Annihilation is a fundamental process in particle physics where a particle and its corresponding antiparticle collide, resulting in the conversion of their mass into energy. This phenomenon is pivotal in various applications, including Positron Emission Tomography (PET) scanning, a crucial diagnostic tool in medical physics. Understanding annihilation and mass conservation is essential for students studying Physics - 9702 at AS & A Level, providing insights into both theoretical concepts and practical applications in medical imaging technologies.

Key Concepts

Particle and Antiparticle Basics

In the realm of particle physics, every fundamental particle has a corresponding antiparticle with equivalent mass but opposite charge and other quantum numbers. For instance, the antiparticle of the electron is the positron. When a particle meets its antiparticle, they can annihilate each other, leading to the conversion of their mass into energy, typically in the form of photons.

Annihilation Process

Annihilation is governed by the principle of conservation of mass-energy, a cornerstone of Einstein's theory of relativity. The process can be described by the equation: $$ E = mc^2 $$ where $ E $ is energy, $ m $ is mass, and $ c $ is the speed of light in a vacuum. When a particle and its antiparticle annihilate, their combined mass is converted into energy, adhering to this equation. For example, when an electron ($ e^- $) collides with a positron ($ e^+ $), their annihilation can produce two gamma-ray photons: $$ e^- + e^+ \rightarrow \gamma + \gamma $$ This reaction ensures the conservation of both energy and momentum.

Mass-Energy Equivalence

The concept of mass-energy equivalence is crucial to understanding annihilation. It posits that mass can be converted into energy and vice versa. In annihilation, the masses of the particle and antiparticle are completely transformed into energy, typically electromagnetic radiation. This transformation is efficient, with nearly 100% of the mass being converted, assuming no other particles are involved in the reaction.

Positron Emission Tomography (PET) Scanning

PET scanning is a medical imaging technique that leverages the annihilation process to produce detailed images of processes within the body. In PET, a radioactive tracer emitting positrons is introduced into the body. When a positron encounters an electron, annihilation occurs, producing gamma photons that are detected by the scanner. By analyzing the origin and distribution of these photons, clinicians can construct precise images of biological tissues and detect abnormalities such as tumors.

Conservation Laws in Annihilation

Annihilation adheres to several conservation laws, including:

Conservation of Energy: The total energy before and after annihilation remains constant.
Conservation of Momentum: The total momentum of the system is preserved during the annihilation process.
Conservation of Charge: The net charge before and after annihilation is the same.

These conservation principles ensure that the annihilation process is consistent with the fundamental laws of physics.

Energy Release in Annihilation

The energy released during annihilation is significant due to the high-speed conversion dictated by $ E = mc^2 $. For example, the annihilation of a single electron-positron pair releases approximately 1.022 MeV (mega-electron volts) of energy, manifested as two gamma-ray photons each with 511 keV (kilo-electron volts). This substantial energy release has practical applications in medical imaging and theoretical implications in particle physics.

Role in Astrophysics

Annihilation processes are not confined to laboratory settings; they also play a role in astrophysical phenomena. In regions with high densities of antimatter, such as near certain types of neutron stars or hypothetical antimatter stars, annihilation can produce observable gamma-ray emissions. Studying these emissions helps astrophysicists understand the distribution of matter and antimatter in the universe.

Mathematical Description of Annihilation

The quantitative analysis of annihilation involves calculating the energy and momentum involved. Considering the annihilation of an electron and a positron at rest, the conservation of energy dictates that: $$ 2m_e c^2 = 2E_\gamma $$ where $ m_e $ is the mass of the electron (or positron), and $ E_\gamma $ is the energy of each gamma photon. Solving for $ E_\gamma $ gives: $$ E_\gamma = m_e c^2 = 511 \text{ keV} $$ This equation illustrates that each photon carries half the total energy released during annihilation.

Detection of Annihilation Events

Detecting annihilation events, especially in medical applications like PET scanning, involves sensitive gamma-ray detectors. These detectors capture the high-energy photons emitted during annihilation, allowing for the reconstruction of the event's origin within the body. The accuracy and resolution of PET images depend heavily on the efficiency and precision of these detection systems.

Applications Beyond PET Scanning

Beyond medical imaging, annihilation processes are utilized in various fields:

Material Science: Studying annihilation can reveal defects and impurities in materials through techniques like positron annihilation spectroscopy.
Fundamental Physics Research: Annihilation is a subject of study in high-energy physics experiments, contributing to our understanding of particle interactions and symmetry violations.
Annihilation Rockets: Theoretical propulsion systems, known as annihilation rockets, propose using matter-antimatter annihilation to achieve unprecedented thrust, although practical implementation remains speculative.

Challenges in Harnessing Annihilation

While annihilation offers immense energy potential, harnessing it presents significant challenges:

Antimatter Production: Creating and storing sufficient quantities of antimatter is currently beyond our technological capabilities due to the energy-intensive processes involved.
Containment: Antimatter must be stored in environments free from regular matter to prevent premature annihilation, necessitating advanced containment systems like magnetic traps.
Cost: The production and storage of antimatter are prohibitively expensive, making large-scale applications economically unfeasible with present technology.

