Prefixes such as pico, nano, micro, and kilo play a crucial role in the International System of Units (SI) by providing scalable measurement units for various physical quantities. Understanding these prefixes is essential for students preparing for AS & A Level Physics (9702), as they facilitate precise scientific communication and enhance problem-solving skills.

Key Concepts

Understanding SI Prefixes

SI prefixes are standardized prefixes used to denote powers of ten in measurement units, facilitating the expression of very large or very small quantities in a manageable form. They are integral to the SI system, which is the most widely used system of measurement in science and engineering.

Common SI Prefixes and Their Multipliers

The most commonly used SI prefixes include:

Kilo (k): Represents a multiplier of $10^{3}$.
Milli (m): Represents a multiplier of $10^{-3}$.
Micro ($\mu$): Represents a multiplier of $10^{-6}$.
Nano (n): Represents a multiplier of $10^{-9}$.
Pico (p): Represents a multiplier of $10^{-12}$.

These prefixes allow for the concise representation of quantities, such as kilograms (kg) for mass or nanometers (nm) for length.

Application of SI Prefixes in Physical Quantities

SI prefixes are applied across various physical quantities to simplify measurements and calculations. For example:

Length: The wavelength of visible light ranges from approximately 400 nm to 700 nm.
Mass: The mass of common objects is often measured in kilograms or grams.
Time: Time intervals in physics experiments might be measured in milliseconds (ms) or picoseconds (ps).

Using SI prefixes ensures clarity and consistency in scientific communication.

SI Prefixes and Unit Conversion

Unit conversion involving SI prefixes requires shifting the decimal point based on the multiplier. For instance, converting 5 kilometers to meters involves multiplying by 1000: $$5 \, \text{km} = 5 \times 10^{3} \, \text{m} = 5000 \, \text{m}$$ Similarly, converting 2500 micrometers to meters: $$2500 \, \mu\text{m} = 2500 \times 10^{-6} \, \text{m} = 0.0025 \, \text{m}$$ Understanding these conversions is fundamental for solving physics problems accurately.

Practical Examples of SI Prefixes

Consider the following examples to illustrate the practical use of SI prefixes:

Electricity: The charge of an electron is approximately $1.602 \times 10^{-19}$ coulombs (C).
Electronics: Capacitors are often rated in microfarads ($\mu$F).
Astronomy: Distances between stars are measured in light-years or kilometers with prefixes like giga (G) and mega (M).

These examples demonstrate how SI prefixes enable precise and efficient measurement across different scientific disciplines.

Advantages of Using SI Prefixes

The adoption of SI prefixes offers several benefits:

Standardization: Provides a universal language for scientific measurements.
Clarity: Reduces ambiguity by clearly indicating the scale of measurement.
Efficiency: Simplifies numerical representation, making calculations more manageable.

These advantages facilitate seamless international collaboration and data sharing in scientific research.

Limitations of SI Prefixes

While SI prefixes are versatile, they have certain limitations:

Scope: Not all units have standardized SI prefixes.
Potential for Misinterpretation: Misuse of prefixes can lead to significant errors in calculations.
Granularity: Extremely large or small quantities may require less common prefixes, complicating communication.

Awareness of these limitations is essential for accurate scientific practice.

Historical Development of SI Prefixes

The development of SI prefixes has evolved to accommodate the growing complexity of scientific measurements. Originating from the metric system, the SI system was formalized in 1960 to provide a coherent framework for unit expressions. Over time, additional prefixes have been introduced to address the needs of various scientific fields, enhancing the system's adaptability and comprehensiveness.

SI Prefixes in Scientific Notation

SI prefixes complement scientific notation by offering a standardized way to express powers of ten. For example, instead of writing $5 \times 10^{3}$ meters, one can write 5 kilometers (5 km). This synergy enhances readability and comprehension, particularly in complex scientific literature.

Implementing SI Prefixes in Experimental Physics

In experimental physics, precision is paramount. Utilizing appropriate SI prefixes ensures that measurements align with the experimental sensitivity and accuracy. For instance, measuring the resistance of a component might require expressing it in kiloohms (kΩ) rather than ohms (Ω) to match the instrument's range and facilitate data analysis.

