Particles & Radiation - A-Level Physics

Atomic Structure

Constituents of the Atom

An atom consists of a small, dense, positively charged nucleus containing protons and neutrons, surrounded by orbiting electrons.

Particle	Relative charge	Relative mass	Actual mass (kg)
Proton	+1	1	1.67 × 10⁻²⁷
Neutron	0	1	1.67 × 10⁻²⁷
Electron	−1	1/1836	9.11 × 10⁻³¹

Specific Charge

The specific charge of a particle is its charge divided by its mass. It is measured in C kg⁻¹.

Specific charge = Qm

Worked Example

Calculate the specific charge of a proton.

Charge = 1.60 × 10⁻¹⁹ C

Mass = 1.67 × 10⁻²⁷ kg

Specific charge = 1.60 × 10⁻¹⁹ / 1.67 × 10⁻²⁷ = 9.58 × 10⁷ C kg⁻¹

Notation and Isotopes

Nuclide notation: ^A_ZX, where A = mass number (protons + neutrons), Z = atomic (proton) number.

Isotopes are atoms with the same number of protons but different numbers of neutrons. They have the same chemical properties but different physical properties (e.g., different mass, some may be radioactive).

Key Facts

The strong nuclear force holds the nucleus together against electrostatic repulsion
Unstable nuclei can decay by alpha, beta, or gamma emission
The specific charge of an electron is about 1840 times that of a proton

Particles & Antiparticles

Antimatter

Every particle has a corresponding antiparticle with the same mass but opposite charge (and opposite quantum numbers).

Particle	Symbol	Antiparticle	Symbol
Electron	e⁻	Positron	e⁺
Proton	p	Antiproton	p̄
Neutron	n	Antineutron	n̄
Neutrino	ν_e	Antineutrino	ν̄_e

Pair Production and Annihilation

Pair production: A photon with sufficient energy creates a particle-antiparticle pair. The minimum photon energy required is 2m₀c² (twice the rest energy of the particle).

Annihilation: A particle meets its antiparticle and they are destroyed, producing two photons travelling in opposite directions (to conserve momentum).

Minimum photon energy for pair production: E = 2m₀c²

Annihilation: e⁻ + e⁺ → 2γ

The Photon Model

Electromagnetic radiation is emitted in discrete packets of energy called photons.

E = hf = hcλ

Where h = 6.63 × 10⁻³⁴ J s (Planck's constant), f = frequency, λ = wavelength, c = 3.00 × 10⁸ m s⁻¹.

Exam Tip

In annihilation, two photons are produced (not one) to conserve momentum. Each photon has energy equal to the rest energy of one of the particles (minimum).

Quarks & Leptons

Particle Classification

Particles are classified into two main groups based on whether they feel the strong nuclear force.

Quarks

Quarks are fundamental particles that make up hadrons. There are six flavours, but at A-level you need to know three: up (u), down (d), and strange (s).

Quark	Symbol	Charge	Baryon number	Strangeness
Up	u	+2/3	+1/3	0
Down	d	−1/3	+1/3	0
Strange	s	−1/3	+1/3	−1

Antiquarks have opposite charge, baryon number, and strangeness.

Quark Composition of Hadrons

Particle	Quark composition	Charge	Baryon number
Proton	uud	+2/3 +2/3 −1/3 = +1	+1
Neutron	udd	+2/3 −1/3 −1/3 = 0	+1
π⁺	ud̄	+2/3 +1/3 = +1	0
π⁻	ūd	−2/3 −1/3 = −1	0
K⁺	us̄	+2/3 +1/3 = +1	0

Leptons

Leptons are fundamental particles that do not feel the strong nuclear force. They include electrons, muons, taus, and their associated neutrinos.

Each lepton generation has its own lepton number: electron lepton number (L_e), muon lepton number (L_μ), tau lepton number (L_τ).

Key Facts

Baryons = 3 quarks, Antibaryons = 3 antiquarks, Mesons = quark + antiquark
Quarks never exist in isolation (confinement)
The proton is the only stable baryon; free neutrons decay with a half-life of about 10 minutes

Particle Interactions

Conservation Laws

In all particle interactions, the following quantities must be conserved:

Quantity	Always conserved?	Notes
Charge (Q)	Always	Must balance on both sides
Baryon number (B)	Always	Baryons = +1, antibaryons = −1, others = 0
Lepton number (L)	Always	Each generation conserved separately
Strangeness (S)	Strong & EM only	Can change by ±1 in weak interactions

Exchange Particles (Gauge Bosons)

Forces between particles are mediated by the exchange of virtual gauge bosons.