Energy Efficiency and Annihilation

The annihilation process is highly energy-efficient in terms of mass-to-energy conversion. However, the net energy gain is contingent upon the energy required to produce and store antimatter. Currently, more energy is invested in creating antimatter than is released through annihilation, resulting in a negative energy balance. Future advancements in antimatter production could potentially change this dynamic, but significant breakthroughs are necessary.

Ethical and Safety Considerations

The potential applications of annihilation, especially in energy production and propulsion, raise ethical and safety concerns:

Safety Risks: Uncontrolled annihilation could release harmful levels of radiation, posing threats to health and the environment.
Weaponization: The immense energy released during annihilation has implications for the development of antimatter-based weapons, necessitating stringent regulatory frameworks.
Resource Allocation: Prioritizing antimatter research and applications must balance scientific advancement with ethical responsibility and societal needs.

Advanced Concepts

Quantum Field Theory and Annihilation

In Quantum Field Theory (QFT), annihilation is described through the interactions of quantum fields representing particles and antiparticles. The annihilation process involves the exchange of virtual particles mediating the interaction between the electron and positron fields. QFT provides a comprehensive framework for calculating annihilation cross-sections and understanding the probabilistic nature of particle interactions at quantum scales.

Feynman Diagrams and Annihilation Processes

Feynman diagrams are graphical representations that depict the interactions between particles in quantum field theory. In the case of electron-positron annihilation:

Lines represent particle paths, with arrows indicating their direction in time.
Vertices represent interaction points where particles annihilate or are created.
Wavy lines denote the exchange of force-carrying particles, such as photons.

The simplest annihilation process involves a vertex where an electron and positron annihilate into a virtual photon, which then decays into two real photons. Higher-order diagrams include additional loops and virtual particle exchanges, contributing to more precise calculations of annihilation rates.

Cross-Section Calculations in Annihilation

The cross-section of an annihilation process quantifies the probability of annihilation occurring under specific conditions. It depends on factors such as the relative velocity of particles and the energy of the interaction. The calculation involves integrating over the possible final states and considering the symmetries and conservation laws governing the process. Mathematically, the cross-section $ \sigma $ for electron-positron annihilation into two photons can be derived using perturbative methods in QFT: $$ \sigma = \frac{\pi \alpha^2}{m_e^2} \left(\frac{v}{c}\right) $$ where $ \alpha $ is the fine-structure constant, $ m_e $ is the electron mass, and $ v $ is the relative velocity of the annihilating particles.

Threshold Energy and Annihilation Channels

For annihilation to occur, the particles must have sufficient energy to overcome any potential barriers or to produce the required number of photons. The minimum energy required for electron-positron annihilation into two photons is twice the rest mass energy of the electron: $$ E_{threshold} = 2m_e c^2 \approx 1.022 \text{ MeV} $$ Beyond this threshold, additional annihilation channels become accessible, such as annihilation into three photons or the production of other particle-antiparticle pairs, depending on the available energy.

Spin and Annihilation Symmetry Considerations

The spins of particles and antiparticles influence the annihilation process. Electrons and positrons are spin-½ particles, and their annihilation must conserve total spin and angular momentum. The symmetry properties of particles under parity (mirror reflection) and charge conjugation (particle-antiparticle interchange) also affect the annihilation outcomes. Selection rules derived from these symmetries determine the allowed final states and the probabilities of different annihilation channels.

Positronium and Its Role in Annihilation

Positronium is a bound state of an electron and a positron, analogous to a hydrogen atom but consisting entirely of leptons. It exists in two distinct forms based on the spin alignment:

Para-Positronium: Spins are antiparallel, leading to a singlet state that annihilates into two photons with a lifetime of approximately 125 picoseconds.
Ortho-Positronium: Spins are parallel, resulting in a triplet state that annihilates into three photons with a longer lifetime of about 142 nanoseconds.

Studying positronium provides deeper insights into the annihilation process, quantum electrodynamics (QED), and bound state interactions.

Energy Spectrum of Annihilation Photons

The energy distribution of photons emitted during annihilation depends on the relative motion of the annihilating particles. For annihilation at rest, each photon carries an energy equal to the rest mass energy of the electron (511 keV). However, if the particles possess kinetic energy, the photons' energies can vary due to Doppler shifts. Analyzing the energy spectrum of annihilation photons aids in determining the dynamics of the annihilation event and the properties of the involved particles.

Role of Conservation Laws in Advanced Annihilation Studies

Beyond basic conservation laws, advanced studies of annihilation incorporate additional principles:

Lepton Number Conservation: Ensures that the total number of leptons minus antileptons remains constant, affecting possible annihilation products.
CP Symmetry: Investigates whether the combined charge conjugation (C) and parity (P) symmetries are conserved or violated during annihilation, contributing to our understanding of matter-antimatter asymmetry in the universe.
Gauge Symmetry: Governs the interactions between particles and antiparticles, influencing the annihilation process's dynamics and allowed pathways.

