A-Level Physics flashcards

About this deck

384 free AQA A-Level Physics flashcards across 13 topics. Every card is a key term and its definition, taken word for word from a published Revise Right lesson, and links back to that lesson so you can read the full notes behind it.

Measurements and their errors

16 cards from 6 lessons. Each term links to the lesson it comes from.

Introduction to SI Units

• Ampere (A): The SI base unit of electric current. As a conceptual description, 1 A corresponds to approximately 6.24 × 10^18 elementary charges per second past a point — this is a consequence of the 2019 SI definition, which fixes the elementary charge exactly. At A Level, you treat the ampere as a base unit and do not need to recall its formal definition.

SI Prefixes and Unit Conversions

• Conversion rule for SI prefixes: To convert from a prefixed unit to the SI base unit: multiply the numerical value by the prefix multiplier (the power of ten). To convert from the SI base unit to a prefixed unit: divide by the prefix multiplier. Always state the conversion step explicitly in examination working.
• Electronvolt (eV): The electronvolt is the kinetic energy gained by an electron when it is accelerated through a potential difference of exactly 1 volt. Its value in SI units is: 1 eV = 1.6 × 10⁻¹⁹ J. It is a non-SI unit of energy used in atomic, nuclear, and particle physics.
• Kilowatt-hour (kW h): The kilowatt-hour is the energy transferred by a device operating at a power of 1 kilowatt for a duration of 1 hour. In SI units: 1 kW h = 1000 W × 3600 s = 3.6 × 10⁶ J. It is a non-SI unit of energy used in domestic and industrial energy accounting.

Errors, Precision, and Accuracy

• Random error: An unpredictable variation in a measured quantity that causes individual readings to scatter both above and below the true value. Sources include human reaction time, small environmental fluctuations, and inherent instrument noise. The effect on the mean is reduced by taking more repeated measurements.
• Systematic error: A consistent, repeatable deviation of all measurements in the same direction from the true value. Sources include a miscalibrated instrument, a zero error on a scale, or a flawed experimental method. Averaging repeated measurements does NOT reduce a systematic error — it must be identified and corrected at source.
• Precision: The closeness of agreement between repeated measurements of the same quantity made under the same conditions. A precise set of measurements has a small range (low spread). Precision is a property of the measurement process, not of a single reading.
• Repeatability: The precision obtained when the same operator uses the same equipment and method to repeat measurements of the same quantity under the same conditions over a short time period. High repeatability means repeated readings by the same person in the same session are very close together.
• Reproducibility: The precision obtained when different operators, using different equipment or methods, measure the same quantity and obtain the same or very similar results. Reproducibility is a stronger claim than repeatability because it tests whether the result holds across different experimental setups.
• Resolution: The smallest change in a quantity that an instrument can detect and display. Resolution is a property of the instrument itself, not of the measurement process. A ruler marked in millimetres has a resolution of 1 mm; a digital calliper reading to 0.01 mm has a much finer resolution.
• Accuracy: The closeness of a measured value to the true or accepted value of the quantity. An accurate measurement has low overall error. Accuracy is improved by identifying and eliminating systematic errors, and by using instruments with appropriate calibration.

Uncertainties: Absolute, Fractional and Percentage

• Absolute Uncertainty: The uncertainty expressed in the same units as the measurement. Written as ± [value] [unit]. For a single reading from an analogue instrument, the absolute uncertainty is typically half the smallest scale division. For a digital instrument, it is the last displayed digit.
• Fractional Uncertainty: The absolute uncertainty divided by the measured value. It has no units. Fractional uncertainty = absolute uncertainty ÷ measured value.

Uncertainties on Graphs

• Error bar: A line drawn through a plotted data point, extending by the absolute uncertainty in each direction along the axis of the measured quantity. A vertical error bar of ±0.5 mm extends 0.5 mm above and 0.5 mm below the point.
• Line of worst fit: The steepest or shallowest straight line that passes through all the error bars on a graph. It is used alongside the line of best fit to calculate the uncertainty in the gradient and intercept.

Orders of Magnitude and Estimation

• Order of magnitude: The power of ten to which a quantity is approximately equal. To find it, write the quantity in the form a × 10^n where 1 ≤ a < 10. If a < √(10) ≈ 3.16, the order of magnitude is n; if a ≥ 3.16, round up to n+1.

Particles and radiation

23 cards from 13 lessons. Each term links to the lesson it comes from.

Particles and Antiparticles

• Antiparticle: For every type of particle, there exists a corresponding antiparticle with identical rest mass and rest energy, but with all additive quantum numbers (including charge) reversed. When a particle and its antiparticle meet, they annihilate and release energy as photons.

Photons and the Planck Constant

• Photon: A photon is a discrete quantum (packet) of electromagnetic radiation. Each photon carries a fixed amount of energy determined entirely by its frequency. Photons have zero rest mass and travel at the speed of light in a vacuum.

Annihilation and Pair Production

• Annihilation: When a particle and its antiparticle collide, they are both destroyed and their combined rest mass-energy is converted into two photons. Each photon carries at least the rest energy of one particle.
• Pair production: A photon with energy at least equal to the total rest energy of a particle-antiparticle pair converts into that pair. For electron-positron pair production, the minimum photon energy required is 2 × 0.511 MeV = 1.02 MeV.

Conservation Laws in Particle Physics

• Conservation of charge: The total electric charge (measured in units of the elementary charge e) must be identical on both sides of any particle interaction equation. This law holds without exception in all interactions.
• Conservation of baryon number: The total baryon number B must be the same before and after any interaction. Baryons (such as protons and neutrons) carry B = +1; antibaryons carry B = -1; mesons and leptons carry B = 0.
• Conservation of lepton number: The total lepton number for each lepton family must be conserved separately. Electron lepton number (Le) and muon lepton number (Lμ) are each independently conserved. Leptons carry L = +1 and antileptons carry L = -1 for their respective family.
• Conservation of strangeness: Strangeness S is conserved in strong and electromagnetic interactions. In weak interactions, strangeness can change by 0 or ±1. Strange particles always carry a non-zero strangeness value; all non-strange particles have S = 0.

Quark Character Changes in Beta Decay

• Beta-minus quark change: In β^- decay, one down quark (d) transforms into one up quark (u). The neutron (udd) becomes a proton (uud). An electron and an electron antineutrino are emitted.
• Beta-plus quark change: In β^+ decay, one up quark (u) transforms into one down quark (d). The proton (uud) becomes a neutron (udd). A positron and an electron neutrino are emitted.

The Strong Nuclear Force

• Strong nuclear force: A fundamental force that acts between nucleons — protons and neutrons — to keep the nucleus stable. It is attractive at short range, overcoming electrostatic repulsion between protons, but becomes repulsive at very short range to prevent nucleons from collapsing into each other.

Alpha and Beta Decay

• Nuclear stability: A nucleus is stable when the strong nuclear force balances electrostatic repulsion between protons. Instability arises from an excess of protons, an unfavourable neutron-to-proton ratio, or excessive total nucleon number. Unstable nuclei decay by emitting particles or radiation to reach a lower-energy, more stable state.

Quarks and Antiquarks: Properties and Combinations

• Strangeness: A quantum number assigned to quarks and hadrons. The strange quark carries strangeness S = -1; the anti-strange quark carries S = +1; up and down quarks carry S = 0. Strangeness is conserved in strong and electromagnetic interactions but can change by ± 1 in weak interactions.

Wave-Particle Duality: Introduction

• de Broglie wavelength: The wavelength associated with a moving particle, given by λ = h/p = h/mv, where h is the Planck constant, p is the momentum, m is the mass, and v is the speed of the particle.
• Peer review: The process by which a scientist's work is evaluated by independent experts in the same field before it is published or accepted. Peer review allows the scientific community to check methodology, identify errors, and assess whether conclusions are supported by the evidence.

Ionisation, Excitation & the Fluorescent Tube

• Ground state: The lowest energy level available to an electron in an atom. An electron in the ground state is in its most stable configuration and has not absorbed any additional energy.
• Excitation: An electron absorbs a photon (or gains energy through collision) and moves from a lower energy level to a higher energy level within the atom. The electron remains bound to the atom. The atom is now in an excited state.
• Ionisation: An electron gains enough energy to be completely removed from the atom, escaping to infinity. The minimum energy required to do this from the ground state is called the ionisation energy. The atom becomes a positive ion.

The Electron Volt and Energy Conversions

• Electron volt (eV): The electron volt is the energy transferred to, or gained by, a single electron when it is accelerated through a potential difference of one volt. One electron volt equals 1.6 × 10⁻¹⁹ J.