SI Prefixes in Data Presentation

Effective data presentation often relies on SI prefixes to convey information succinctly. Graphs, tables, and figures benefit from standardized units with prefixes, as they enhance the clarity and interpretability of the data. Consistent use of SI prefixes across different sections of a report or publication ensures uniformity and professionalism.

Impact of SI Prefixes on Computational Physics

In computational physics, algorithms and simulations frequently handle large datasets and complex calculations. SI prefixes streamline the representation of input parameters and output results, optimizing computational efficiency and reducing the likelihood of numerical errors. Proper scaling using SI prefixes is essential for maintaining computational integrity.

Advanced Concepts

Mathematical Derivation of SI Prefix Scaling

The scaling introduced by SI prefixes is fundamentally based on powers of ten. Mathematically, each prefix represents a specific exponent in the decimal system. For example, the prefix "kilo" denotes $10^{3}$, meaning: $$\text{1 km} = 1 \times 10^{3} \, \text{m}$$ Conversely, "micro" represents $10^{-6}$: $$\text{1 } \mu\text{m} = 1 \times 10^{-6} \, \text{m}$$ This exponential relationship simplifies the multiplication and division of units, especially when dealing with logarithmic scales or exponential growth and decay processes in physics.

Dimensional Analysis with SI Prefixes

Dimensional analysis is a critical tool in physics for checking the consistency of equations and computations. SI prefixes facilitate dimensional analysis by standardizing the units used across different terms. For instance, in calculating kinetic energy: $$E_k = \frac{1}{2} m v^2$$ If mass (m) is in kilograms (kg) and velocity (v) in meters per second (m/s), the resulting energy will be in joules (J), maintaining dimensional consistency: $$\text{kg} \cdot \left(\frac{\text{m}}{\text{s}}\right)^2 = \text{kg} \cdot \frac{\text{m}^2}{\text{s}^2} = \text{J}$$ Incorporating SI prefixes ensures that scale factors do not disrupt the dimensional integrity of physical equations.

Advanced Problem-Solving with SI Prefixes

Consider the following problem:

Problem: A nanoparticle has a diameter of 5 nm. Calculate its diameter in meters.
Solution: Using the nano prefix: $$5 \, \text{nm} = 5 \times 10^{-9} \, \text{m} = 5 \times 10^{-9} \, \text{m}$$

This problem illustrates the straightforward conversion facilitated by SI prefixes, enabling efficient computation and comprehension of scales in nanotechnology.

Interdisciplinary Connections: SI Prefixes in Chemistry and Engineering

SI prefixes are not confined to physics but are integral to other scientific disciplines:

Chemistry: The concentration of solutions is often expressed in micromolar (µM) units.
Engineering: Electrical engineers use kilohertz (kHz) to denote frequency ranges in circuits.

These interdisciplinary applications demonstrate the versatility and universal applicability of SI prefixes across various fields of study.

Historical Evolution and Future of SI Prefixes

The SI prefix system has evolved to meet the expanding needs of scientific research. Initially limited to a select few prefixes, the system now encompasses a broader range to accommodate increasingly precise measurements. Looking forward, the development of new prefixes may continue as scientific exploration delves into even more extreme scales, ensuring that the SI system remains robust and adaptable.

Dimensional Homogeneity and SI Prefixes

Dimensional homogeneity is essential for the consistency of physical equations. SI prefixes contribute to dimensional homogeneity by providing a standardized scaling mechanism. For example, in the equation for electrical resistance: $$R = \rho \frac{L}{A}$$ Where $\rho$ is resistivity in ohm-meters (Ω.m), L is length in meters (m), and A is area in square meters (m²). Using appropriate prefixes ensures that each term in the equation is dimensionally consistent, facilitating accurate computations.

