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📚 Table of Contents
- 1. The α-Particle Scattering Experiment
- 2. Simple Model of the Nuclear Atom
- 3. Nucleon Number and Proton Number
- 4. Isotopes
- 5. Nuclide Notation
- 6. Conservation Laws
- 7. Types of Nuclear Radiation
- 8. Antiparticles
- 9. Neutrinos in Beta Decay
- 10. Energy in Radioactive Decay
- 11. Radioactive Decay Equations
- 12. The Unified Atomic Mass Unit
1. The α-Particle Scattering Experiment
Background
Before Rutherford's groundbreaking experiment in 1909, physicists believed in the "plum pudding model" proposed by J.J. Thomson. This model suggested that atoms were spheres of positive charge with electrons embedded throughout.
The Experiment
Ernest Rutherford, working with Hans Geiger and Ernest Marsden, designed an elegant experiment to test the structure of the atom. They fired α-particles (helium nuclei) at a thin gold foil and observed their scattering patterns.
Key Observations
- Most α-particles passed straight through with little or no deflection
- A small number were deflected through large angles (greater than 90°)
- Very few (approximately 1 in 8000) were deflected backwards
Conclusions About Nuclear Structure
- Most of the atom is empty space – explains why most α-particles passed through
- The nucleus is extremely small – only tiny fraction came close enough to deflect
- The nucleus contains most of the atom's mass – needed to deflect massive α-particles
- The nucleus is positively charged – repulsive electrostatic force causes deflection
Size Scale: The nucleus has diameter ≈ 10-15 m, while the atom has diameter ≈ 10-10 m. The nucleus is about 100,000 times smaller than the atom!
2. Simple Model of the Nuclear Atom
The Nucleus (Central Core)
- Protons: Positive charge +e (+1.60 × 10-19 C)
- Neutrons: Neutral, no charge
- Contains virtually all the atom's mass
- Diameter ~10-15 m
- Held together by the strong nuclear force
Orbital Electrons
- Negative charge -e (-1.60 × 10-19 C)
- Orbit the nucleus in shells or energy levels
- Very small mass compared to protons and neutrons
- Occupy space around nucleus (~10-10 m diameter)
Particle Masses
| Particle | Mass (kg) | Mass (u) |
|---|---|---|
| Proton | 1.673 × 10-27 | ≈ 1 |
| Neutron | 1.675 × 10-27 | ≈ 1 |
| Electron | 9.109 × 10-31 | ≈ 0.0005 |
Key Point: Proton and neutron are ~2000 times more massive than electron. In neutral atoms, number of protons = number of electrons.
3. Nucleon Number and Proton Number
Proton Number (Z) – Atomic Number
- Number of protons in the nucleus
- Defines the element
- Determines chemical properties
- In neutral atom, Z = number of electrons
Nucleon Number (A) – Mass Number
- Total number of protons and neutrons
- A = Z + N (where N = neutrons)
Neutron Number (N)
- Number of neutrons in nucleus
- N = A - Z
Example: Carbon-12: 126C
- Proton number (Z) = 6
- Nucleon number (A) = 12
- Neutron number (N) = 12 - 6 = 6
4. Isotopes
Definition
Isotopes are atoms of the same element (same Z) with different numbers of neutrons (different A).