Energy Levels and Photon Emission

• Emission line spectrum: A series of discrete bright lines on a dark background, each corresponding to a specific photon frequency emitted when electrons transition between fixed energy levels. The pattern of lines is unique to each element, acting as an atomic fingerprint.

Threshold Frequency and Work Function

• Work Function (): The minimum energy required to remove one electron from the surface of a metal. It is a fixed property of the metal, measured in joules (J) or electron-volts (eV). One electron-volt equals 1.6 × 10^-19 J.
• Threshold Frequency (f0): The minimum frequency of incident radiation that will cause photoelectric emission from a given metal surface. At f0, the photon energy exactly equals the work function: hf0 = . Below f0, no emission occurs regardless of intensity.
• Stopping Potential (Vs): The minimum potential difference applied in the reverse direction across a photoelectric cell that is just sufficient to stop the most energetic photoelectrons from reaching the collecting electrode. At this voltage, the photocurrent falls to zero.

Waves

20 cards from 11 lessons. Each term links to the lesson it comes from.

Longitudinal vs. Transverse Waves

• Transverse wave: A wave in which the oscillation of particles (or the oscillation of electric and magnetic fields) is perpendicular to the direction of energy propagation.
• Longitudinal wave: A wave in which the oscillation of particles is parallel to the direction of energy propagation, producing compressions (regions of high pressure) and rarefactions (regions of low pressure).

Polarisation of Transverse Waves

• Unpolarised wave: A transverse wave in which the oscillations occur in all planes perpendicular to the direction of propagation simultaneously. Ordinary light from a lamp or the Sun is unpolarised.

Introduction to Stationary Waves

• Stationary wave: A stationary (standing) wave is formed by the superposition of two progressive waves of the same frequency and amplitude travelling in opposite directions through the same medium. The resulting pattern has fixed points of zero displacement (nodes) and fixed points of maximum displacement (antinodes). No energy is transferred along the medium.
• Node: A node is a point on a stationary wave at which the displacement is always zero. It arises because the two component waves are always in antiphase (phase difference of π radians or 180°) at that point, producing permanent destructive interference. Adjacent nodes are separated by half a wavelength (λ/2).
• Antinode: An antinode is a point on a stationary wave at which the amplitude is maximum (2A, where A is the amplitude of each component wave). It arises because the two component waves are always in phase at that point, producing permanent constructive interference. Adjacent antinodes are also separated by λ/2.

Understanding Progressive Waves

• Progressive wave: A wave that transfers energy from one location to another through the oscillation of particles in a medium. The wave profile advances in the direction of energy transfer; matter is not transferred.
• Amplitude: The maximum displacement of a particle from its equilibrium (rest) position. Amplitude is always a positive value and is measured in metres. A larger amplitude means more energy is carried by the wave.
• Phase difference: The difference in the stage of oscillation between two points on a wave at the same instant. It can be expressed in degrees (°), radians (rad), or as a fraction of a complete cycle. Two points in phase have a phase difference of 0 (or a whole number multiple of 2π rad); two points in antiphase have a phase difference of π rad (180°).

Refraction and Snell's Law

• Refractive index of air: The refractive index of air is approximately 1. This is because the speed of light in air is almost identical to the speed of light in a vacuum. For all standard AQA calculations, treat air as having n = 1 exactly.

Total Internal Reflection and Fibre Optics

• Critical angle θc: The angle of incidence (measured from the normal) at which the angle of refraction is exactly 90°. For any angle of incidence greater than θc, total internal reflection occurs. It exists only when light travels from a medium of higher refractive index n1 into a medium of lower refractive index n2.
• Cladding (in optical fibres): The outer layer of an optical fibre, made from a material with a lower refractive index than the core. Its primary function is to ensure that the angle of incidence at the core-cladding boundary exceeds the critical angle, maintaining total internal reflection. It also protects the core surface from damage and prevents signal leakage between adjacent fibres.

Dispersion in Optical Fibres

• Modal dispersion: Pulse broadening that occurs because different rays (modes) travel different path lengths through the fibre. Rays at steeper angles to the axis travel longer total distances and therefore arrive later than axial rays, spreading the pulse out in time.
• Material dispersion: Pulse broadening that occurs because the refractive index of the fibre material varies with wavelength. Different wavelength components of the same pulse travel at different speeds, so they arrive at the receiver at slightly different times, spreading the pulse.

Single Slit Diffraction

• Diffraction: The spreading of a wave as it passes through a gap or around an obstacle. The effect is greatest when the gap width is of a similar order of magnitude to the wavelength of the wave.
• Central diffraction maximum: The brightest and widest fringe at the centre of a single slit diffraction pattern. Its angular half-width increases as slit width decreases or as wavelength increases.

Diffraction Gratings

• Normal incidence: The condition in which the incident light beam travels perpendicular to the plane of the diffraction grating (i.e. along the normal to the grating surface). The grating equation dsin θ = nλ is derived and applied under this condition.

Path Difference and Coherence

• Path difference: The difference in the distances travelled by two waves from their respective sources to a given point. If source S1 is a distance d1 from point P, and source S2 is a distance d2 from point P, then path difference = |d2 − d1|. It is often expressed as a multiple of the wavelength λ.
• Coherence: Two sources are coherent if they emit waves of the same frequency and maintain a constant phase difference. The phase difference does not have to be zero — it just must not change over time. Coherence is the essential condition for a stable interference pattern.

Interference with Sound and EM Waves and Practical Activity

• Constructive interference: Occurs when two waves arrive at a point in phase (crest meets crest). The resultant amplitude equals the sum of the individual amplitudes. Path difference must be a whole number of wavelengths: Δ = nλ where n = 0, 1, 2,...

Mechanics and materials

27 cards from 13 lessons. Each term links to the lesson it comes from.

Work Done and Energy Transfer

• Work done (W): The energy transferred when a force causes a displacement. W = Fscos θ, where F is the applied force in newtons (N), s is the displacement in metres (m), and θ is the angle between the force and the direction of displacement. Measured in joules (J), where 1 J = 1 N m.
• Area under a force–displacement graph: The total work done (and therefore energy transferred) by a force over a given displacement. For a constant force, this area is a rectangle: W = F × s. For a variable force, the area must be calculated by counting squares, using geometric shapes, or integration (for a known function). The unit of this area is N m = J.

Power and Efficiency

• Power: Power is the rate of doing work, equal to the rate of energy transfer. P = Δ W/Δ t, where Δ W is the work done in joules and Δ t is the time interval in seconds. The SI unit of power is the watt (W), where 1 W = 1 J s⁻¹.
• Efficiency: Efficiency is the ratio of useful output power to total input power: efficiency = useful output powerinput power. It is dimensionless and always lies between 0 and 1. Multiplying by 100 gives efficiency as a percentage.

Calculating Projectile Motion

• Independence of horizontal and vertical motion: In a uniform gravitational field (with air resistance neglected), the horizontal component of a projectile's velocity is unaffected by gravity and remains constant throughout the flight. The vertical component changes at a constant rate equal to the gravitational field strength g = 9.8 m s⁻². The two components are completely independent: knowing one tells you nothing about the other.

Friction, Lift, and Drag Forces

• Friction: A contact force acting between two surfaces that are in contact, directed parallel to the surfaces and opposing the relative motion (or tendency of motion) between them.
• Drag (fluid resistance): A resistive force exerted by a fluid on an object moving through it, acting in the direction opposite to the object's velocity. Drag increases as the speed of the object through the fluid increases.

Terminal Speed and Air Resistance

• Terminal speed: The constant speed reached when the drag force on a moving object equals the driving force (such as weight for a falling object), giving a resultant force of zero and therefore zero acceleration.

Newton's Laws of Motion

• Newton's First Law of Motion: An object will remain at rest or continue to move with constant velocity (constant speed in a straight line) unless acted upon by a resultant force.
• Newton's Second Law of Motion: The resultant force acting on an object equals the rate of change of its momentum. For an object of constant mass, this simplifies to: resultant force = mass × acceleration, or F = ma.
• Newton's Third Law of Motion: When object A exerts a force on object B, object B exerts an equal and opposite force on object A. The two forces are equal in magnitude, opposite in direction, act on different objects, and are of the same type.

F=ma and Constant Mass

• Newton's Second Law (F = ma, constant mass): The resultant (net) force F on an object of constant mass m equals the product of that mass and its acceleration a. The direction of the acceleration is always the same as the direction of the resultant force. Measured in: F in newtons (N), m in kilograms (kg), a in m s^-2.

