The electromagnetic spectrum encompasses a vast range of wavelengths, from the longest radio waves to the shortest γ-rays. Understanding this spectrum is fundamental in AS & A Level Physics (9702), as it underpins many concepts in wave theory, energy transfer, and technological applications. This article delves into the comprehensive range of electromagnetic wavelengths, exploring their properties, interactions, and significance in both scientific and everyday contexts.

Key Concepts

Understanding the Electromagnetic Spectrum

The electromagnetic (EM) spectrum is a continuum of all electromagnetic waves arranged according to their wavelengths and frequencies. These waves propagate through space carrying energy from one place to another. The spectrum is traditionally divided into seven regions: radio waves, microwaves, infrared (IR), visible light, ultraviolet (UV), X-rays, and gamma (γ) rays. Each region has distinct characteristics and applications based on its wavelength and frequency.

Wavelength and Frequency

Wavelength ($\lambda$) and frequency ($f$) are fundamental properties of electromagnetic waves. They are inversely related, as described by the equation:

$$c = \lambda f$$

where $c$ is the speed of light in a vacuum ($3 \times 10^8$ m/s). This relationship indicates that as wavelength increases, frequency decreases, and vice versa. For instance, radio waves have longer wavelengths and lower frequencies compared to gamma rays, which have extremely short wavelengths and high frequencies.

Radio Waves

Radio waves occupy the longest wavelength range in the electromagnetic spectrum, typically from 1 millimeter to 100 kilometers. They are extensively used in communication technologies, including radio broadcasting, television, and mobile phones. Radio waves can penetrate through various media, making them suitable for long-distance transmission.

Applications: Broadcasting, satellite communication, radar systems.
Characteristics: Low energy, can diffract around obstacles, less likely to be absorbed by the atmosphere.

Microwaves

Microwaves have shorter wavelengths than radio waves, ranging from 1 millimeter to 30 centimeters. They are commonly used in microwave ovens for heating food, as well as in radar technology and wireless communication systems like Wi-Fi and Bluetooth.

Applications: Cooking, radar, satellite communication, wireless networking.
Characteristics: Can be focused into narrow beams, susceptible to atmospheric absorption by water vapor.

Infrared (IR)

Infrared waves span wavelengths from approximately 700 nanometers (nm) to 1 millimeter. They are primarily associated with thermal radiation, as objects emit IR radiation based on their temperature. IR technology is used in various applications, including night-vision equipment, remote controls, and thermal imaging.

Applications: Thermal imaging, remote controls, fiber optic communication.
Characteristics: Carries heat energy, absorbed by water and organic materials.

Visible Light

Visible light is the portion of the electromagnetic spectrum that can be detected by the human eye, with wavelengths ranging from approximately 400 nm (violet) to 700 nm (red). It plays a crucial role in vision and various optical technologies. Visible light is also fundamental in studying the properties of materials and astronomical objects.

Applications: Lighting, photography, optical instruments, displays.
Characteristics: Can be refracted, reflected, and diffracted, enabling the formation of images.

Ultraviolet (UV) Light

UV light has shorter wavelengths than visible light, ranging from about 10 nm to 400 nm. It possesses higher energy and can induce chemical reactions, such as the formation of vitamin D in the skin. However, excessive UV exposure can be harmful, causing skin burns and increasing the risk of skin cancer.

Applications: Sterilization, fluorescent lighting, forensic analysis.
Characteristics: High energy, capable of ionizing atoms and molecules, absorbed by ozone in the atmosphere.

X-Rays

X-rays have wavelengths from approximately 0.01 nm to 10 nm and are known for their ability to penetrate various materials, including human tissue. This property makes them invaluable in medical imaging and security scanning. X-rays also play a significant role in crystallography and astrophysics.

Applications: Medical imaging (e.g., CT scans), security scanners, material analysis.
Characteristics: High energy, ionizing radiation, can cause cellular damage.

Gamma Rays

Gamma rays occupy the shortest wavelength range in the electromagnetic spectrum, typically less than 0.01 nm. They are emitted by radioactive nuclei and certain astronomical processes. Due to their immense energy, gamma rays are used in cancer treatment (radiation therapy) and are studied in high-energy astrophysics.

Applications: Cancer treatment, sterilization of medical equipment, astrophysical research.
Characteristics: Extremely high energy, highly penetrating, can ionize atoms and disrupt molecular bonds.