These advanced considerations enrich the theoretical framework surrounding annihilation and its implications in fundamental physics.

Mathematical Modeling of Annihilation Processes

Mathematical models of annihilation incorporate various factors, including particle spin, relative velocity, and interaction potential. Differential cross-sections provide detailed predictions of annihilation probabilities as functions of angles and energies. Numerical simulations and computational physics techniques are often employed to solve complex models that account for multiple interacting variables, enabling accurate predictions and comparisons with experimental data.

Annihilation in High-Energy Physics Experiments

In high-energy physics, annihilation processes are studied in particle accelerators where beams of particles and antiparticles collide at high velocities. These experiments investigate the fundamental properties of matter, the forces governing particle interactions, and the creation of new particles. Observing annihilation events in such settings helps validate theoretical models and discover phenomena beyond the Standard Model of particle physics.

Thermodynamics and Annihilation

Annihilation impacts the thermodynamic properties of systems containing matter and antimatter. The release of energy during annihilation affects the temperature and entropy of the system. In cosmological contexts, annihilation of particles and antiparticles in the early universe influenced the thermal history and evolution of cosmic structures. Understanding these thermodynamic effects is essential for constructing accurate models of the universe's development.

Interdisciplinary Connections: Annihilation in Chemistry and Biology

Annihilation principles extend beyond physics into other scientific disciplines:

Chemistry: Positron annihilation spectroscopy is used to study molecular structures, chemical bonding, and defects in materials.
Biology: PET scanning, relying on annihilation, plays a vital role in medical diagnostics, enabling the visualization of metabolic processes and the detection of diseases at the cellular level.

These interdisciplinary applications highlight the broad relevance and impact of annihilation studies across various fields of science.

Future Directions in Annihilation Research

Ongoing research in annihilation aims to explore new frontiers:

Advanced Medical Imaging: Enhancing PET technology for higher resolution and more accurate diagnostics.
Quantum Computing: Investigating the role of annihilation in quantum information processing and quantum state control.
Energy Generation: Exploring theoretical models for harnessing antimatter annihilation as a potent energy source, despite current technological limitations.

Future advancements promise to deepen our understanding of annihilation and expand its practical applications.

Comparison Table

Aspect	Particle-Antiparticle Annihilation	Other Particle Interactions
Definition	Process where a particle and its antiparticle collide, converting their mass into energy.	Includes interactions like scattering, decay, and fusion without necessarily involving particle-antiparticle pairs.
Energy Conversion	Mass is fully converted into energy, adhering to $ E = mc^2 $.	Energy changes depend on the specific interaction; mass may not be conserved.
Conservation Laws	Conserves energy, momentum, charge, and other quantum numbers.	Generally conserves energy and momentum, but specifics vary by interaction type.
Applications	PET scanning, material science, theoretical physics research.	Varies widely: from nuclear power generation to fundamental particle research.
Energy Released	High energy release due to complete mass-to-energy conversion.	Energy release varies; not all interactions result in significant energy change.

Summary and Key Takeaways

Annihilation occurs when a particle meets its antiparticle, converting their mass into energy.
This process is fundamental in applications like PET scanning, aiding medical diagnostics.
Conservation laws of energy, momentum, and charge govern annihilation events.
Advanced studies delve into quantum field theory, cross-section calculations, and interdisciplinary applications.
Despite its potential, harnessing annihilation faces significant technological and ethical challenges.

Examiner Tip

Tips

• **Memorize Key Equations:** Ensure you remember $ E = mc^2 $ and the annihilation reaction $ e^- + e^+ \rightarrow \gamma + \gamma $ for quick recall during exams.
• **Understand Conservation Laws:** Focus on how energy, momentum, and charge are conserved during annihilation to solve related problems accurately.
• **Use Mnemonics:** Remember "A.M.C." for Annihilation, Mass-energy conservation, and Charge conservation to recall key concepts.

Did You Know

1. The concept of antimatter was first predicted by Paul Dirac in 1928, long before any antimatter particles were experimentally discovered.
2. Antimatter is extremely rare in the observable universe, with scientists still trying to understand why there is an imbalance between matter and antimatter.
3. The annihilation of matter and antimatter produces some of the most energetic events in the universe, similar to those seen in gamma-ray bursts.

Common Mistakes

1. **Confusing Energy and Mass Conservation:** Students often think energy is created during annihilation. In reality, energy is conserved by converting mass into energy.
2. **Incorrect Photon Count:** Believing annihilation always produces two photons. While two-photon annihilation is common for electron-positron pairs at rest, higher energy levels can result in more photons.
3. **Ignoring Relativistic Effects:** Neglecting the effects of particle velocity on annihilation outcomes, leading to inaccurate energy calculations.

FAQ

What is antimatter?

Antimatter consists of particles that are counterparts to regular matter particles, having the same mass but opposite charges and quantum numbers.

How does annihilation conserve mass?

Annihilation conserves mass by converting the mass of the particle and antiparticle entirely into energy, as described by $ E = mc^2 $.