Moments and Couples

• Moment of a force: The moment of a force about a point is defined as: force multiplied by the perpendicular distance from the point to the line of action of the force. The unit is the newton-metre (N m).
• Couple: A couple is a pair of forces that are equal in magnitude, opposite in direction, and coplanar (acting in the same plane), whose lines of action are parallel but do not coincide. A couple produces a pure turning effect and has zero resultant force.

Density, Hooke's Law and Elasticity

• Density (ρ): Density is the mass per unit volume of a substance. It is defined by the equation ρ = m/V, where m is mass in kilograms (kg) and V is volume in cubic metres (m³). The SI unit of density is kg m⁻³.
• Hooke's Law: The extension of a spring (or elastic material) is directly proportional to the applied force, provided the elastic limit is not exceeded. Mathematically: F = kΔL, where F is the applied force in newtons (N), k is the spring constant (stiffness) in N m⁻¹, and ΔL is the extension in metres (m).
• Tensile Stress (σ): Tensile stress is the force applied per unit cross-sectional area of a material under tension. σ = F/A, where F is the tensile force in newtons (N) and A is the cross-sectional area in m². The unit of tensile stress is the pascal (Pa), where 1 Pa = 1 N m⁻².
• Tensile Strain (ε): Tensile strain is the fractional change in length of a material under tension. ε = ΔL/L₀, where ΔL is the extension in metres (m) and L₀ is the original length in metres (m). Strain has no units — it is a dimensionless ratio.
• Breaking Stress: Breaking stress is the maximum tensile stress a material can withstand before fracture. It is measured in pascals (Pa) and is a fixed property of the material, independent of the sample's dimensions. Note: at A-level, breaking stress is treated as the stress at fracture. Strictly, ultimate tensile stress (UTS) refers to the peak stress on the engineering stress–strain curve, which may occur before fracture in ductile materials; at A-level these distinctions are not required.

Elastic Strain Energy and Material Behaviour

• Elastic limit: The maximum force (or stress) beyond which a material will not return to its original dimensions when the load is removed. Below the elastic limit, deformation is fully reversible.
• Stress (σ): The force applied per unit cross-sectional area of a material. σ = F/A, measured in pascals (Pa) or N m⁻².
• Strain (): The fractional change in length of a material under stress. = Δ L / L0, a dimensionless ratio.

Energy Conservation and Ethical Transport Design

• Elastic potential energy: The energy stored in a spring (or any elastic material) when it is compressed or stretched from its natural length. Given by Eel = 1/2kx^2, where k is the spring constant (N/m) and x is the extension or compression (m). Measured in joules (J).
• Energy dissipation: The transfer of energy from useful mechanical stores (kinetic or potential) to thermal energy, typically due to friction or air resistance. Dissipated energy is not destroyed — it raises the temperature of the surroundings. In exam contexts, it is quantified as the difference between the theoretical and actual useful energy output.

Defining the Young Modulus

• Tensile stress (σ): The tensile force F applied divided by the cross-sectional area A through which it acts. σ = F/A The SI unit is the pascal (Pa), where 1 Pa = 1 N m^-2.
• Tensile strain (): The extension Δ L of a material divided by its original length L. = Δ L/L Strain is a ratio of two lengths, so it has no units — it is dimensionless. It is sometimes expressed as a percentage, but in calculations always use the decimal form.

Young Modulus from Stress-Strain Graphs

• Young modulus (E): The ratio of tensile stress to tensile strain within the limit of proportionality. E = σ / , measured in pascals (Pa). It quantifies the stiffness of a material — a higher Young modulus means the material is harder to stretch for a given stress.

Electricity

11 cards from 7 lessons. Each term links to the lesson it comes from.

Electric Current, Potential Difference, and Resistance

• Electric current (I): The rate of flow of electric charge. Defined as the charge Δ Q passing a point divided by the time interval Δ t. Measured in amperes (A), where 1 A = 1 C s^-1.
• Potential difference (V): The work done per unit charge moved between two points in a circuit. Defined as V = W/Q, where W is work done in joules and Q is charge in coulombs. Measured in volts (V), where 1 V = 1 J C^-1.
• Resistance (R): The ratio of the potential difference across a component to the current through it. Defined as R = V/I. Measured in ohms (Ω), where 1 Ω = 1 V A^-1.

Potential Dividers: Principles and Applications

• Potential divider: Two or more resistors connected in series across a supply voltage Vin, with the output voltage Vout taken across one of the resistors. The output is a fraction of the supply determined by the resistance ratio.

Resistivity and Temperature Effects

• Resistivity (ρ): The resistance of a material per unit length per unit cross-sectional area. Defined by ρ = RA/L, where R is resistance in ohms (Ω), A is cross-sectional area in m², and L is length in m. The SI unit of resistivity is the ohm-metre (Ω m).
• NTC Thermistor: A semiconductor device with a negative temperature coefficient of resistance: as temperature rises, resistance falls. At A Level, only NTC thermistors are considered. The resistance-temperature relationship is non-linear (exponential in character), unlike the approximately linear relationship seen in metals.

Superconductivity and Applications

• Superconductivity: Superconductivity is a property of certain materials in which the electrical resistivity becomes exactly zero at and below a material-specific critical temperature. Above the critical temperature the material behaves as a normal conductor with non-zero resistance.

I-V Characteristics: Ohmic Conductors and Ohm's Law

• Ohm's Law: The current through an ohmic conductor is directly proportional to the potential difference across it, provided physical conditions — especially temperature — remain constant. In symbols: I V, or equivalently V = IR where R is constant.

Electromotive Force (EMF) and Terminal Potential Difference

• Electromotive Force (EMF),: The energy transferred per unit charge by a source. Defined by = E/Q, where E is the total energy transferred in joules and Q is the charge in coulombs. Measured in volts (V), where 1 V = 1 J C^-1.
• Terminal Potential Difference: The potential difference across the external terminals of a source when current is flowing. Given by V = - Ir. It is always less than the EMF when current flows, because of the voltage drop across the internal resistance.

Practical: Investigating EMF and Internal Resistance

• Terminal potential difference (terminal pd), V: The potential difference measured across the external terminals of the cell while current is flowing. It equals the emf minus the voltage dropped across the internal resistance: V = - Ir.

Further mechanics and thermal physics (A-level only)

23 cards from 13 lessons. Each term links to the lesson it comes from.

Introduction to Circular Motion

• Centripetal acceleration: The acceleration experienced by an object moving in a circular path, always directed towards the centre of the circle. Its magnitude is constant for uniform circular motion, but its direction continuously changes as the object moves around the path.
• Radian (rad): The angle subtended at the centre of a circle when the arc length equals the radius. Since the full circumference is 2π r, a complete revolution corresponds to 2π radians. Conversion: multiply degrees by π/180 to get radians.

Understanding Simple Harmonic Motion

• Simple Harmonic Motion (SHM): An oscillation in which the acceleration of the object is directly proportional to its displacement from the equilibrium position, and is always directed towards that equilibrium position. The defining condition is a -x.

SHM Equations: Displacement, Velocity & Time

• Maximum speed in SHM: The greatest speed reached during an oscillation, occurring at the equilibrium position (x = 0). Given by vmax = ω A. Measured in m s^-1.

Graphical Representations of SHM

• Amplitude (A): The maximum displacement from the equilibrium position, measured in metres (m). It is the peak value on the x–t graph and remains constant for undamped SHM.
• Antiphase: Two oscillating quantities are in antiphase when they are separated by exactly half a period (T/2, or equivalently π radians). In SHM, displacement and acceleration are always in antiphase, reflecting the negative sign in a = -ω^2 x.

Mass-Spring Systems & Simple Pendulums

• Small-angle approximation: For angles below approximately 10°, sin θ ≈ θ (in radians). This approximation is what makes pendulum motion simple harmonic. Beyond 10°, the motion is no longer accurately described as SHM and the period formula becomes unreliable.

Energy in SHM & Damping

• Total mechanical energy in SHM: The sum of kinetic and potential energy at any instant, which remains constant for an undamped oscillator: Etotal = Ek + Ep = 1/2mω^2 A^2, where m is mass, ω is angular frequency, and A is amplitude.
• Damping: The reduction in amplitude of an oscillation caused by a resistive force that removes energy from the system. The resistive force typically acts in the opposite direction to velocity, so it does negative work on the oscillator.

Ideal Gas Laws and Absolute Zero

• Boyle's Law: For a fixed mass of gas at constant temperature, pressure is inversely proportional to volume. Mathematically: p 1/V, or equivalently p1 V1 = p2 V2.
• Charles's Law: For a fixed mass of gas at constant pressure, volume is directly proportional to absolute temperature (in kelvin): V T, or equivalently V1/T1 = V2/T2.
• Pressure Law (Gay-Lussac's Law): For a fixed mass of gas at constant volume, pressure is directly proportional to absolute temperature (in kelvin): p T, or equivalently p1/T1 = p2/T2.