Key Characteristics
- Identical chemical properties – same electron configuration
- Different physical properties – different masses
- Variable stability – some stable, some radioactive
Carbon Isotopes Example
- Carbon-12: 126C (6p, 6n) – stable, most abundant
- Carbon-13: 136C (6p, 7n) – stable, less abundant
- Carbon-14: 146C (6p, 8n) – radioactive, carbon dating
Hydrogen Isotopes Example
- Protium: 11H (1p, 0n)
- Deuterium: 21H (1p, 1n)
- Tritium: 31H (1p, 2n) – radioactive
5. Nuclide Notation
Standard Notation
AZX
Where:
- X = chemical symbol
- A = nucleon number (top left)
- Z = proton number (bottom left)
Examples
| Notation | Name | Protons | Neutrons |
|---|---|---|---|
| 23892U | Uranium-238 | 92 | 146 |
| 23490Th | Thorium-234 | 90 | 144 |
| 42He | Helium-4 (α) | 2 | 2 |
| 0-1e | Electron (β-) | - | - |
6. Conservation Laws in Nuclear Processes
In ALL nuclear reactions:
- Nucleon number (A) is conserved – total before = total after
- Charge/Proton number (Z) is conserved – total before = total after
Alpha Decay Example:
23892U → 23490Th + 42He
Check:
- Nucleon: 238 = 234 + 4 ✓
- Proton: 92 = 90 + 2 ✓
Beta Decay Example:
146C → 147N + 0-1e
Check:
- Nucleon: 14 = 14 + 0 ✓
- Proton: 6 = 7 + (-1) ✓
7. Types of Nuclear Radiation
Alpha (α) Radiation
- Composition: 42He nuclei (2 protons, 2 neutrons)
- Charge: +2e (positive)
- Mass: ≈ 4 u (heavy)
- Ionizing power: Very high
- Penetration: Very low (stopped by paper)
- Speed: ~5% speed of light
- Energy: Discrete (fixed values)
Beta-minus (β-) Radiation
- Composition: 0-1e (electrons from nucleus)
- Charge: -e (negative)
- Mass: ≈ 1/2000 u (light)
- Ionizing power: Medium
- Penetration: Medium (stopped by few mm Al)
- Speed: 30-99% speed of light
- Energy: Continuous range (0 to Emax)
Beta-plus (β+) Radiation
- Composition: 0+1e (positrons)
- Charge: +e (positive)
- Similar properties to β-
- Energy: Continuous range
Gamma (γ) Radiation
- Composition: EM radiation (photons)
- Charge: Zero
- Mass: Zero
- Ionizing power: Low
- Penetration: Very high (needs thick lead)
- Speed: Speed of light (3 × 108 m/s)
- Energy: Discrete values
- Not deflected by fields
Comparison Summary
| Property | α | β- | β+ | γ |
|---|---|---|---|---|
| Charge | +2e | -e | +e | 0 |
| Mass | 4 u | ~1/2000 u | ~1/2000 u | 0 |
| Ionizing | Very high | Medium | Medium | Low |
| Penetration | Very low | Medium | Medium | Very high |
| Energy | Discrete | Continuous | Continuous | Discrete |
8. Antiparticles
Definition
An antiparticle has the same mass as its particle but opposite charge.
Key Examples
- Electron: 0-1e, charge = -e
- Positron: 0+1e, charge = +e (antiparticle of electron)
- Proton: charge = +e
- Antiproton: charge = -e
Annihilation
When particle meets antiparticle, they annihilate, converting mass to energy (gamma rays):
e+ + e- → 2γ
Pair Production
Reverse process - high-energy γ-rays create particle-antiparticle pairs:
γ → e+ + e-
(Requires γ-ray energy ≥ 1.02 MeV)
9. Neutrinos in Beta Decay
The Problem
Early β-decay observations showed:
- β-particles had continuous energy range (not discrete)
- Energy and momentum didn't appear conserved
- Violated fundamental physics principles
The Solution: Neutrinos
In 1930, Pauli proposed neutrinos to explain this. Properties:
- Symbol: ν (nu)
- Charge: Zero
- Mass: Nearly zero
- Interaction: Very weak (can pass through Earth)
- Not detected until 1956
Beta-minus Decay
Neutron transforms, emitting electron + antineutrino:
n → p + e- + ν̄e
146C → 147N + 0-1e + ν̄e
Beta-plus Decay
Proton transforms, emitting positron + neutrino:
p → n + e+ + νe
Why Continuous Energy?
Energy is shared between β-particle and (anti)neutrino in variable proportions. This gives β-particles a continuous range from 0 to Emax.
10. Energy in Radioactive Decay
Alpha Decay - Discrete Energy
All α-particles from a specific isotope have the same kinetic energy.
Reason:
- Two-body decay (α + daughter nucleus)
- Energy released is fixed
- Energy sharing ratio is fixed
- α-particle carries most energy (lighter than daughter)
Example: 238U → 234Th + α
All α-particles have KE ≈ 4.2 MeV
Beta Decay - Continuous Energy
β-particles have continuous range from 0 to Emax.