Scaling Laws and SI Prefixes

Scaling laws describe how different physical quantities change relative to one another. SI prefixes enable the expression of scaling laws across various magnitudes. For instance, gravitational force between two masses: $$F = G \frac{m_1 m_2}{r^2}$$ If masses are expressed in kilograms (k), and distance in meters (m), the gravitational constant (G) inherently accounts for the scaling factors, ensuring that the force calculation remains accurate across different scales.

SI Prefixes in Quantum Physics

In quantum physics, measurements often involve extremely small scales. SI prefixes like pico (p) and nano (n) are essential for expressing quantities such as the wavelength of photons or the energy levels of electrons. For example, the energy of a photon can be expressed in picojoules (pJ), facilitating precise calculations and theoretical modeling.

Implications of Incorrect SI Prefix Usage

Incorrect application of SI prefixes can lead to significant errors in scientific calculations, potentially impacting experimental outcomes and theoretical models. For example, mistaking kilo (k) for milli (m) would result in a factor discrepancy of $10^{3}$, leading to incorrect measurements and interpretations. Therefore, meticulous attention to SI prefix usage is imperative in all scientific endeavors.

Comparison Table

Prefix	Symbol	Multiplier
Kilo	k	$10^{3}$
Milli	m	$10^{-3}$
Micro	$\mu$	$10^{-6}$
Nano	n	$10^{-9}$
Pico	p	$10^{-12}$

Summary and Key Takeaways

SI prefixes facilitate scalable and standardized measurements in physics.
Understanding prefixes like kilo, milli, micro, nano, and pico is essential for accurate unit conversions.
Proper application of SI prefixes enhances clarity and precision in scientific communication and problem-solving.
SI prefixes are integral across various scientific disciplines, demonstrating their universal applicability.

Examiner Tip

Tips

- **Mnemonic for Prefixes:** Use "King Henry Died By Drinking Chocolate Milk" to remember kilo (k), hecto (h), deka (da), base unit, deci (d), centi (c), milli (m).
- **Practice Conversions:** Regularly practice converting between units with different prefixes to build familiarity.
- **Check Your Work:** Always verify the multiplier used in conversions to avoid significant errors on exams.

Did You Know

1. The prefix "nano" is derived from the Greek word "nanos," meaning "dwarf," reflecting the incredibly small scale it represents.
2. The invention of the picometer ($\text{pm}$) allowed scientists to measure atomic and subatomic structures with unprecedented precision, revolutionizing material science.
3. Kilo prefix is widely used not only in physics but also in everyday contexts, such as in "kilobytes" of digital information.

Common Mistakes

1. **Confusing Prefixes:** Students often mix up "milli" (m) and "micro" ($\mu$), leading to errors in calculations.
  - *Incorrect:* 5 m = $5 \times 10^{-3}$ units.
  - *Correct:* 5 m = 5 meters; 5 millimeters (mm) = $5 \times 10^{-3}$ meters.
2. **Incorrect Unit Conversion:** Forgetting to apply the correct multiplier when converting units with prefixes.
  - *Incorrect:* 3 km = 300 meters.
  - *Correct:* 3 km = $3 \times 10^{3}$ meters = 3000 meters.

FAQ

What is the difference between milli and micro prefixes?

Milli (m) represents $10^{-3}$, while micro ($\mu$) represents $10^{-6}$. This means a millimeter is 1000 times larger than a micrometer.

How do SI prefixes aid in scientific communication?

SI prefixes provide a standardized way to express large and small quantities, enhancing clarity and avoiding ambiguity in scientific discourse.

Can SI prefixes be used with any unit?

While SI prefixes can be applied to many SI units, not all units have standardized prefixes. It's essential to verify the applicability for specific units.

Why is understanding SI prefixes important for physics exams?

Mastery of SI prefixes is crucial for accurate unit conversions, problem-solving, and interpreting scientific data, which are fundamental skills assessed in physics exams.

How can I avoid mistakes with SI prefixes?

Regular practice with unit conversions, using mnemonics, and double-checking multipliers can help prevent common errors related to SI prefixes.

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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Use of Prefixes (pico, nano, micro, kilo, etc.)

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