The Ideal Gas Equation and Work Done

• Ideal Gas: A gas whose molecules occupy negligible volume compared to the container, experience no intermolecular forces except during collisions, and undergo perfectly elastic collisions with each other and the container walls. Real gases approximate ideal behaviour at low pressures and high temperatures.

Avogadro Constant, Molar Gas Constant, Boltzmann Constant, and Molar/Molecular Mass

• Avogadro constant NA: The number of particles contained in exactly one mole of any substance. NA = 6.02 × 10^23 mol^-1.
• Molar mass M: The mass of one mole of a substance. SI unit: kg mol^-1. In chemistry contexts, g mol^-1 is also used — the numerical value equals the relative molecular mass. For example, oxygen gas (O2) has a molar mass of 0.032 kg mol^-1 (or 32 g mol^-1).
• Molar gas constant R: A universal constant equal to 8.31 J mol^-1 K^-1. It appears in the ideal gas equation pV = nRT, where n is the number of moles. It sets the energy scale per mole per kelvin.
• Boltzmann constant k: A fundamental constant equal to k = 1.38 × 10^-23 J K^-1. It is the per-particle equivalent of R: it sets the energy scale for a single molecule per kelvin. It appears in pV = NkT, where N is the total number of molecules.

Internal Energy and the First Law of Thermodynamics

• Internal energy: The sum of the randomly distributed kinetic energies and potential energies of all the particles in a body. The word 'randomly distributed' is key — the particles do not all move at the same speed or in the same direction.
• First law of thermodynamics (qualitative statement): The internal energy of a system is increased when energy is transferred to it by heating or when work is done on it. The internal energy decreases when the system transfers energy by heating its surroundings or does work on them. Energy is always conserved.

Specific Heat Capacity

• Specific heat capacity (c): The energy required to raise the temperature of 1 kg of a substance by 1 °C (or 1 K), without causing a change of state. The SI unit is J kg⁻¹ K⁻¹, which is numerically identical to J kg⁻¹ °C⁻¹.

Specific Latent Heat

• Specific latent heat (l): The energy required to change the state of 1 kg of a substance at constant temperature. Measured in joules per kilogram (J kg⁻¹). The word 'specific' means per unit mass — always include it in exam definitions.

Brownian Motion & Molecular Model

• Brownian motion: The random, erratic motion of small visible particles (such as smoke particles or pollen grains) suspended in a fluid, resulting from continuous, unequal bombardment by the surrounding fluid molecules. It is direct observational evidence for the existence of atoms and molecules.
• Empirical law: A law established purely from experimental observation and measurement. It describes what happens without explaining why. The gas laws are empirical: they were found by experiment before any molecular model existed to account for them.

Fields and their consequences (A-level only)

42 cards from 30 lessons. Each term links to the lesson it comes from.

Introduction to Force Fields

• Force Field: A region of space in which a body experiences a non-contact force. The field is a property of the space itself — it exists whether or not a second body is present to feel it.
• Field Line (Line of Force): A line drawn in a field such that the tangent to the line at any point gives the direction of the force on a small test mass (for gravitational fields) or a positive test charge (for electric fields) at that point. The spacing of field lines indicates relative field strength.

Gravitational vs. Electrostatic Fields

• Gravitational field strength, g: The gravitational force per unit mass experienced by a small test mass placed at a point in the field. Defined as g = F/m, measured in N kg⁻¹ (equivalent to m s⁻²). It is a vector quantity pointing towards the source mass.
• Potential (gravitational and electric): The work done per unit mass (gravitational potential, Vg, in J kg⁻¹) or per unit positive charge (electric potential, V, in J C⁻¹ = V) in bringing the test quantity from infinity to that point in the field. Both are scalar quantities.

Gravitational Potential Fundamentals

• Gravitational Potential, V: The work done per unit mass in bringing a small test mass from infinity to a point in the gravitational field. Mathematically, V = W/m, where W is the work done and m is the mass moved. Measured in joules per kilogram (J kg⁻¹).
• Gravitational Potential Difference, Δ V: The difference in gravitational potential between two points A and B in a field: Δ V = VB - VA. Measured in J kg⁻¹. A positive Δ V means moving to a point of higher (less negative) potential; a negative Δ V means moving to a point of lower (more negative) potential.
• Equipotential Surface: A surface connecting all points in a gravitational field that have the same gravitational potential. For a spherical mass, equipotential surfaces are concentric spheres centred on the mass. Moving along an equipotential surface involves zero potential difference, so zero work is done.

Gravitational Potential in Radial Fields

• Gravitational potential V at a point: The work done per unit mass in bringing a small test mass from infinity to that point in the gravitational field. V is a scalar, measured in J kg^-1.

Linking g, V and ΔV

• The g–V relationship: The gravitational field strength at a point equals the negative of the potential gradient at that point: g = -Δ V/Δ r. Here Δ V is the change in gravitational potential over a small radial distance Δ r. The units of Δ V/Δ r are J kg⁻¹ m⁻¹, which simplify to N kg⁻¹, consistent with g.

Orbital Motion and Energy

• Gravitational potential energy of a satellite: The gravitational potential energy of a satellite of mass m at orbital radius r from the centre of a body of mass M is Ep = -GMm/r. The negative sign arises because the zero of potential energy is defined at infinity; work must be done on the satellite to move it away from the gravitational field.

Escape Velocity and Orbit Types

• Escape velocity: The minimum speed at which an object must be projected from a planet's surface so that it can escape the planet's gravitational field, reaching an infinite distance with zero remaining kinetic energy. Given by vesc = √(2GM/R).
• Synchronous orbit: An orbit in which the satellite's orbital period equals the rotational period of the body being orbited. For Earth, a synchronous orbit has a period of 24 hours (one sidereal day, more precisely 23 hours 56 minutes, but 24 hours is used at A-level). If the orbit is also circular and equatorial, it is called a geostationary orbit.

Gravitational Field Strength

• Gravitational field line: A line drawn in a gravitational field such that the tangent at any point gives the direction of the gravitational force on a small test mass at that point. The density of lines represents the relative field strength.

Newton's Law of Gravitation

• Gravity as a universal force: Gravity is an attractive force that acts between all objects with mass. It is always attractive — never repulsive — and it acts along the line joining the centres of the two masses. There is no material or distance that can shield or block it.

Electric Fields and Field Strength

• Electric field line: A line drawn in an electric field such that the tangent to the line at any point gives the direction of the electric field (and therefore the force on a positive test charge) at that point. Lines never cross.
• Electric field strength, E: The force per unit positive charge at a point in an electric field. Defined by E = F/Q, where F is the force in newtons (N) on a charge Q in coulombs (C). The unit of E is newtons per coulomb, N C⁻¹. Electric field strength is a vector — its direction is the direction of the force on a positive charge.

Uniform Electric Fields

• Electric field strength (E) in a uniform field: The force per unit positive charge, equal to E = V/d, where V is the potential difference between the plates (in volts) and d is the plate separation (in metres). The unit is V m^-1, which is identical to N C^-1.

Radial Electric Fields

• Point charge: An idealised charge treated as if all its charge is concentrated at a single point. Real charged spheres behave as point charges for any point outside the sphere, which makes this model widely applicable.

Coulomb's Law: Force Between Charges

• Permittivity of free space (0): The permittivity of free space 0 = 8.85 × 10^-12 C² N⁻¹ m⁻² is a fundamental constant that quantifies how easily an electric field is established in a vacuum. A larger permittivity would mean the medium 'resists' the field more, reducing the force between charges. In Coulomb's law it appears in the denominator, so a larger 0 gives a smaller force.

Electrostatic vs. Gravitational Forces

• Force ratio FE / FG: The ratio of electrostatic force to gravitational force between two particles. Because both forces follow an inverse-square law with the same r^2 denominator, this ratio is independent of the separation between the particles. It depends only on the charges and masses involved.

Electric Potential: Definition and Work Done

• Absolute Electric Potential (V): The work done per unit positive charge in bringing a small positive test charge from infinity to that point in the field. Measured in volts (V), where 1 V = 1 J C⁻¹. The potential at infinity is defined as zero.
• Electric Potential Difference (ΔV): The difference in electric potential between two points: Δ V = VB - VA. It represents the work done per unit positive charge in moving between those two points. Measured in volts (V).

E and V Relationships

• Gradient of the V-r graph: At any point on the V-r graph, the gradient (slope of the tangent) equals −E at that distance; that is, E = −dV/dr. The magnitude of the gradient gives the field strength: the steeper the potential-distance graph, the stronger the field. For AQA calculations, the magnitude form E = ΔV/Δr is used, where ΔV and Δr are both taken as positive quantities over the interval.