Energy and Photon Concepts

The energy ($E$) of an electromagnetic wave is directly proportional to its frequency, as expressed by the equation:

$$E = hf$$

where $h$ is Planck's constant ($6.626 \times 10^{-34}$ J.s). This equation highlights that higher frequency waves, such as UV and gamma rays, carry more energy per photon compared to lower frequency waves like radio and microwave.

Propagation and Interaction with Matter

Electromagnetic waves interact with matter in various ways, including reflection, refraction, absorption, and transmission. The extent and nature of these interactions depend on the wavelength of the wave and the properties of the material. For instance, visible light is readily absorbed and reflected by surfaces, while radio waves can pass through buildings with minimal attenuation.

Reflection: The bouncing back of waves when they encounter a surface.
Refraction: The bending of waves as they pass from one medium to another.
Absorption: The conversion of wave energy into other forms, such as heat.
Transmission: The passing of waves through a medium.

Speed of Electromagnetic Waves

All electromagnetic waves propagate at the speed of light ($c = 3 \times 10^8$ m/s) in a vacuum. However, their speed can vary when traversing different media. The refractive index ($n$) of a medium determines the speed ($v$) of a wave within it, calculated by:

$$v = \frac{c}{n}$$

For example, light slows down when passing through glass or water, leading to phenomena like the bending of light in lenses.

Electromagnetic Spectrum in Technology and Communications

The diverse range of wavelengths in the electromagnetic spectrum enables a multitude of technological advancements. From the long wavelengths of radio waves facilitating global communication networks to the high-energy gamma rays used in medical diagnostics, each segment of the spectrum serves unique purposes. Understanding these wavelengths is essential for developing and optimizing technologies in telecommunications, healthcare, and scientific research.

Telecommunications: Utilizes radio and microwave frequencies for data transmission.
Healthcare: Employs X-rays and gamma rays for diagnostic imaging and treatment.
Scientific Research: Leverages the entire spectrum for studying physical phenomena and cosmic events.

Advanced Concepts

Theoretical Foundations of the Electromagnetic Spectrum

The electromagnetic spectrum is grounded in Maxwell's equations, which describe how electric and magnetic fields propagate and interact. These equations predict the existence of electromagnetic waves and their behavior in different media. The spectrum's continuous nature arises from the ability to generate waves of any wavelength by varying the oscillation of electric and magnetic fields.

Maxwell's equations are as follows:

$$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$ $$\nabla \cdot \mathbf{B} = 0$$ $$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$$ $$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}$$

These equations collectively describe how time-varying electric fields generate magnetic fields and vice versa, leading to the self-propagating nature of electromagnetic waves.

Quantum Mechanics and Photons

At the quantum level, electromagnetic waves are quantized into particles called photons. Each photon carries energy proportional to its frequency ($E = hf$) and momentum ($p = \frac{h}{\lambda}$). This particle-wave duality is critical in understanding phenomena such as the photoelectric effect, where photons eject electrons from a material, and Compton scattering, where photons collide with electrons, altering their energy and wavelength.

Photoelectric Effect: Demonstrates the particle nature of light, leading to the development of quantum mechanics.
Compton Scattering: Provides evidence for the wave-particle duality of photons.

Wave-Particle Duality and the Uncertainty Principle

The wave-particle duality concept posits that electromagnetic waves exhibit both wave-like and particle-like properties. This duality is fundamental in quantum mechanics, where particles such as photons do not have precise positions and momenta simultaneously, as dictated by Heisenberg's Uncertainty Principle:

$$\Delta x \Delta p \geq \frac{\hbar}{2}$$

where $\Delta x$ is the uncertainty in position, $\Delta p$ is the uncertainty in momentum, and $\hbar$ is the reduced Planck's constant. This principle highlights the inherent limitations in measuring quantum systems accurately.

Electromagnetic Spectrum and Relativity

Einstein's theory of relativity intertwines with the electromagnetic spectrum through the invariant speed of light. According to Special Relativity, the speed of light in a vacuum is constant and does not depend on the observer's frame of reference. This constancy has profound implications for the behavior of electromagnetic waves at high velocities, including time dilation and length contraction effects.