Reason:
- Three-body decay (β + neutrino + daughter)
- Energy shared variably between β and neutrino
- When neutrino takes most → β has low energy
- When neutrino takes minimal → β has max energy
Example: 14C → 14N + e- + ν̄e
- Emax = 156 keV
- Most β-particles: 0 to 156 keV
- Average ≈ 49 keV
Energy Spectrum Comparison
| Radiation | Energy Spectrum | Reason |
|---|---|---|
| α-particles | Discrete | Two-body decay |
| β-particles | Continuous | Three-body decay (with neutrino) |
| γ-rays | Discrete | Fixed nuclear energy levels |
11. Radioactive Decay Equations
Alpha Decay
AZX → A-4Z-2Y + 42α
Changes:
- A decreases by 4
- Z decreases by 2
- Element moves 2 places back in periodic table
23892U → 23490Th + 42α
22688Ra → 22286Rn + 42α
22688Ra → 22286Rn + 42α
Beta-minus Decay
AZX → AZ+1Y + 0-1e + ν̄e
Changes:
- A stays same
- Z increases by 1
- Neutron converts to proton
- Element moves 1 place forward
146C → 147N + 0-1e + ν̄e
23490Th → 23491Pa + 0-1e + ν̄e
23490Th → 23491Pa + 0-1e + ν̄e
Beta-plus Decay
AZX → AZ-1Y + 0+1e + νe
Changes:
- A stays same
- Z decreases by 1
- Proton converts to neutron
- Element moves 1 place back
2211Na → 2210Ne + 0+1e + νe
Gamma Decay
AZX* → AZX + γ
(*) = excited state
Changes:- No change in A or Z
- Nucleus drops from excited to lower energy state
- Often follows α or β decay
Key Points for Equations:
- Always check: sum of A values equal on both sides
- Always check: sum of Z values equal on both sides
- Include neutrino in β-decay for completeness
12. The Unified Atomic Mass Unit (u)
Definition
1 u = exactly 1/12 the mass of a carbon-12 atom
1 u = 1.66054 × 10-27 kg
Alternative Names
- Atomic mass unit (amu)
- Dalton (Da)
Why Use It?
Makes atomic masses simple numbers instead of tiny powers of 10:
- Proton: 1.007276 u ≈ 1 u
- Neutron: 1.008665 u ≈ 1 u
- Electron: 0.000549 u ≈ 1/2000 u
- Carbon-12: exactly 12 u (by definition)
Standard Masses
| Particle/Atom | Mass (u) | Approx |
|---|---|---|
| Proton | 1.007276 | ≈ 1 |
| Neutron | 1.008665 | ≈ 1 |
| Electron | 0.000549 | ≈ 1/2000 |
| Carbon-12 | 12.000000 | exactly 12 |
11.2 Fundamental Particles - Complete Study Guide
📚 Table of Contents
1. Quarks - The Building Blocks
What Are Quarks?
Quarks are fundamental particles - they cannot be broken down into anything smaller. They are the basic building blocks of matter, combining to form protons, neutrons, and other particles.
Key Point: Unlike protons and neutrons (which are made of quarks), quarks themselves are truly fundamental - they have no internal structure.
The Six Flavours of Quarks
There are six types (flavours) of quarks, organized in three generations:
| Generation | Quark Flavours | Importance |
|---|---|---|
| First (lightest) | Up (u) and Down (d) | Make up ordinary matter (protons & neutrons) |
| Second | Charm (c) and Strange (s) | Found in unstable particles |
| Third (heaviest) | Top (t) and Bottom (b) | Very massive, only in high-energy collisions |
Properties of Quarks
- Fractional charges: Quarks have electric charges of +⅔e or -⅓e
- Never found alone: Quarks are always found in combinations (confinement)
- Color charge: Quarks carry "color charge" (not actual color) - red, green, or blue
- Strong force: Held together by the strong nuclear force via gluons
For A-Level: You need to focus primarily on the up (u) and down (d) quarks, as these make up protons and neutrons. Knowledge of the other four flavours is useful for context but not always required in detail.