Energy in a Capacitor

• Area under a charge-against-pd graph: The area enclosed between the Q-V line and the horizontal (pd) axis equals the energy stored in the capacitor. For a linear Q-V relationship (constant capacitance), this area is a triangle of area 1/2QV.

Capacitor Charging & Discharging: Graphs & the Time Constant

• Initial charging current: At the instant of connection (t = 0), the capacitor has zero voltage across it, so the full e.m.f. drives current through the resistor. The initial current is I0 = / R. This is the maximum current during charging.

Time to Halve & Quantitative Discharge

• Time constant = RC: The time constant (tau) equals the product of resistance and capacitance. After one time constant, the charge (or voltage or current) has fallen to e^-1 ≈ 0.37 of its initial value — that is, to about 37%. After five time constants, the capacitor is considered fully discharged for practical purposes.

Quantitative Charging & Practical Investigation

• Time constant ( = RC): The time constant equals R × C and has units of seconds. After one time constant, a charging capacitor reaches approximately 63% of its maximum charge. After five time constants, it is considered fully charged (above 99%). The time constant sets the timescale of the entire charging process.

Dielectrics in Parallel Plate Capacitors

• Polarisation of a dielectric: When an electric field is applied across a dielectric, polar molecules rotate to align their dipoles with the field. Non-polar molecules develop induced dipoles as electron clouds are displaced. In both cases, a layer of negative charge appears at the surface nearest the positive plate, and a layer of positive charge appears at the surface nearest the negative plate.
• Relative permittivity r (dielectric constant): The ratio of the capacitance of a capacitor with the dielectric filling the gap to the capacitance of the same capacitor with a vacuum between the plates: r = Cdielectric / Cvacuum. It is dimensionless and always greater than or equal to 1.

Capacitance: Definition

• Capacitance: The charge stored per unit potential difference across a capacitor. Mathematically: C = Q/V. The unit is the farad (F), where 1 F = 1 C V^-1.

Magnetic Forces on Moving Charges

• Magnetic force on a moving charge: A force that acts on a charged particle moving through a magnetic field, provided the particle's velocity has a component perpendicular to the field direction. The force is always perpendicular to both the velocity and the field — it never does work on the particle.
• Direction of force on negative charges: For a negative charge (such as an electron), apply Fleming's left-hand rule as if the charge were positive, then reverse the direction of the force. Equivalently, point the second finger opposite to the electron's velocity (since conventional current is opposite to electron flow), then read off the thumb direction directly.

Circular Motion and Cyclotrons

• Magnetic force on a charged particle: The force on a particle of charge q moving at speed v perpendicular to a uniform magnetic field of flux density B is F = Bqv. The direction is given by Fleming's left-hand rule (for positive charges). This force is always perpendicular to the velocity, so it acts as the centripetal force and causes the particle to travel in a circle.
• Cyclotron frequency: The frequency at which the alternating voltage must be set to keep accelerating a particle in a cyclotron. Given by f = Bq/2π m. This is independent of the particle's speed and orbital radius, which is why a fixed-frequency alternating voltage works throughout the acceleration process.

Electromagnetic Induction: Experiments & Laws

• Magnetic flux (): The product of the component of magnetic flux density perpendicular to a surface and the area of that surface: = BAcos θ, where B is the flux density in tesla (T), A is the area in m², and θ is the angle between the field direction and the normal to the surface. Measured in webers (Wb), where 1 Wb = 1 T m².
• Lenz's law: The induced current flows in a direction such that its magnetic effect opposes the change in flux that produced it. This is a direct consequence of conservation of energy: if the induced current aided the change, it would create energy from nothing.

Quantifying Electromagnetic Induction

• Flux Linkage: The product of the number of turns N in a coil and the magnetic flux through each turn. Flux linkage = N, measured in weber-turns (Wb). It represents the total magnetic flux threading the entire coil.

EMF in a Rotating Coil

• Peak EMF (0): The maximum value of the induced EMF in a rotating coil, given by 0 = BANω. It is reached when the plane of the coil is parallel to the magnetic field, because the rate of change of flux linkage is greatest at that instant.

Magnetic Forces on Current-Carrying Wires

• Magnetic flux density (B): The force per unit current per unit length acting on a conductor placed perpendicular to the magnetic field. Measured in tesla (T). It is a vector quantity — direction matters as well as magnitude.

Understanding Magnetic Flux

• Flux Linkage (N): The product of the number of turns N in a coil and the magnetic flux through each turn: flux linkage = N. Measured in weber-turns (Wb). It represents the total flux threading through the entire coil and determines the magnitude of any induced EMF.

Understanding RMS and Peak Values

• Peak value (V0 or I0): The maximum magnitude of the sinusoidal voltage or current, measured from the zero line to the crest of the waveform. It is the amplitude of the oscillation. For UK mains, V0 ≈ 325 V.
• Root mean square (RMS) value: The equivalent steady DC value that would dissipate the same average power in a purely resistive load. For a sinusoidal waveform only: Vrms = V0/√(2) and Irms = I0/√(2).

Nuclear physics (A-level only)

10 cards from 8 lessons. Each term links to the lesson it comes from.

Radioactive Decay: Randomness and Rate

• Random decay: Each nucleus has the same constant probability of decaying per unit time, regardless of its history or environment. The moment of any individual decay cannot be predicted.

Mastering Decay Equations

• Decay constant (λ): The probability per unit time that any individual nucleus will decay. Its SI unit is s^-1. A nuclide with a large λ decays quickly; a nuclide with a small λ is long-lived.

Half-Life: Calculations and Applications

• Half-life equation: T1/2 = ln 2/λ where T1/2 is the half-life (s), λ is the decay constant (s^-1), and ln 2 ≈ 0.693.

N-Z Graph and Decay Modes

• Stability band (belt of stability): The narrow region on an N-Z graph within which all stable nuclei lie. For Z up to approximately 20, stable nuclei have N ≈ Z. For Z greater than 20, stable nuclei have N > Z, with the ratio N/Z increasing towards approximately 1.5 for the heaviest stable nuclei near Z = 82.

Radioactive Decay Equations

• Neutron number N: N = A - Z. This is not written explicitly in the symbol, but it is the quantity that changes most revealingly during decay. Tracking N alongside Z tells you the full story of what the nucleus is doing.
• Nuclear energy level diagram: A diagram showing the energy states of a nucleus, with horizontal lines representing energy levels and arrows showing transitions. Downward arrows represent energy release; the type of emission (alpha, beta, gamma) is labelled on each arrow. The ground state is the lowest energy level.

Nuclear Excited States and Gamma Emission

• Nuclear excited state: A state in which a nucleus possesses energy above its ground-state energy following a radioactive decay. The nucleus is unstable and will release the excess energy as a gamma ray photon when it transitions to the ground state.
• Metastable isomer: A nucleus in a long-lived excited state that decays by gamma emission on a timescale long enough to be measured and exploited. Denoted by the suffix 'm' in the nuclide symbol, for example ^99m43Tc.

Estimating Nuclear Radius

• Closest approach distance (d): The distance between the centre of an alpha particle and the centre of the target nucleus at the point where the alpha particle's kinetic energy is entirely converted to electrostatic potential energy. It sets an upper limit on nuclear radius.

Nuclear Size, Density, and the A Relation

• Femtometre (fm): A unit of length equal to 1 × 10^-15 m. Used exclusively for nuclear-scale distances. The nuclear radius constant R0 ≈ 1.2 fm.

Astrophysics (A-level only)

32 cards from 23 lessons. Each term links to the lesson it comes from.

Telescope Resolution and Collecting Power

• Rayleigh criterion: Two point sources are just resolvable when the central maximum of one diffraction pattern falls on the first minimum of the other. At this limit, the minimum angular separation θ (in radians) satisfies θ ≈ λ/D, where λ is the wavelength of light and D is the diameter of the objective.

Detectors: CCD vs. Eye

• Quantum efficiency: The ratio of the number of photons detected to the number of photons incident on the detector, usually expressed as a percentage. A quantum efficiency of 80% means 80 out of every 100 incident photons produce a detectable signal.

Ray Diagrams for Astronomical Telescopes

• Objective lens: A large-diameter converging lens at the front of the telescope. It receives parallel rays from a very distant (effectively infinite) object and refracts them to form a real, inverted, diminished intermediate image at its principal focus Fo.
• Eyepiece lens: A shorter-focal-length converging lens positioned so that, in normal adjustment, the intermediate image formed by the objective lies exactly at the eyepiece's principal focus Fe. The eyepiece acts as a magnifying glass, producing a final virtual image at infinity.