Why is annihilation important in PET scans?

In PET scans, positrons emitted from radioactive tracers annihilate with electrons in the body, producing gamma photons that are detected to create detailed images of internal processes.

Can annihilation occur with any particle and its antiparticle?

Yes, annihilation can occur with any particle and its corresponding antiparticle, provided they come into contact under suitable conditions.

What are the main challenges in using antimatter as an energy source?

The main challenges include the immense difficulty and cost of producing and storing antimatter, as well as ensuring safe containment to prevent unintended annihilation.

1. Capacitance

1.1 Energy Stored in a Capacitor

1.1.1 Determine electric potential energy stored in a capacitor from the area under the potential–charge g

1.1.2 Recall and use W = ½QV = ½CV²

1.2 Discharging a Capacitor

1.2.1 Analyze graphs of potential difference, charge, and current during capacitor discharge

1.2.2 Recall and use τ = RC for the time constant during discharge

1.2.3 Use equations of the form x = x₀e^(-t / RC) for current, charge, or potential during discharge

1.3 Capacitors and Capacitance

1.3.1 Define capacitance for isolated spherical conductors and parallel plate capacitors

1.3.2 Recall and use C = Q / V

1.3.3 Derive formulae for combined capacitance of capacitors in series and parallel

1.3.4 Use capacitance formulae for capacitors in series and parallel

2. Nuclear Physics

2.1 Mass Defect and Nuclear Binding Energy

2.1.1 Sketch the variation of binding energy per nucleon with nucleon number

2.1.2 Explain nuclear fusion and nuclear fission

2.1.3 Calculate the energy released in nuclear reactions using E = c²∆m

2.1.4 Understand the equivalence between energy and mass (E = mc²)

2.1.5 Define and use the terms mass defect and binding energy

2.2 Radioactive Decay

2.2.1 Understand that fluctuations in count rate provide evidence for random decay

2.2.2 Understand that radioactive decay is spontaneous and random

2.2.3 Define activity and decay constant, and recall A = λN

2.2.4 Define half-life

2.2.5 Use λ = 0.693 / t₁/₂ for the half-life relationship

2.2.6 Understand exponential decay and use the relationship x = x₀e^(-λt)

3. Kinematics

3.1 Equations of Motion

3.1.1 Define and use distance, displacement, speed, velocity, acceleration

3.1.2 Use graphical methods to represent motion

3.1.3 Determine displacement from velocity–time graph

3.1.4 Determine velocity using gradient of displacement–time graph

3.1.5 Determine acceleration using gradient of velocity–time graph

3.1.6 Derive equations for uniformly accelerated motion

3.1.7 Solve problems of uniformly accelerated motion

3.1.8 Describe experiment to determine acceleration due to gravity

3.1.9 Explain motion with uniform velocity and perpendicular acceleration

4. Deformation of Solids

4.1 Stress and Strain

4.1.1 Understand and use the terms load, extension, compression, and limit of proportionality

4.1.2 Recall and use Hooke’s law

4.1.3 Recall and use the formula for spring constant k = F / x

4.1.4 Define and use terms stress, strain, and Young's modulus

4.1.5 Describe an experiment to determine Young’s modulus

4.1.6 Understand deformation caused by tensile or compressive forces

4.2 Elastic and Plastic Behaviour

4.2.1 Understand elastic and plastic deformation and elastic limit

4.2.2 Understand area under the force–extension graph as work done

4.2.3 Calculate elastic potential energy using EP = ½kx²

5. Gravitational Fields

5.1 Gravitational Field of a Point Mass

5.1.1 Understand that g is approximately constant for small height changes near Earth's surface

5.1.2 Recall and use g = GM / r²

5.1.3 Derive and use g = GM / r² for gravitational field strength

5.2 Gravitational Potential

5.2.1 Define gravitational potential as work done per unit mass in bringing a test mass from infinity

5.2.2 Use ϕ = -GM / r for gravitational potential due to a point mass

5.2.3 Use EP = -GMm / r for gravitational potential energy between two point masses

5.3 Gravitational Field

5.3.1 Define gravitational field as force per unit mass

5.3.2 Represent a gravitational field using field lines

5.4 Gravitational Force Between Point Masses

5.4.1 For point outside uniform sphere, treat mass as a point mass at its center

5.4.2 Analyze circular orbits in gravitational fields

5.4.3 Recall and use Newton's law of gravitation F = Gm₁m₂ / r²

6. Electricity

6.1 Resistance and Resistivity

6.1.1 Understand that the resistance of a thermistor decreases as temperature increases

6.1.2 Define resistance and recall and use V = IR

6.1.3 Sketch I–V characteristics for metallic conductor, semiconductor diode, and filament lamp

6.1.4 Explain that the resistance of a filament lamp increases as current increases

6.1.5 State Ohm’s law and recall and use R = ρL / A

6.1.6 Understand that the resistance of an LDR decreases as light intensity increases