Spectroscopy and the Electromagnetic Spectrum

Spectroscopy involves the study of the interaction between matter and electromagnetic radiation. By analyzing the absorption, emission, and scattering of different wavelengths, scientists can determine the composition, structure, and properties of substances. Techniques such as UV-Vis spectroscopy, infrared spectroscopy, and X-ray spectroscopy are pivotal in fields like chemistry, astronomy, and materials science.

UV-Vis Spectroscopy: Analyzes electronic transitions in molecules.
Infrared Spectroscopy: Investigates vibrational modes of molecules.
X-Ray Spectroscopy: Examines atomic and molecular structures.

Advanced Applications of the Electromagnetic Spectrum

The electromagnetic spectrum's versatility extends to cutting-edge applications in various domains:

Telecommunications: Utilizes specific frequency bands for data transmission, optimizing bandwidth and minimizing interference.
Medical Imaging and Treatment: Employs X-rays for diagnostics and gamma rays for targeted cancer therapy.
Astrophysics: Uses different wavelengths to study celestial objects and phenomena, such as cosmic microwave background radiation and gamma-ray bursts.
Environmental Monitoring: Applies infrared and ultraviolet sensing for tracking atmospheric pollutants and climate change indicators.

Mathematical Modeling of Electromagnetic Waves

Mathematical models of electromagnetic waves involve complex numbers and vector calculus to describe wave propagation, polarization, and interference. Solutions to Maxwell's equations in various coordinate systems yield wave equations that predict the behavior of EM waves in different environments. For example, plane wave solutions represent uniform waves propagating in a single direction, while spherical wave solutions model waves emanating from a point source.

One such solution for a plane wave propagating in the $z$-direction is:

$$\mathbf{E}(z, t) = \mathbf{E}_0 e^{i(kz - \omega t)}$$ $$\mathbf{B}(z, t) = \mathbf{B}_0 e^{i(kz - \omega t)}$$

where $\mathbf{E}_0$ and $\mathbf{B}_0$ are the electric and magnetic field amplitudes, $k$ is the wave number, and $\omega$ is the angular frequency.

Polarization of Electromagnetic Waves

Polarization describes the orientation of the electric field vector in an electromagnetic wave. It can be linear, circular, or elliptical. Polarization is crucial in various technologies, such as polarized sunglasses, liquid crystal displays (LCDs), and optical communication systems, where it is used to encode information.

Linear Polarization: Electric field oscillates in a single plane.
Circular Polarization: Electric field rotates in a circular motion as the wave propagates.
Elliptical Polarization: Combines linear and circular polarization, resulting in an elliptical path.

Interference and Diffraction

Interference occurs when two or more electromagnetic waves superimpose, leading to constructive or destructive patterns. Diffraction refers to the bending of waves around obstacles or through apertures, causing spreading and the formation of characteristic patterns. These phenomena are fundamental in understanding wave behavior and are exploited in technologies like interferometers and diffraction gratings.

Constructive Interference: Waves add up to create regions of higher amplitude.
Destructive Interference: Waves cancel each other out, resulting in lower amplitude regions.
Applications: Holography, optical fibers, and the design of anti-reflective coatings.

Electromagnetic Spectrum and Quantum Field Theory

In quantum field theory, electromagnetic waves are described as excitations of the electromagnetic field, with photons being the quanta that mediate electromagnetic interactions. This framework is essential for understanding particle physics and the interactions governing fundamental forces.

Photon Interactions: Describe how photons interact with charged particles, influencing electromagnetic processes.
Gauge Symmetry: Underpins the formulation of quantum electrodynamics (QED), the theory describing electromagnetic interactions.

Nonlinear Optics and Electromagnetic Waves

Nonlinear optics explores the behavior of electromagnetic waves in nonlinear media, where the response of the material depends nonlinearly on the electric field of the light. This leads to phenomena such as harmonic generation, self-focusing, and the Kerr effect, enabling applications like frequency conversion, ultrafast lasers, and optical switching.

Second-Harmonic Generation: Converts photons to twice their original frequency.
Self-Focusing: Intense laser beams can cause the medium to become more refractive, focusing the beam.

Relativistic Electromagnetic Waves

At high velocities near the speed of light, relativistic effects become significant in the study of electromagnetic waves. Time dilation and length contraction influence wave propagation and interactions, necessitating the use of relativistic electrodynamics to accurately describe phenomena in high-energy environments.