Angular Magnification of Telescopes

• Angular magnification M: The ratio of the angle β subtended at the eye by the final image to the angle α subtended at the unaided eye by the object. Written as M = β/α. It is dimensionless — both angles are in radians (or both in degrees), so the units cancel.

Cassegrain Reflecting Telescopes

• Primary mirror (parabolic concave): The large, light-gathering mirror at the base of the telescope tube. Its surface is concave — curving inward like the inside of a bowl — and is shaped as a paraboloid. Parallel rays arriving from a distant star strike this mirror and are reflected to converge towards a single focal point in front of the mirror. The parabolic shape is essential: a spherical concave mirror would bring rays from different zones to slightly different focal points (spherical aberration), blurring the image. The paraboloid eliminates this defect for on-axis sources.
• Secondary mirror (convex): A smaller mirror positioned in front of the primary mirror's focal point, along the optical axis. Its surface curves outward — convex — so it diverges the converging beam arriving from the primary. This diverged beam is redirected back along the optical axis, passing through a small central hole in the primary mirror, and comes to focus behind the primary mirror where the eyepiece is located.

Reflectors vs. Refractors

• Primary mirror: The large concave mirror in a reflecting telescope that collects and focuses incoming light by reflection. Its diameter sets the light-gathering power and resolving ability of the instrument.

Radio vs. Optical Telescopes

• Parabolic dish (radio telescope): A curved reflective surface shaped as a paraboloid, which focuses parallel incoming radio waves to a single focal point where the receiver is positioned. The same principle as a concave mirror in an optical reflecting telescope, but operating at radio wavelengths.

Apparent Magnitude and the Hipparcos Scale

• Apparent magnitude, m: The apparent magnitude of a star is a measure of its brightness as observed from Earth. It is a dimensionless number: a smaller (or more negative) value means the star appears brighter. The scale is logarithmic, not linear.

Stellar Spectral Classes: O, B, A

• Balmer series: The set of hydrogen absorption (or emission) lines produced by electron transitions to or from the second energy level (n = 2). These lines fall in the visible part of the spectrum and are the dominant feature of A-class stellar spectra.

Stellar Spectral Classes: F, G

• Balmer series absorption: Absorption of photons that excite hydrogen electrons from the n = 2 level to higher energy levels. These lines appear in the visible spectrum and are strongest in A-type stars, weakening progressively through F and G classes as fewer atoms are in the n = 2 state.

Stellar Spectral Classes: K, M

• K-type star: A main-sequence or giant star with a surface temperature of approximately 3500–5000 K. Its spectrum is dominated by strong absorption lines of calcium (Ca II H and K lines at ~393 nm and ~397 nm), sodium, and neutral metals such as iron. Hydrogen Balmer lines are weak because the temperature is too low to excite hydrogen atoms to the required energy levels. Colour appears orange.
• M-type star: A star with a surface temperature below approximately 3500 K. Its spectrum is dominated by molecular absorption bands, most notably titanium oxide (TiO), which appear as broad dark bands across the red and near-infrared regions of the spectrum. Metal lines remain strong, hydrogen lines are very weak, and the star appears deep red in colour.

Absolute Magnitude and Distance Modulus

• Parsec (pc): The distance at which the mean Earth–Sun separation (1 AU) subtends an angle of exactly 1 arcsecond. One parsec equals approximately 3.26 light years, or 3.09 × 10^16 m.
• Absolute magnitude (M): The apparent magnitude a star would have if it were located exactly 10 parsecs from Earth. It is a measure of the star's intrinsic luminosity, independent of its actual distance.

Black-Body Radiation Laws: Stefan's and Wien's

• Black body: An idealised object that absorbs all incident electromagnetic radiation and re-emits radiation with a continuous spectrum determined solely by its absolute temperature. Stars are treated as black bodies in astrophysics calculations.
• Stefan's law (Stefan-Boltzmann law): The total power radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature: P/A = σ T^4, where σ = 5.67 × 10^-8 W m^-2 K^-4 is the Stefan-Boltzmann constant.

Inverse Square and Stefan's Law: Stellar Properties

• Assumptions of the Inverse Square Law: The law holds exactly only when: (1) the star radiates uniformly in all directions (isotropic emission); (2) no energy is absorbed or scattered between the star and the observer (no interstellar absorption); and (3) the medium between star and observer is transparent. In practice, interstellar dust can absorb or redden starlight, causing the observed flux to be lower than the inverse square law predicts.

Hertzsprung-Russell Diagram Basics

• Absolute Magnitude: The magnitude a star would have if observed from a standard distance of 10 parsecs. It measures intrinsic luminosity, independent of how far away the star actually is. The scale runs from approximately -10 (extremely luminous) to +15 (very faint), with each step of 5 magnitudes corresponding to a factor of 100 in brightness.
• Main Sequence: The diagonal band on the HR diagram, running from top-left (hot, luminous O-type stars) to bottom-right (cool, faint M-type stars), where stars are in the stable phase of hydrogen fusion in their cores. Stars spend most of their lives on the main sequence.

The Challenge of Detecting Exoplanets

• Luminosity contrast ratio: The ratio of the flux received from a star to the flux received from its orbiting planet at the same distance. In visible light, this is typically 10^9 for a Sun-like star with an Earth-like planet, and 10^6 in the mid-infrared. This contrast means the planet's signal is buried within the noise and glare of the stellar image.

Radial Velocity & Transit Methods

• Radial Velocity: The component of a star's velocity directed along the line of sight between the star and the observer. A positive radial velocity indicates recession (redshift); a negative radial velocity indicates approach (blueshift). Measured in metres per second (m/s) or kilometres per second (km/s).

Discovering Quasars: Bright Giants of the Universe

• Quasi-stellar radio source (quasar): An extremely luminous, compact extragalactic object that was first identified as a strong radio source with a star-like optical appearance. Quasars show very large redshifts, indicating they are among the most distant objects observable in the universe.
• Flux (F): The power received per unit area at the observer's location, measured in W/m². For a source of luminosity L at distance d, flux is given by F = L / (4π d^2), assuming the source radiates isotropically.

Quasars: Supermassive Black Holes and Energy Output

• Redshift parameter z: Defined as z = λobs - λemitλemit, where λobs is the observed wavelength and λemit is the rest wavelength of the same spectral line. A value of z = 1 means the wavelength has doubled.
• Accretion disc: A rotating disc of gas and dust spiralling inward towards a supermassive black hole. Conservation of angular momentum prevents material falling straight in; instead it forms a disc, heats up through friction and compression, and radiates across a broad electromagnetic spectrum — from radio waves to X-rays. The gravitational potential energy released by infalling matter is the source of the quasar's luminosity.

Hubble's Law and Redshift

• Redshift (cosmological): The observed increase in wavelength of light from a distant galaxy, caused by the galaxy moving away from Earth. Quantified as z = Δ λ/λ0, where Δ λ is the change in wavelength and λ0 is the rest wavelength. For recession speeds much less than the speed of light, z ≈ v/c.

The Expanding Universe and Age Estimation

• Cosmological Redshift: The increase in wavelength of electromagnetic radiation from a distant galaxy, caused by the expansion of space between the source and the observer. The fractional shift z = Δ λ/λ is used to infer recession speed for nearby galaxies via v ≈ zc.

Big Bang Theory and Evidence

• Cosmic microwave background radiation (CMBR): Electromagnetic radiation, peaking in the microwave region, that fills the universe uniformly in all directions. It corresponds to a blackbody temperature of approximately 2.7 K and is interpreted as the redshifted remnant of the thermal radiation emitted when the universe first became transparent to light, approximately 380,000 years after the Big Bang.

Doppler Effect in Astronomy

• Rest wavelength / rest frequency: The wavelength or frequency of a spectral line measured from a stationary source in the laboratory. This is the reference value used in all Doppler calculations. Astronomers identify rest wavelengths from known atomic emission spectra (for example, the hydrogen-alpha line at 656 nm).
• Orbital speed from Doppler data: For a binary star viewed in the plane of orbit, the maximum Doppler shift corresponds to the full orbital speed v of the star. Using v = c × |Δ f| / f (or the wavelength equivalent), the orbital speed is found directly. The orbital circumference is 2π r, so the orbital radius is r = vT / (2π), where T is the orbital period.

Medical physics (A-level only)

68 cards from 34 lessons. Each term links to the lesson it comes from.

The Eye as an Optical System

• Refractive index (n): The ratio of the speed of light in a vacuum to the speed of light in a medium: n = c/v. A higher refractive index means light travels more slowly in that medium and bends more at the boundary. For the eye's optical surfaces, the refractive index contrast at each boundary determines how strongly light is redirected.