6.2 Electric Current

6.2.1 Understand that an electric current is a flow of charge carriers

6.2.2 Understand that the charge on charge carriers is quantised

6.2.3 Recall and use Q = It

6.2.4 Use I = Anvq for current-carrying conductors

6.3 Potential Difference and Power

6.3.1 Define potential difference as energy transferred per unit charge

6.3.2 Recall and use V = W / Q

6.3.3 Recall and use P = VI, P = I²R, P = V² / R

7. D.C. Circuits

7.1 Practical Circuits

7.1.1 Recall and use the circuit symbols in the syllabus

7.1.2 Draw and interpret circuit diagrams using circuit symbols

7.1.3 Define electromotive force (e.m.f.) of a source as energy transferred per unit charge

7.1.4 Distinguish between e.m.f. and potential difference (p.d.)

7.1.5 Understand the effects of internal resistance on terminal potential difference

7.2 Kirchhoff’s Laws

7.2.1 Recall Kirchhoff’s first law: conservation of charge

7.2.2 Recall Kirchhoff’s second law: conservation of energy

7.2.3 Derive the formula for combined resistance of resistors in series using Kirchhoff’s laws

7.2.4 Use the formula for combined resistance of resistors in series

7.2.5 Derive the formula for combined resistance of resistors in parallel using Kirchhoff’s laws

7.2.6 Use the formula for combined resistance of resistors in parallel

7.2.7 Use Kirchhoff’s laws to solve simple circuit problems

7.3 Potential Dividers

7.3.1 Understand the principle of a potential divider circuit

7.3.2 Recall and use the principle of the potentiometer for comparing potential differences

7.3.3 Understand the use of a galvanometer in null methods

7.3.4 Explain the use of thermistors and LDRs in potential dividers to provide a potential dependent on te

8. Thermal Equilibrium

8.1 Thermal Energy Transfer

8.1.1 Understand that thermal energy transfers from higher to lower temperature

8.1.2 Understand that regions of equal temperature are in thermal equilibrium

9. Temperature Scales

9.1 Temperature Measurement

9.1.1 Understand physical properties that vary with temperature (e.g., density, gas volume, resistance)

9.1.2 Convert temperatures between Kelvin and Celsius, and recall T(K) = θ(°C) + 273.15

10. Magnetic Fields

10.1 Concept of a Magnetic Field

10.1.1 Understand that a magnetic field is a field of force produced by moving charges or permanent magnets

10.1.2 Represent a magnetic field using field lines

10.2 Force on a Current-Carrying Conductor

10.2.1 Understand that a force acts on a current-carrying conductor in a magnetic field

10.2.2 Recall and use F = BIL sin θ for the force on a current-carrying conductor in a magnetic field

10.2.3 Define magnetic flux density as the force per unit current per unit length on a wire at right angles

10.3 Force on a Moving Charge

10.3.1 Determine the direction of the force on a charge moving in a magnetic field

10.3.2 Recall and use F = BQv sin θ for the force on a moving charge in a magnetic field

10.3.3 Understand the origin of the Hall voltage and use the expression VH = BI / (ntq) for the Hall voltag

10.3.4 Understand the use of a Hall probe to measure magnetic flux density

10.4 Magnetic Fields Due to Currents

10.4.1 Sketch magnetic field patterns due to currents in a straight wire, flat coil, and solenoid

10.4.2 Understand that magnetic field in a solenoid is increased by a ferrous core

10.4.3 Explain the origin of forces between current-carrying conductors and determine the direction of the

10.5 Electromagnetic Induction

10.5.1 Define magnetic flux as the product of magnetic flux density and area perpendicular to flux directio

10.5.2 Recall and use Φ = BA for magnetic flux

10.5.3 Understand and use the concept of magnetic flux linkage

10.5.4 Explain experiments that show changing magnetic flux induces an e.m.f.

10.5.5 Recall and use Faraday’s and Lenz’s laws of electromagnetic induction

11. Specific Heat Capacity and Latent Heat

11.1 Specific Heat Capacity

11.1.1 Define and use specific heat capacity

11.2 Latent Heat

11.2.1 Define and use specific latent heat; distinguish between fusion and vaporisation

12. Dynamics

12.1 Momentum and Newton’s Laws of Motion

12.1.1 Mass resists change in motion

12.1.2 Recall F = ma and solve related problems

12.1.3 Define and use linear momentum

12.1.4 Force as rate of change of momentum

12.1.5 State and apply Newton’s laws

12.1.6 Describe weight as effect of gravitational field

12.1.7 Weight of an object is mass × gravitational acceleration

12.2 Non-uniform Motion

12.2.1 Understand frictional and drag forces

12.2.2 Describe motion in uniform gravitational field with air resistance

12.2.3 Objects moving against resistive force may reach terminal velocity

12.3 Linear Momentum and its Conservation

12.3.1 State conservation of momentum

12.3.2 Apply conservation of momentum to solve problems

12.3.3 For elastic collision, kinetic energy and relative speed are conserved

12.3.4 Momentum is conserved, but some kinetic energy may change