Electromagnetic Spectrum and Information Theory

The electromagnetic spectrum is integral to information theory, particularly in the encoding, transmission, and decoding of data. Techniques like modulation, multiplexing, and compression rely on varying the properties of EM waves to optimize communication systems for efficiency and reliability.

Modulation: Adjusting wave parameters (amplitude, frequency, phase) to encode information.
Multiplexing: Combining multiple signals into one medium for simultaneous transmission.
Compression: Reducing the bandwidth required for data transmission.

Comparison Table

Wavelength Range	Frequency Range	Typical Applications
1 km – 1 mm	300 kHz – 300 GHz	Radio Broadcasting, Radar
30 cm – 1 mm	1 GHz – 300 GHz	Microwave Ovens, Satellite Communication
1 µm – 700 nm	430 THz – 300 THz	Infrared Imaging, Fiber Optics
700 nm – 400 nm	430 THz – 750 THz	Visible Light, Photography
400 nm – 10 nm	750 THz – 30 PHz	Ultraviolet Sterilization, Fluorescent Lighting
10 nm – 0.01 nm	30 PHz – 30 EHz	X-Ray Imaging, Material Analysis
< 0.01 nm	> 30 EHz	Gamma-Ray Therapy, Astrophysics Research

Summary and Key Takeaways

The electromagnetic spectrum ranges from radio waves with long wavelengths to γ-rays with extremely short wavelengths.
Wavelength and frequency are inversely related, governing the energy each wave carries.
Diverse applications across technology, medicine, and scientific research utilize different spectrum regions.
Advanced concepts include quantum mechanics, relativity, and nonlinear optics, enhancing our understanding and application of EM waves.
A comprehensive comparison highlights the unique properties and uses of each electromagnetic wave type.

Examiner Tip

Tips

Remember the acronym "RMIUVXG" to sequence the electromagnetic spectrum from longest to shortest wavelength: Radio, Microwave, Infrared, Ultraviolet, X-rays, Gamma rays. To distinguish wavelength from frequency, recall that "Wavelength is Wide, Frequency is Fast." Utilize mnemonic devices like "Red Moving Under X-rays Gives Great Insights" to associate colors with their respective wave types. Regularly practice drawing and labeling the spectrum to reinforce the inverse relationship between wavelength and frequency.

Did You Know

Did you know that gamma rays are so powerful they can penetrate through dense materials like lead, making them invaluable in medical treatments such as cancer radiotherapy? Additionally, radio waves have been used to communicate with spacecraft millions of miles away, showcasing their incredible range and reliability. Another fascinating fact is that infrared waves are not only used in remote controls but also play a crucial role in astronomy, allowing scientists to observe celestial objects obscured by dust.

Common Mistakes

Students often confuse wavelength and frequency, thinking that higher wavelengths mean higher frequencies, which is incorrect due to their inverse relationship ($c = \lambda f$). Another common mistake is overlooking the energy differences across the spectrum, leading to misconceptions about the potential dangers of various waves. Additionally, students may incorrectly assume that all electromagnetic waves behave the same way when interacting with matter, ignoring how different wavelengths interact uniquely with different materials.

FAQ

What determines the classification of electromagnetic waves?

Electromagnetic waves are classified based on their wavelength and frequency. From longest to shortest wavelength, the primary categories are radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

How do wavelength and frequency relate to the energy of electromagnetic waves?

Wavelength and frequency are inversely related, as described by the equation $c = \lambda f$. The energy of an electromagnetic wave is directly proportional to its frequency ($E = hf$), meaning higher frequency waves carry more energy.

Why are gamma rays used in cancer treatment?

Gamma rays are highly penetrating and carry significant energy, which allows them to destroy cancerous cells effectively. Their ability to ionize atoms disrupts the DNA of cancer cells, inhibiting their growth and proliferation.

Can radio waves interfere with visible light?

No, radio waves and visible light operate at vastly different frequencies and wavelengths, so they do not interfere with each other. They interact with different technologies and applications independently.

How does the electromagnetic spectrum impact everyday technology?

The electromagnetic spectrum is integral to various technologies, including communication systems (radio, microwave), medical imaging (X-rays, gamma rays), household appliances (microwave ovens, infrared heaters), and entertainment devices (visible light displays).

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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Recall the Range of Wavelengths from Radio Waves to γ-Rays

Introduction