Force	Exchange particle	Acts on
Electromagnetic	Virtual photon (γ)	Charged particles
Strong nuclear	Gluon (g)	Quarks and gluons
Weak nuclear	W⁺, W⁻, Z⁰	All particles
Gravity	Graviton (hypothetical)	All particles with mass

Beta Decay and the Weak Interaction

β⁻ decay: A neutron decays into a proton, emitting an electron and an electron antineutrino. Mediated by a W⁻ boson.

n → p + e⁻ + ν̄_e

At quark level: d → u + e⁻ + ν̄_e (via W⁻)

β⁺ decay: A proton decays into a neutron, emitting a positron and an electron neutrino. Mediated by a W⁺ boson.

p → n + e⁺ + ν_e

At quark level: u → d + e⁺ + ν_e (via W⁺)

Worked Example

Verify that charge, baryon number and lepton number are conserved in β⁻ decay: n → p + e⁻ + ν̄_e

Charge: 0 → +1 + (−1) + 0 = 0. Conserved.

Baryon number: +1 → +1 + 0 + 0 = +1. Conserved.

Lepton number: 0 → 0 + 1 + (−1) = 0. Conserved.

Exam Tip

The W boson determines which type of weak decay occurs. W⁻ carries away negative charge, W⁺ carries away positive charge. The Z⁰ mediates interactions where no charge is transferred (e.g., neutrino scattering).

Photoelectric Effect

Key Observations

When electromagnetic radiation is incident on a metal surface, electrons may be emitted. This is the photoelectric effect.

Emission occurs only above a certain threshold frequency (f₀), regardless of intensity
Increasing intensity increases the number of electrons emitted, not their maximum kinetic energy
Emission is instantaneous (no time delay)
Maximum kinetic energy of photoelectrons depends on frequency, not intensity

These observations cannot be explained by the wave model of light. They require the photon model.

Einstein's Photoelectric Equation

E_k(max) = hf − φ

Where:

hf = energy of the incident photon
φ (phi) = work function of the metal (minimum energy needed to release an electron)
E_k(max) = maximum kinetic energy of the emitted photoelectron

At the threshold frequency: hf₀ = φ, so f₀ = φ/h

Worked Example

The work function of sodium is 3.65 × 10⁻¹⁹ J. UV light of frequency 8.0 × 10¹⁴ Hz is incident on its surface. Calculate the maximum kinetic energy of the emitted electrons.

E_k(max) = hf − φ

= (6.63 × 10⁻³⁴ × 8.0 × 10¹⁴) − 3.65 × 10⁻¹⁹

= 5.30 × 10⁻¹⁹ − 3.65 × 10⁻¹⁹

= 1.65 × 10⁻¹⁹ J

Exam Tip

A common exam question is to plot a graph of E_k(max) vs frequency. The gradient = h (Planck's constant), the y-intercept = −φ, and the x-intercept = threshold frequency f₀.

Energy Levels & Line Spectra

Discrete Energy Levels

Electrons in atoms can only exist at specific, discrete energy levels. The lowest energy level is the ground state (n = 1).

When an electron moves between energy levels, it must absorb or emit a photon with energy exactly equal to the difference between the two levels.

ΔE = E₂ − E₁ = hf = hcλ

Emission and Absorption Spectra

Emission spectrum: When excited atoms de-excite, they emit photons at specific frequencies, producing bright lines on a dark background.

Absorption spectrum: When white light passes through a cool gas, atoms absorb photons at specific frequencies, producing dark lines on a continuous spectrum.

The emission and absorption lines for a given element occur at the same frequencies, as they correspond to the same energy level transitions.

Electron Volt

The electron volt (eV) is a unit of energy commonly used in particle physics.

1 eV = 1.60 × 10⁻¹⁹ J

Worked Example

The ground state of hydrogen is −13.6 eV and the first excited state is −3.4 eV. Calculate the wavelength of the photon emitted when an electron drops from the first excited state to the ground state.

ΔE = −3.4 − (−13.6) = 10.2 eV = 10.2 × 1.60 × 10⁻¹⁹ = 1.63 × 10⁻¹⁸ J

λ = hc / ΔE = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) / 1.63 × 10⁻¹⁸

λ = 1.22 × 10⁻⁷ m = 122 nm (ultraviolet)

Key Facts

Energy levels are negative because energy must be supplied to remove the electron (ionise the atom)
The ionisation energy corresponds to raising the electron from the ground state to E = 0
Line spectra provide evidence for discrete energy levels in atoms

Atomic Structure

Constituents of the Atom

Specific Charge

Worked Example

Notation and Isotopes

Key Facts

Particles & Antiparticles

Antimatter

Pair Production and Annihilation

The Photon Model

Exam Tip

Quarks & Leptons

Particle Classification

Quarks

Quark Composition of Hadrons

Leptons

Key Facts

Particle Interactions

Conservation Laws

Exchange Particles (Gauge Bosons)

Beta Decay and the Weak Interaction

Worked Example

Exam Tip

Photoelectric Effect

Key Observations

Einstein's Photoelectric Equation

Worked Example

Exam Tip

Energy Levels & Line Spectra

Discrete Energy Levels

Emission and Absorption Spectra

Electron Volt

Worked Example

Key Facts

Particles & Radiation Flashcards

Particles & Radiation Quiz

Particles & Radiation - Mock Exam Questions