13. Medical Physics

13.1 Production and Use of Ultrasound

13.1.1 Understand that a piezo-electric crystal changes shape when a p.d. is applied and generates an e.m.f

13.1.2 Understand how ultrasound waves are generated and detected by a piezoelectric transducer

13.1.3 Understand how ultrasound reflection at boundaries provides diagnostic information about internal st

13.1.4 Define specific acoustic impedance as Z = ρc

13.1.5 Use the equation IR / I₀ = (Z₁ – Z₂)² / (Z₁ + Z₂)² for the intensity reflection coefficient

13.2 Production and Use of X-rays

13.2.1 Explain that X-rays are produced by electron bombardment of a metal target and calculate the minimum

13.2.2 Understand the use of X-rays in imaging internal body structures and the term 'contrast' in X-ray im

13.2.3 Recall and use I = I₀e^(-μx) for the attenuation of X-rays in matter

13.2.4 Understand how computed tomography (CT) produces 3D images by combining multiple 2D X-ray images

13.3 PET Scanning

13.3.1 Understand that a tracer contains radioactive nuclei and is introduced into the body for imaging

13.3.2 Understand that β+ decay is used in positron emission tomography (PET)

13.3.3 Understand that annihilation occurs when a particle interacts with its antiparticle, conserving mass

13.3.4 Explain how gamma-ray photons from annihilation are detected to create an image of tracer concentrat

14. Waves

14.1 Progressive Waves

14.1.1 Describe wave motion in ropes, springs, and ripple tanks

14.1.2 Understand and use the terms displacement, amplitude, phase difference, period, frequency, wavelengt

14.1.3 Use time-base and y-gain on a cathode-ray oscilloscope (CRO) to determine frequency and amplitude

14.1.4 Derive and use v = f λ for the wave equation

14.1.5 Recall and use v = f λ

14.1.6 Understand energy transfer by a progressive wave

14.1.7 Recall and use intensity = power / area, intensity ∝ (amplitude)²

14.2 Transverse and Longitudinal Waves

14.2.1 Compare transverse and longitudinal waves

14.2.2 Analyze and interpret graphical representations of transverse and longitudinal waves

14.3 Doppler Effect for Sound Waves

14.3.1 Understand the change in frequency when a sound source moves relative to a stationary observer

14.3.2 Use the expression f₀ = fₛ(v / (v ± vₛ)) for the observed frequency

14.4 Electromagnetic Spectrum

14.4.1 State all electromagnetic waves are transverse waves traveling at the same speed in free space

14.4.2 Recall the range of wavelengths from radio waves to γ-rays

14.4.3 Recall that wavelengths 400–700 nm are visible to the human eye

14.5 Polarisation

14.5.1 Understand that polarisation is a phenomenon associated with transverse waves

14.5.2 Recall and use Malus's law (I = I₀ cos²θ) to calculate intensity of a plane-polarised wave after pas

15. The Mole

15.1 The Mole

15.1.1 Understand that amount of substance is an SI base quantity with the unit mol

15.1.2 Use molar quantities where one mole contains Avogadro's constant of particles

16. Equation of State

16.1 Ideal Gas Law

16.1.1 Understand that a gas obeying pV ∝ T is an ideal gas

16.1.2 Recall and use the equation pV = nRT for an ideal gas

16.1.3 Recall pV = NkT, where N = number of molecules and k is Boltzmann constant

16.1.4 Use the relationship k = R / NA

17. Kinetic Theory of Gases

17.1 Kinetic Theory

17.1.1 State the basic assumptions of the kinetic theory of gases

17.1.2 Explain pressure exerted by a gas due to molecular movement

17.1.3 Derive and use pV = (3/2)NmkT for pressure of a gas

17.1.4 Compare pV = (3/2)NmkT with pV = NkT to deduce average kinetic energy of a molecule

18. Particle Physics

18.1 Atoms, Nuclei and Radiation

18.1.1 Infer the existence and small size of the nucleus from α-particle scattering

18.1.2 Describe the nuclear atom model: protons, neutrons, and electrons

18.1.3 Distinguish between nucleon number and proton number

18.1.4 Understand isotopes as forms of the same element with different neutrons

18.1.5 Use the notation AZX for nuclides representation

18.1.6 Understand conservation of nucleon number and charge in nuclear processes

18.1.7 Describe the composition, mass, and charge of α-, β-, and γ-radiations

18.1.8 Understand antiparticles and positrons as antiparticles of electrons

18.1.9 State that (electron) antineutrinos are produced during β- decay and neutrinos during β+ decay

18.1.10 Represent α- and β-decay using radioactive decay equations

18.1.11 Use unified atomic mass unit (u) for mass

18.2 Fundamental Particles

18.2.1 Understand quarks as fundamental particles with six flavours

18.2.2 Understand hadrons as baryons (three quarks) or mesons (one quark and one antiquark)

18.2.3 Describe changes in quark composition during β- and β+ decay

18.2.4 Describe protons and neutrons as composed of quarks

18.2.5 Recall and use the charge of each quark and its respective antiquark

18.2.6 Recall electrons and neutrinos as fundamental particles (leptons)

