
1 MeV = 1.6 × 10⁻¹³ J
1 GeV = 1.6 × 10⁻¹⁰ J
To convert eV → J: multiply by 1.6 × 10⁻¹⁹
To convert J → eV: divide by 1.6 × 10⁻¹⁹
Converting Atomic Mass Units
📖 Atomic Mass Unit (u)
1 u = 1.6605 × 10⁻²⁷ kg
To convert from u to kg: multiply by 1.6605 × 10⁻²⁷
To convert from u to kg: multiply by 1.6605 × 10⁻²⁷
Decision Guide — Which Formula?
🔍 Read the question and ask:
- Particle accelerated through a voltage? → Use QV = ½mv²
- Nuclear reaction with different masses? → Use E = Δmc²
- Protons collide, new particles made? → Use E = mc² (KE → mass)
- Gamma ray creates particles? → Use hf = 2mc²
- Electron meets positron? → Use mₑc² = hf
Worked Examples
📐 Worked Examples
Step-by-step solutions to the most common exam calculation types
Here are all the key calculation types you might face in the exam, worked out in full detail.
Type 1 — Linear Accelerator Speed
[2007] What is the velocity of a proton accelerated through 700 kV?
Equation
QV = ½mv² → v = √(2QV/m)Values
Q = 1.6 × 10⁻¹⁹ C, V = 700,000 V, m = 1.673 × 10⁻²⁷ kgAnswer
v = √((2)(1.6 × 10⁻¹⁹)(7 × 10⁵) / 1.673 × 10⁻²⁷) = 1.16 × 10⁷ m/sType 2 — Energy from Nuclear Reaction (Cockcroft-Walton)
[2002] p + ⁷Li → 2α. Calculate the energy released.
Mass before
(1.6726 × 10⁻²⁷) + (1.1646 × 10⁻²⁶) = 1.33186 × 10⁻²⁶ kgMass after
2 × (6.6443 × 10⁻²⁷) = 1.32886 × 10⁻²⁶ kgMass lost
Δm = 1.33186 × 10⁻²⁶ − 1.32886 × 10⁻²⁶ = 3.0 × 10⁻²⁹ kgEnergy released
E = mc² = (3.0 × 10⁻²⁹)(3 × 10⁸)² = 2.7 × 10⁻¹² JType 3 — New Particle Mass from Proton Collision
[2020] Two protons (29 GeV each) collide. KE after = 16 GeV. Find mass of new particles.
KE → mass
Energy converted = 58 − 16 = 42 GeV= (42 × 10⁹)(1.6 × 10⁻¹⁹) = 6.72 × 10⁻⁹ J
m = E/c²
m = (6.72 × 10⁻⁹) / (3 × 10⁸)² = 7.47 × 10⁻²⁶ kgType 4a — Minimum Frequency for Pair Production
[2003] γ → e⁺ + e⁻. Find minimum frequency.
hf = 2mₑc²
f = 2mₑc²/h = 2(9.1 × 10⁻³¹)(3 × 10⁸)² / (6.6 × 10⁻³⁴) = 2.48 × 10²⁰ HzType 4b — Frequency from Pair Annihilation
[2012, 2014] e⁺ + e⁻ → 2γ. Find frequency of each photon.
mₑc² = hf
f = mₑc²/h = (9.109 × 10⁻³¹)(3 × 10⁸)² / (6.626 × 10⁻³⁴) = 1.237 × 10²⁰ HzType 5 — Pair Production with Kinetic Energy
[2010] Photon frequency = 3.6 × 10²⁰ Hz causes pair production. Find KE of each particle.
Photon energy
hf = (6.6 × 10⁻³⁴)(3.6 × 10²⁰) = 2.376 × 10⁻¹³ JEnergy to create particles
2mₑc² = 2(9.1 × 10⁻³¹)(3 × 10⁸)² = 1.638 × 10⁻¹³ JTotal KE of both
2.376 × 10⁻¹³ − 1.638 × 10⁻¹³ = 7.38 × 10⁻¹⁴ JKE per particle (÷2)
3.69 × 10⁻¹⁴ JRevision
📖 All Definitions — Exam Ready
Every definition you could be asked in the Leaving Cert, word-perfect
Learn these off by heart. Many exam questions ask you to "define" or "explain what is meant by" these terms.