2. Quark Charges and Antiquarks
Electric Charges of Quarks
Each quark flavour has a specific electric charge (in units of the elementary charge e):
| Quark | Symbol | Charge | Approximate Mass |
|---|---|---|---|
| Up | u | +⅔e | ~2-3 MeV/c² |
| Down | d | -⅓e | ~4-8 MeV/c² |
| Charm | c | +⅔e | ~1.3 GeV/c² |
| Strange | s | -⅓e | ~95 MeV/c² |
| Top | t | +⅔e | ~173 GeV/c² |
| Bottom | b | -⅓e | ~4.2 GeV/c² |
Pattern: Notice that up, charm, and top all have charge +⅔e, while down, strange, and bottom all have charge -⅓e.
Antiquarks
Every quark has a corresponding antiquark with opposite properties:
- Opposite charge: If a quark has charge +⅔e, its antiquark has -⅔e
- Same mass: Antiquarks have the same mass as their corresponding quarks
- Anticolor: Antiquarks carry anticolor (antired, antigreen, antiblue)
| Quark | Charge | Antiquark | Charge |
|---|---|---|---|
| u (up) | +⅔e | ū (anti-up) | -⅔e |
| d (down) | -⅓e | đ̄ (anti-down) | +⅓e |
| c (charm) | +⅔e | c̄ (anti-charm) | -⅔e |
| s (strange) | -⅓e | s̄ (anti-strange) | +⅓e |
| t (top) | +⅔e | t̄ (anti-top) | -⅔e |
| b (bottom) | -⅓e | b̄ (anti-bottom) | +⅓e |
Important: You do NOT need to memorize the properties of charm, strange, top, or bottom quarks for most A-Level exams. However, you MUST know the charges and properties of up and down quarks.
3. Protons and Neutrons - Quark Composition
Protons and Neutrons Are NOT Fundamental
A crucial understanding in particle physics is that protons and neutrons are not fundamental particles - they are made of quarks.
Key Concept: Protons and neutrons are composite particles made up of three quarks each. They belong to a class of particles called baryons.
Proton Quark Composition
A proton consists of two up quarks and one down quark:
Proton = uud
Calculating Proton Charge
Charge calculation:
2 up quarks: 2 × (+⅔e) = +4/3 e
1 down quark: 1 × (-⅓e) = -⅓e
Total charge = +4/3 e - ⅓e = +3/3 e = +e ✓
2 up quarks: 2 × (+⅔e) = +4/3 e
1 down quark: 1 × (-⅓e) = -⅓e
Total charge = +4/3 e - ⅓e = +3/3 e = +e ✓
This confirms the proton has a charge of +1e (or +1.60 × 10-19 C).
Neutron Quark Composition
A neutron consists of one up quark and two down quarks:
Neutron = udd
Calculating Neutron Charge
Charge calculation:
1 up quark: 1 × (+⅔e) = +⅔e
2 down quarks: 2 × (-⅓e) = -⅔e
Total charge = +⅔e - ⅔e = 0 ✓
1 up quark: 1 × (+⅔e) = +⅔e
2 down quarks: 2 × (-⅓e) = -⅔e
Total charge = +⅔e - ⅔e = 0 ✓
This confirms the neutron is electrically neutral (charge = 0).
Summary Comparison
| Particle | Quark Composition | Charge Calculation | Total Charge |
|---|---|---|---|
| Proton | uud | (+⅔) + (+⅔) + (-⅓) | +e |
| Neutron | udd | (+⅔) + (-⅓) + (-⅓) | 0 |
Exam Tip: You should be able to describe protons and neutrons in terms of their quark composition and calculate their charges. This is a common exam question!
Antiproton and Antineutron
The antiparticles of protons and neutrons are made of antiquarks:
- Antiproton: ūūđ̄ (two anti-up, one anti-down) - charge = -e
- Antineutron: ūđ̄đ̄ (one anti-up, two anti-down) - charge = 0
4. Hadrons: Baryons and Mesons
What Are Hadrons?
Hadrons are particles made of quarks. There are two main types:
Hadron Definition: Any particle made of quarks that experiences the strong nuclear force.
Baryons - Three Quarks
A baryon is a hadron consisting of three quarks (or three antiquarks for antibaryons).