19. Internal Energy

19.1 Internal Energy

19.1.1 Understand that internal energy is the sum of kinetic and potential energies of molecules in a syste

19.1.2 Relate rise in temperature to an increase in internal energy

20. Forces, Density and Pressure

20.1 Turning Effects of Forces

20.1.1 Weight acts at a single point: centre of gravity

20.1.2 Define and apply the moment of a force

20.1.3 Understand the concept of a couple

20.1.4 Define and apply torque of a couple

20.2 Equilibrium of Forces

20.2.1 State and apply the principle of moments

20.2.2 System in equilibrium has no resultant force or torque

20.2.3 Use a vector triangle to represent coplanar forces in equilibrium

20.3 Density and Pressure

20.3.1 Define and use density

20.3.2 Define and use pressure

20.3.3 Derive equation for hydrostatic pressure ∆p = ρg∆h

20.3.4 Use the equation ∆p = ρg∆h

20.3.5 Understand upthrust as the effect of hydrostatic pressure

20.3.6 Calculate upthrust using F = ρgV (Archimedes' principle)

21. Astronomy and Cosmology

21.1 Standard Candles

21.1.1 Understand luminosity as the total power radiated by a star

21.1.2 Recall and use the inverse square law F = L / (4πd²) for radiant flux intensity

21.1.3 Understand that an object with known luminosity is a standard candle

21.1.4 Use standard candles to determine distances to galaxies

21.2 Stellar Radii

21.2.1 Recall and use Wien’s displacement law λmax ∝ 1 / T to estimate the surface temperature of a star

21.2.2 Use Stefan–Boltzmann law L = 4πσr²T⁴

21.2.3 Use Wien’s law and Stefan–Boltzmann law to estimate the radius of a star

21.3 Hubble’s Law and Big Bang Theory

21.3.1 Understand redshift and the increase in wavelength of light from distant objects

21.3.2 Use ∆λ / λ = ∆f / f = v / c for redshift

21.3.3 Explain why redshift suggests the Universe is expanding

21.3.4 Recall and use Hubble’s law v = H₀d to explain the Big Bang theory

22. First Law of Thermodynamics

22.1 First Law

22.1.1 Recall and use W = p∆V for work done when the volume of a gas changes at constant pressure

22.1.2 Understand the difference between work done by a gas and work done on a gas

22.1.3 Recall and use the first law of thermodynamics: ∆U = q + W

23. Alternating Currents

23.1 Characteristics of Alternating Currents

23.1.1 Understand and use terms period, frequency, and peak value for alternating current or voltage

23.1.2 Use x = x₀ sin(ωt) for sinusoidal alternating current or voltage

23.1.3 Recall that the mean power in a resistive load is half the maximum power for sinusoidal current

23.1.4 Distinguish between root-mean-square (r.m.s.) and peak values and recall I₀r.m.s = I₀ / √2 and V₀r.m

23.2 Rectification and Smoothing

23.2.1 Distinguish graphically between half-wave and full-wave rectification

23.2.2 Explain the use of a single diode for half-wave rectification

23.2.3 Explain the use of four diodes (bridge rectifier) for full-wave rectification

23.2.4 Analyze the effect of a capacitor in smoothing, including the effect of capacitance and load resista

24. Superposition

24.1 Stationary Waves

24.1.1 Explain and use the principle of superposition

24.1.2 Understand experiments demonstrating stationary waves using microwaves, stretched strings, and air c

24.1.3 Explain the formation of stationary waves using graphical methods and identify nodes and antinodes

24.1.4 Determine wavelength from the positions of nodes or antinodes

24.2 Diffraction

24.2.1 Explain diffraction and show understanding of related experiments

24.2.2 Understand the effect of gap width relative to wavelength in diffraction experiments

24.3 Interference

24.3.1 Understand the terms interference and coherence

24.3.2 Demonstrate two-source interference using water waves, sound, light, and microwaves

24.3.3 Understand the conditions required for two-source interference fringes

24.3.4 Recall and use λ = ax / D for double-slit interference with light

24.4 Diffraction Grating

24.4.1 Recall and use d sin θ = nλ for diffraction grating calculations

24.4.2 Describe the use of a diffraction grating to determine the wavelength of light

25. Simple Harmonic Oscillations

25.1 Simple Harmonic Motion

25.1.1 Understand and use terms displacement, amplitude, period, frequency, angular frequency, and phase di

25.1.2 Understand that simple harmonic motion occurs when acceleration is proportional to displacement from

25.1.3 Use a = -ω²x and recall x = x₀ sin(ωt) as the solution

25.1.4 Use v = v₀ cos(ωt) and v = ±ω√(x₀² - x²) for velocity

26. Energy in Simple Harmonic Motion

26.1 Energy in SHM

26.1.1 Describe the interchange between kinetic and potential energy during SHM

26.1.2 Recall and use E = ½mω²x₀² for the total energy of a system undergoing SHM

27. Quantum Physics

27.1 Energy and Momentum of a Photon

27.1.1 Understand that electromagnetic radiation has a particulate nature

27.1.2 Recall and use E = hf for the energy of a photon