Antimatter
Antimatter has the same mass as ordinary matter but opposite charge. Each particle has a corresponding antiparticle.
Positron
The positron (or anti-electron) is the antiparticle of the electron. It has the same mass as an electron but a positive charge. Symbol: e⁺.
Pair Production
Pair production occurs when a high-energy gamma-ray photon is converted into a particle and its antiparticle (usually an electron and positron).
Pair Annihilation
Pair annihilation occurs when a particle and its antiparticle meet and are both destroyed, with their combined mass converted into two gamma-ray photons.
Neutrino
A neutrino is an extremely small, nearly massless, chargeless particle produced in beta decay. Symbol: ν. Name means "little neutral one".
Quark
Quarks are fundamental particles that make up hadrons. They carry fractional electric charges and are never found alone. There are six flavours: up, down, charm, strange, top, bottom.
Hadron
A hadron is a particle made up of quarks. Hadrons experience all four fundamental forces, including the strong nuclear force. Divided into baryons (3 quarks) and mesons (quark + antiquark).
Baryon
A baryon is a hadron composed of three quarks (or three antiquarks). Examples: proton (uud), neutron (udd).
Meson
A meson is a hadron composed of one quark and one antiquark. Mesons are unstable and annihilate almost immediately. Examples: pion, kaon.
Lepton
A lepton is a fundamental particle that is not made of quarks and does not experience the strong nuclear force. Examples: electron, muon, tau, neutrinos.
Strong Nuclear Force
The strong nuclear force is the force that binds quarks together and holds the nucleus together. It is the strongest of the four fundamental forces and has a very short range (within the nucleus only).
Weak Nuclear Force
The weak nuclear force is responsible for radioactive beta decay (where a neutron transforms into a proton). It acts on both quarks and leptons and has a very short range.
Electromagnetic Force
The electromagnetic force acts between charged particles. It follows an inverse square law and has infinite range. Responsible for atomic structure and all chemical reactions.
Gravitational Force
The gravitational force acts between all massive objects. It is always attractive, follows an inverse square law, has infinite range, and is the weakest of the four fundamental forces.
The Particle Zoo
The "particle zoo" refers to the large number of subatomic particles discovered in particle accelerator experiments. The quark model was proposed to bring order to the zoo.
Anti-quark
An anti-quark has the same mass as its corresponding quark but the opposite charge. For example, the anti-up quark (ū) has a charge of −2/3.
Significance of Cockcroft-Walton Experiment
It was: (1) the first artificial splitting of the nucleus; (2) the first transmutation using artificially accelerated particles; (3) the first experimental verification of E = mc²; (4) the world's first particle accelerator.
🧠 Quick-Fire: Who Did What?
| Physicist | Nationality | Contribution |
|---|---|---|
| Ernest Walton | 🇮🇪 Irish | Built first particle accelerator with Cockcroft; split the lithium nucleus |
| John Cockcroft | 🇬🇧 English | Built first particle accelerator with Walton |
| Paul Dirac | 🇬🇧 English | Mathematically predicted the existence of antimatter |
| Wolfgang Pauli | 🇦🇹 Austrian | Predicted the existence of the neutrino |
| Enrico Fermi | 🇮🇹 Italian | Named the neutrino; developed theory of radioactive decay |
| Murray Gell-Mann | 🇺🇸 American | Proposed the quark model; named quarks after James Joyce |
| James Joyce | 🇮🇪 Irish | Author of Finnegans Wake — the source of the word "quark" |
Revision Quiz
🎯 Quick Quiz
Test yourself on everything from Particle Physics!
Answer all 12 questions, then see your score. Good luck! 🍀
1. What was the historical significance of the Cockcroft-Walton experiment?
2. Why did most protons pass through the lithium target without causing a reaction?
3. What is pair production?
4. Why are two gamma-ray photons produced in pair annihilation (not one)?
5. Why was the neutrino proposed?
6. What is the quark composition of a proton?
7. What is the difference between a baryon and a meson?
8. Arrange the four fundamental forces from weakest to strongest.
9. Which physicist mathematically predicted the existence of antimatter?
10. The word "quark" was taken from a book by which Irish writer?
11. Give two reasons why the neutrino is difficult to detect.
12. A lepton does NOT experience which fundamental force?
Your Score
0/12