Properties of Baryons
- Made of three quarks (qqq)
- Baryon number = +1 (antibaryons have baryon number = -1)
- Examples: proton, neutron
- Relatively stable (protons are stable, neutrons decay outside nucleus)
Baryon Examples:
- Proton (p): uud - charge +e
- Neutron (n): udd - charge 0
- Lambda (Λ): uds - charge 0 (contains strange quark)
- Sigma+ (Σ+): uus - charge +e
- Antiproton: ūūđ̄ - charge -e
Mesons - Quark-Antiquark Pairs
A meson is a hadron consisting of one quark and one antiquark.
Properties of Mesons
- Made of quark-antiquark pair (qQ̄)
- Baryon number = 0
- Generally unstable - decay quickly
- Examples: pions, kaons
Meson Examples:
- Pion+ (π+): uđ̄ - charge +e
- Pion- (π-): ūd - charge -e
- Pion⁰ (π⁰): uū or dđ̄ - charge 0
- Kaon+ (K+): us̄ - charge +e
- Kaon- (K-): ūs - charge -e
Calculating Meson Charges
Example 1: Pion+ (π+) = uđ̄
u quark charge: +⅔e
đ̄ antiquark charge: +⅓e (opposite of d quark)
Total: +⅔e + ⅓e = +e ✓
u quark charge: +⅔e
đ̄ antiquark charge: +⅓e (opposite of d quark)
Total: +⅔e + ⅓e = +e ✓
Example 2: Pion- (π-) = ūd
ū antiquark charge: -⅔e
d quark charge: -⅓e
Total: -⅔e - ⅓e = -e ✓
ū antiquark charge: -⅔e
d quark charge: -⅓e
Total: -⅔e - ⅓e = -e ✓
Hadron Classification Summary
| Type | Composition | Baryon Number | Examples |
|---|---|---|---|
| Baryon | 3 quarks (qqq) | +1 | Proton (uud), Neutron (udd) |
| Antibaryon | 3 antiquarks (Q̄Q̄Q̄) | -1 | Antiproton (ūūđ̄) |
| Meson | quark + antiquark (qQ̄) | 0 | Pions (π+, π-, π⁰), Kaons (K+, K-) |
Common Mistake: Don't confuse baryons with mesons! Baryons have THREE quarks, mesons have ONE quark and ONE antiquark.
5. Quark Changes in Beta Decay
Beta Decay at the Quark Level
Beta decay can be understood as transformations of quarks inside nucleons. This gives us a deeper understanding of what's really happening during radioactive decay.
Beta-minus (β-) Decay
In β- decay, a neutron transforms into a proton.
At the Nucleon Level
n → p + e- + ν̄e
At the Quark Level
Looking at the quark composition:
Before: Neutron = udd
After: Proton = uud
What changed? One down quark transformed into an up quark
After: Proton = uud
What changed? One down quark transformed into an up quark
d → u + e- + ν̄e
Charge Conservation Check
Before:
Down quark charge: -⅓e
After:
Up quark: +⅔e
Electron: -e
Antineutrino: 0
Total: +⅔e - e = +⅔e - 3/3e = -⅓e ✓
Charge is conserved!
Down quark charge: -⅓e
After:
Up quark: +⅔e
Electron: -e
Antineutrino: 0
Total: +⅔e - e = +⅔e - 3/3e = -⅓e ✓
Charge is conserved!
Beta-plus (β+) Decay
In β+ decay, a proton transforms into a neutron.
At the Nucleon Level
p → n + e+ + νe
At the Quark Level
Looking at the quark composition:
Before: Proton = uud
After: Neutron = udd
What changed? One up quark transformed into a down quark
After: Neutron = udd
What changed? One up quark transformed into a down quark
u → d + e+ + νe
Charge Conservation Check
Before:
Up quark charge: +⅔e
After:
Down quark: -⅓e
Positron: +e
Neutrino: 0
Total: -⅓e + e = -⅓e + 3/3e = +⅔e ✓
Charge is conserved!
Up quark charge: +⅔e
After:
Down quark: -⅓e
Positron: +e
Neutrino: 0
Total: -⅓e + e = -⅓e + 3/3e = +⅔e ✓
Charge is conserved!