27.1.3 Use the electronvolt (eV) as a unit of energy

27.1.4 Understand that a photon has momentum and use p = E / c for photon momentum

27.2 Photoelectric Effect

27.2.1 Understand that photoelectrons are emitted from a metal surface when illuminated by electromagnetic

27.2.2 Understand and use the terms threshold frequency and threshold wavelength

27.2.3 Explain photoelectric emission in terms of photon energy and work function

27.2.4 Recall and use hf = Φ + ½mv² for the maximum kinetic energy of photoelectrons

27.2.5 Explain why the maximum kinetic energy of photoelectrons is independent of intensity, while current

27.3 Wave-Particle Duality

27.3.1 Understand that the photoelectric effect shows the particulate nature of light, while diffraction sh

27.3.2 Describe and interpret electron diffraction as evidence for the wave nature of particles

27.3.3 Understand the de Broglie wavelength as the wavelength associated with a moving particle

27.3.4 Recall and use λ = h / p for de Broglie wavelength

27.4 Energy Levels in Atoms and Line Spectra

27.4.1 Understand discrete electron energy levels in atoms (e.g., atomic hydrogen)

27.4.2 Understand the appearance and formation of emission and absorption line spectra

27.4.3 Recall and use hf = E₁ – E₂ for the energy difference between electron energy levels

28. Damped and Forced Oscillations, Resonance

28.1 Damped Oscillations

28.1.1 Understand that damping occurs due to resistive forces

28.1.2 Understand the types of damping: light, critical, and heavy damping

28.2 Resonance

28.2.1 Understand that resonance occurs when an oscillating system is forced to oscillate at its natural fr

29. Work, Energy and Power

29.1 Energy Conservation

29.1.1 Understand the concept of work, and recall W = F × s

29.1.2 Apply the principle of conservation of energy

29.1.3 Understand efficiency as useful energy output / total energy input

29.1.4 Use efficiency concept to solve problems

29.1.5 Define power as work done per unit time

29.1.6 Solve problems using P = W / t

29.1.7 Derive P = Fv and solve problems

29.2 Gravitational Potential Energy and Kinetic Energy

29.2.1 Derive ∆EP = mg∆h for gravitational potential energy changes

29.2.2 Recall and use ∆EP = mg∆h for gravitational potential energy changes

29.2.3 Derive EK = ½mv² for kinetic energy

29.2.4 Recall and use EK = ½mv² for kinetic energy

30. Electric Fields

30.1 Electric Fields and Field Lines

30.1.1 Understand that an electric field is a field of force and define it as force per unit positive charg

30.1.2 Represent an electric field using field lines

30.2 Uniform Electric Fields

30.2.1 Recall and use E = ∆V / ∆d to calculate electric field strength between charged parallel plates

30.2.2 Describe the effect of a uniform electric field on the motion of charged particles

30.3 Electric Force Between Point Charges

30.3.1 Understand that, for a point outside a spherical conductor, the charge may be considered a point mas

30.3.2 Recall and use Coulomb’s law F = Q₁Q₂ / (4πε₀r²) for the force between two point charges

30.4 Electric Field of a Point Charge

30.4.1 Recall and use E = Q / (4πε₀r²) for the electric field strength due to a point charge

30.5 Electric Potential

30.5.1 Define electric potential as work done per unit positive charge in bringing a test charge from infin

30.5.2 Recall and use V = Q / (4πε₀r) for electric potential due to a point charge

30.5.3 Understand how electric potential leads to electric potential energy of two point charges and use EP

31. Physical Quantities and Units

31.1 Physical Quantities

31.1.1 Physical quantities consist of magnitude and unit

31.1.2 Estimate physical quantities from the syllabus

31.2 SI Units

31.2.1 SI base units: mass, length, time, current, temperature

31.2.2 Express derived units from SI base units

31.2.3 Check homogeneity of physical equations

31.2.4 Use prefixes (pico, nano, micro, kilo, etc.)

31.3 Errors and Uncertainties

31.3.1 Understand systematic and random errors

31.3.2 Assess uncertainty in derived quantities

31.4 uniform Electric Fields

31.4.1 Distinguish between precision and accuracy

31.5 Scalars and Vectors

31.5.1 Difference between scalar and vector quantities

31.5.2 Add and subtract coplanar vectors

31.5.3 Represent a vector as components

32. Motion in a Circle

32.1 Centripetal Acceleration

32.1.1 Understand centripetal acceleration and its role in circular motion

32.1.2 Recall and use a = rω² and a = v² / r

32.1.3 Recall and use F = mrω² and F = mv² / r

32.1.4 Understand force causing centripetal acceleration is always perpendicular to motion

32.2 Kinematics of Uniform Circular Motion

32.2.1 Recall and use ω = 2π / T and v = rω

32.2.2 Understand and use angular speed

32.2.3 Define and express angular displacement in radians

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Understand that Annihilation Occurs When a Particle Interacts with Its Antiparticle, Conserving Mass

Introduction