Sensitivity and Spectral Response of the Eye

• Photodetector: A device that converts incident electromagnetic radiation into a measurable electrical signal. The human eye acts as a biological photodetector, with its retinal photoreceptor cells generating nerve impulses in response to absorbed photons.
• Luminosity function V(λ): The standardised relative spectral sensitivity of the human eye under photopic (bright-light) conditions, normalised to a peak value of 1.0 at approximately 555 nm. It quantifies how efficiently the eye detects light of different wavelengths relative to its most sensitive wavelength.

Spatial Resolution and Rods & Cones

• Rods: Photoreceptors that are highly sensitive to light intensity but cannot distinguish colour. They are concentrated in the peripheral retina and are absent from the fovea. Rods contain the pigment rhodopsin, which is sensitive enough to be activated (bleached) even by very low light intensities, making rods effective in low-light (scotopic) conditions.
• Cones: Photoreceptors sensitive to colour and fine detail. They require relatively bright light (photopic conditions) to function. Three types of cone respond to different wavelengths (roughly red, green, and blue). Cones are densely packed at the fovea and become sparse towards the periphery.
• Retinal convergence: The arrangement in which multiple photoreceptors synapse onto a single bipolar cell. High convergence (many rods to one bipolar cell) increases sensitivity to light but reduces spatial resolution. Low convergence (one cone to one bipolar cell at the fovea) preserves spatial detail.

Converging and Diverging Lenses

• Real-is-positive sign convention: Distances are measured from the optical centre of the lens. Object distance u is positive when the object is on the incoming-light side (real object). Image distance v is positive when the image forms on the outgoing-light side (real image). Focal length f is positive for a converging lens and negative for a diverging lens.

Common Eye Defects

• Myopia (short-sightedness): A condition in which parallel rays from a distant object are refracted to a focus at a point in front of the retina, producing a blurred image of distant objects. Near objects remain clear because the eye can accommodate sufficiently for shorter distances.
• Hypermetropia (long-sightedness): A condition in which rays from a near object would converge at a point behind the retina, producing a blurred image of near objects. The eye lacks sufficient converging power, typically because the eyeball is too short or the cornea is insufficiently curved.
• Astigmatism: A refractive defect caused by an irregularly shaped cornea or lens, in which the curvature differs between perpendicular planes (meridians). Rays in one plane are focused at a different distance from rays in the perpendicular plane, so no single sharp image forms on the retina at any distance.

Correcting Eye Defects

• Dioptre (D): The SI unit of lens power. One dioptre is the power of a lens with a focal length of exactly one metre. A +2 D lens converges light; a −3 D lens diverges light.
• Far point: The most distant point that the eye can focus on clearly without accommodation. For a normal eye this is at infinity; for a myopic eye it is at a finite distance in front of the eye.
• Near point: The closest point that the eye can focus on clearly with maximum accommodation. For a standard adult eye this is taken as 25 cm. A hypermetropic eye has a near point beyond 25 cm.
• Astigmatism prescription format: Written as: Sphere (SPH) / Cylinder (CYL) × Axis. SPH gives the spherical correction in dioptres. CYL gives the cylindrical correction in dioptres (the additional power needed in one meridian). Axis gives the orientation of the cylindrical lens in degrees (0°–180°).

Equal Loudness Curves & Intensity Perception

• Intensity level (dB): The intensity level L of a sound is defined as L = 10 10(I/I0), where I is the intensity of the sound in W m^-2 and I0 = 1 × 10^-12 W m^-2 is the reference intensity (the threshold of hearing at 1 kHz). The unit is the decibel (dB).
• Phon: The phon is the unit of loudness level. A sound of any frequency has a loudness level of N phons if it is judged by a normal listener to be equally loud as a 1 kHz tone with an intensity level of N dB SPL. The phon scale is defined by the equal loudness curves.

Sound Intensity and the Decibel Scale

• Intensity (I): The power transmitted per unit area perpendicular to the direction of propagation of the wave. SI unit: watts per square metre (W m⁻²). Mathematically: I = P/A, where P is the power in watts and A is the area in m².

Noise Damage and Age-Related Hearing Loss

• Noise-induced hearing loss (NIHL): A reduction in hearing sensitivity caused by damage to cochlear hair cells from excessive sound exposure. Characterised by a notch — a localised upward shift in the equal loudness curve — centred around 4 kHz, with recovery of sensitivity at higher frequencies such as 8 kHz.

The Ear: Structure and Sound Transmission

• Outer ear: Consists of the pinna (the visible, curved flap of cartilage) and the ear canal (external auditory meatus). The pinna funnels sound waves into the ear canal, which directs them towards the tympanic membrane. The shape of the pinna also provides directional cues.
• Middle ear: An air-filled cavity containing the three ossicles (malleus, incus, and stapes) and connected to the throat via the Eustachian tube. It transmits vibrations from the tympanic membrane to the oval window of the cochlea, providing mechanical amplification through impedance matching.
• Inner ear: Contains the cochlea (responsible for hearing) and the semicircular canals (responsible for balance). The cochlea is a fluid-filled, coiled structure divided into three compartments: the scala vestibuli and scala tympani (both containing perilymph) and the scala media (cochlear duct, containing endolymph). The scala media is separated from the scala vestibuli above by Reissner's membrane, and bounded below by the basilar membrane. Mechanical vibrations are transduced into nerve impulses by sensory hair cells on the basilar membrane.

Understanding ECG Waveforms

• Electrocardiogram (ECG): A recording of the electrical potential differences generated by the heart's muscle activity, detected at the body surface using electrodes and plotted as voltage against time. It reflects the sequence of depolarisation and repolarisation events during each cardiac cycle.
• P wave: The small, rounded, upward deflection at the start of each cardiac cycle on the ECG. It represents the depolarisation of the atrial muscle as the electrical impulse spreads outward from the sinoatrial (SA) node across both atria, triggering atrial contraction.
• QRS complex: The sharp, large deflection on the ECG trace representing the rapid depolarisation of the ventricular muscle. Its large amplitude (typically around 1–1.5 mV) reflects the much greater muscle mass of the ventricles. It triggers ventricular contraction (systole). Duration is normally less than 0.12 s.
• T wave: The broad, rounded deflection following the QRS complex on the ECG trace. It represents the repolarisation of the ventricular muscle — the recovery of the membrane potential — as the ventricles relax (diastole). It is broader and lower in amplitude than the QRS complex because repolarisation is a slower, less synchronised process.

Ultrasound Principles: Acoustic Impedance and Wave Behaviour

• Acoustic impedance, Z: The acoustic impedance of a medium is defined as the product of its density ρ (in kg m⁻³) and the speed of sound c (in m s⁻¹) within that medium. It is measured in kg m⁻² s⁻¹, sometimes called the rayl. The equation is Z = ρ c.

Generating and Detecting Ultrasound Pulses

• Piezoelectric effect: When an alternating voltage is applied across a piezoelectric crystal, the crystal oscillates mechanically at the same frequency as the applied voltage, producing a pressure wave (ultrasound). Conversely, when a pressure wave deforms the crystal, a corresponding alternating voltage is produced across it.
• A-scan (Amplitude scan): A display in which the amplitude of each returning echo is plotted on the vertical axis against the time of arrival (and therefore depth) on the horizontal axis. It produces a one-dimensional trace showing the positions and relative strengths of reflecting boundaries along a single line through the tissue.
• B-scan (Brightness scan): A two-dimensional image formed by sweeping the ultrasound beam across the tissue (either by moving the transducer or using an array of elements) and converting each echo amplitude into a pixel brightness at the corresponding position. Stronger echoes appear brighter. The result is a cross-sectional image of internal structures.

Applications of Ultrasound Imaging

• Acoustic impedance (Z): The product of a medium's density (ρ, in kg m^-3) and the speed of sound in that medium (v, in m s^-1). Expressed as Z = ρ v, with units kg m^-2 s^-1 (also written as rayl). The larger the difference in Z between two adjacent media, the greater the fraction of ultrasound reflected at their boundary.

Fibre Optics in Medical Physics

• Critical angle (θc): The angle of incidence in the denser medium at which the refracted ray travels along the boundary (angle of refraction = 90°). For angles of incidence greater than θc, total internal reflection occurs. Calculated using sin θc = n2/n1, where n1 is the refractive index of the denser medium and n2 is the refractive index of the less dense medium.
• Cladding: A layer of material surrounding the core of an optical fibre, with a lower refractive index than the core. Its function is to ensure total internal reflection occurs at the core-cladding boundary, keeping light confined within the core.