Summary of Quark Changes
| Decay Type | Quark Change | Nucleon Change | Particles Emitted |
|---|---|---|---|
| β- decay | d → u | n → p | e- + ν̄e |
| β+ decay | u → d | p → n | e+ + νe |
Key Understanding: Beta decay is fundamentally about quarks changing flavour:
- β- decay: down quark becomes up quark
- β+ decay: up quark becomes down quark
The Weak Force
These quark transformations are mediated by the weak nuclear force, one of the four fundamental forces of nature. The weak force is responsible for:
- Changing quark flavour
- Beta decay processes
- Interactions involving neutrinos
6. Leptons - The Other Fundamental Particles
What Are Leptons?
Leptons are fundamental particles that do NOT experience the strong nuclear force. Unlike protons and neutrons (which are made of quarks), leptons are truly fundamental - they have no internal structure.
Key Distinction:
- Quarks: Experience strong force, found in combinations (protons, neutrons, mesons)
- Leptons: Do NOT experience strong force, exist independently
The Six Leptons
There are six leptons, organized in three generations:
| Generation | Charged Lepton | Charge | Neutrino | Charge |
|---|---|---|---|---|
| First | Electron (e-) | -e | Electron neutrino (νe) | 0 |
| Second | Muon (μ-) | -e | Muon neutrino (νμ) | 0 |
| Third | Tau (τ-) | -e | Tau neutrino (ντ) | 0 |
Properties of Leptons
Charged Leptons (Electron, Muon, Tau)
- Charge: -e (or +e for antileptons)
- Experience: Electromagnetic force, weak force, gravity
- Do NOT experience: Strong nuclear force
- Fundamental: No internal structure
Neutrinos (νe, νμ, ντ)
- Charge: Zero (neutral)
- Mass: Extremely small (nearly zero)
- Experience: Only weak force and gravity
- Interaction: Very weak - can pass through matter easily
Electron - The Most Important Lepton
The electron is the most familiar lepton and crucial for:
- Atomic structure (orbits nucleus)
- Chemical bonding
- Electrical current
- Beta decay processes
Electron Properties:
- Symbol: e-
- Charge: -e (-1.60 × 10-19 C)
- Mass: 9.109 × 10-31 kg (≈ 0.0005 u)
- Lepton number: +1
- Fundamental particle (no internal structure)
Neutrinos in Beta Decay
Neutrinos play a crucial role in beta decay:
- β- decay: Emits electron antineutrino (ν̄e)
- β+ decay: Emits electron neutrino (νe)
Beta-minus decay:
n → p + e- + ν̄e
Beta-plus decay:
p → n + e+ + νe
n → p + e- + ν̄e
Beta-plus decay:
p → n + e+ + νe
Antileptons
Every lepton has a corresponding antilepton:
| Lepton | Charge | Antilepton | Charge |
|---|---|---|---|
| Electron (e-) | -e | Positron (e+) | +e |
| Electron neutrino (νe) | 0 | Electron antineutrino (ν̄e) | 0 |
| Muon (μ-) | -e | Antimuon (μ+) | +e |
Lepton Number Conservation
In all particle interactions, lepton number is conserved:
- Leptons: lepton number = +1
- Antileptons: lepton number = -1
- Non-leptons: lepton number = 0
abel.masitsa.com Works
In quantum chromodynamics (QCD)—the theory describing the strong force—quarks carry a type of “charge” called color charge. It’s not related to actual colors; the names “red,” “green,” and “blue” are just labels to help visualize it.
Here’s the idea:
Three colors: Every quark can have one of three color charges: red, green, or blue. Antiquarks have the corresponding anticolors: antired, antigreen, or antiblue.
Strong interaction: The color charge is what allows quarks to interact via the strong force, mediated by gluons. Gluons themselves also carry color charge, which makes the strong force extremely complex.
Color confinement: Quarks are never found alone because of color confinement. They always combine to form “color-neutral” particles:
Baryons (like protons and neutrons) have three quarks—one of each color—so they combine to “white” (neutral).
Mesons have a quark and an antiquark, combining a color with its anticolor to be neutral.
So when we say a quark has a color charge, it means it interacts via the strong force and must combine with other quarks in a way that the overall particle is color-neutral.