Endoscopes: Principles and Applications

• Critical angle: The angle of incidence (measured from the normal to the boundary) at which the refracted ray travels along the boundary surface, giving a refraction angle of exactly 90°. For any angle of incidence greater than the critical angle, total internal reflection occurs.
• Coherent fibre bundle: A bundle of optical fibres in which each fibre maintains the same spatial position relative to all other fibres at both the input and output ends. This positional correspondence means the pattern of light entering one end is faithfully reproduced at the other end, transmitting a recognisable image.

MRI: Alignment and Precession

• Superconducting magnet: A magnet whose coils operate at temperatures close to absolute zero, giving zero electrical resistance and allowing a persistent current to flow. This produces the strong, uniform magnetic field needed to align proton spins throughout a patient's body.
• Parallel alignment: The orientation of a proton's spin magnetic moment in the same direction as the applied external magnetic field. This is the lower-energy state. In MRI, the net excess of protons in this state creates the bulk magnetisation that the scanner detects.
• Larmor frequency: The frequency at which a proton's spin axis precesses about an applied magnetic field. It is proportional to the magnetic field strength: f = γ B, where γ is the gyromagnetic ratio for hydrogen and B is the magnetic flux density. For clinical MRI fields, this frequency lies in the radiofrequency range.

MRI: Excitation, Detection, and Imaging

• Gradient field coil: An electromagnet that superimposes a spatially varying magnetic field onto the main static field B0, making the proton Larmor frequency vary linearly with position. This allows the scanner to select a specific cross-sectional slice — or, with two orthogonal gradients, a specific voxel — for excitation.
• RF excitation pulse: A short burst of radiofrequency electromagnetic radiation, tuned to the Larmor frequency of the target slice, that causes protons to absorb energy and change spin state from the lower-energy alignment to the higher-energy state. The pulse duration and amplitude determine the flip angle.

X-ray Attenuation

• Exponential attenuation: X-ray intensity decreases exponentially with the thickness of absorbing material. Each equal increment of thickness reduces the intensity by the same multiplicative factor. The relationship is described by I = I0 e^-μ x.

Differential Tissue Absorption

• Differential tissue absorption: The variation in the degree to which different biological tissues attenuate an X-ray beam. Tissues that absorb more X-rays allow fewer photons to reach the detector, producing a lighter (whiter) region on the image. Tissues that absorb fewer X-rays allow more photons through, producing a darker region.
• Radiodensity (radiographic density): A qualitative description of how strongly a tissue attenuates X-rays. High radiodensity tissues (bone, metal) appear white on an X-ray image. Low radiodensity tissues (air, lung) appear black. The term is used clinically to describe and compare the appearance of structures on an image.

CT Scanner Principles

• Gantry: The large ring-shaped housing of a CT scanner within which the X-ray tube and detector array rotate around the patient. The patient lies on a motorised table that passes through the central aperture of the gantry during scanning.
• Monochromatic beam: An X-ray beam in which all photons carry the same energy (equivalently, the same frequency and wavelength). In CT scanning, monochromaticity ensures that each tissue type has a single, consistent linear attenuation coefficient, making quantitative image reconstruction mathematically reliable.
• CT number (Hounsfield unit): A quantitative measure of the X-ray attenuation of a tissue voxel relative to water, expressed in Hounsfield units (HU). Water = 0 HU; air ≈ −1000 HU; cortical bone ≈ +1000 HU. The CT number determines the greyscale value assigned to each voxel in the reconstructed image.

CT Scanner: Advantages and Disadvantages

• Spatial resolution in CT imaging: The ability of the scanner to distinguish between two closely spaced structures as separate objects. Modern CT scanners can resolve structures separated by less than 1 mm, far exceeding the capability of a standard planar X-ray.
• Effective dose: A measure of the biological risk from ionising radiation exposure, accounting for the type of radiation and the sensitivity of the tissues irradiated. Measured in millisieverts (mSv). It allows comparison of radiation risk across different imaging procedures.

X-ray Production and Energy Spectrum

• Accelerating voltage (V): The potential difference applied between cathode and anode in an X-ray tube. It determines the kinetic energy gained by each electron: Ek = eV. Increasing V increases both the maximum photon energy and the overall intensity of the X-ray beam.
• Characteristic X-ray energy: The energy of a characteristic X-ray photon equals the difference between the energy levels of the two electron shells involved in the transition: Ephoton = Eupper shell - Elower shell, where energy levels are negative quantities and the lower (inner) shell has a more negative energy level than the upper (outer) shell. This difference is always positive, giving the photon energy. These energies are fixed for a given target element and appear as sharp peaks on the X-ray spectrum.

X-ray Tube Design and Image Control

• Focal spot: The small area on the anode where the electron beam strikes and X-rays are produced. A smaller focal spot improves image sharpness but concentrates heat; the rotating anode allows a small effective focal spot without localised overheating.

Flat Panel Detectors vs. Photographic Detection

• Latent image: The invisible pattern of altered silver halide crystals formed in photographic film upon X-ray exposure, which becomes a visible image only after chemical development.
• Scintillation: The process by which a material absorbs high-energy radiation (such as X-ray photons) and re-emits the energy as lower-energy visible light photons.

Contrast Enhancement and Photographic Methods

• Contrast enhancement: The deliberate introduction of an X-ray opaque (or X-ray transparent) material into a body cavity or vessel to create a detectable difference in X-ray attenuation between that structure and its surroundings, making the structure visible on a radiograph.
• Intensifying screen: A screen coated with a fluorescent material (such as calcium tungstate or rare-earth phosphors) that is placed in close contact with photographic film inside a light-tight cassette. X-ray photons are absorbed by the fluorescent material, which then emits visible light photons. The film is far more sensitive to visible light than to X-rays, so the light from the screen exposes the film efficiently.
• Fluoroscopic image intensification: An electronic system that converts a continuous, real-time X-ray image into a bright, visible image suitable for viewing or recording. X-ray photons strike the input phosphor screen, producing visible light photons; these strike the photocathode, releasing photoelectrons via the photoelectric effect; the electrons are accelerated through a high voltage and focused onto a small output phosphor screen, producing a bright, magnified image.

High-Energy X-Ray Therapy

• Linear accelerator (linac): The machine used to produce therapeutic X-ray beams. It accelerates electrons to near-light speed using microwave radiation, then directs them at a tungsten target. The rapid deceleration of electrons produces a beam of high-energy X-ray photons (bremsstrahlung radiation).
• Multi-leaf collimator (MLC): A device within the linac treatment head consisting of many individually movable tungsten leaves. The leaves are positioned to shape the beam aperture to match the tumour profile from each beam angle, minimising irradiation of adjacent healthy tissue.
• Fractionation: The division of the total radiotherapy dose into multiple smaller doses (fractions) delivered over days or weeks. Exploits the greater capacity of healthy cells to repair sub-lethal radiation damage between fractions, allowing a higher total tumour dose than a single session would permit.

Beta Emitting Implants for Internal Treatment

• Linear energy transfer (LET): The energy deposited per unit path length by a radiation type as it travels through matter, measured in keV per micrometre. Beta particles have moderate LET, sufficient to cause DNA strand breaks in target cells without the very high LET of alpha particles.

Comparing Imaging Techniques

• Spatial resolution: The minimum distance between two points that can be distinguished as separate in an image. Typically quoted in millimetres (mm) or line pairs per millimetre (lp/mm). Smaller values mean finer detail.
• ALARA principle: As Low As Reasonably Achievable — the guiding principle for radiation protection in medical imaging. Doses should be minimised while still obtaining diagnostically useful images.

Gamma Camera: Structure & Function

• Collimator: A thick lead plate containing thousands of narrow, parallel, lead-lined channels (holes). Only gamma photons travelling parallel to the channels — that is, perpendicular to the detector face — pass through to the crystal. Photons arriving at any other angle strike the lead walls and are absorbed.

Gamma-Emitting Radioisotopes as Tracers

• Radioactive tracer: A gamma-emitting radioisotope introduced into the body, attached to a biologically active compound, whose emitted gamma radiation is detected externally to produce a functional image of a target organ.

The Molybdenum-Technetium Generator

• Metastable state: A nuclear configuration in which the nucleus holds excess energy above its ground state but does not immediately release it. The nucleus eventually de-excites by emitting a gamma photon. In Tc-99m, this de-excitation has a half-life of approximately 6 hours.
• Elution (in the generator context): The process of passing saline through the generator column to wash out the accumulated Tc-99m as sodium pertechnetate solution, leaving the Mo-99 parent bound to the alumina support.

Introduction to PET Scans

• Positron (β^+ particle): A particle with the same mass as an electron (9.11 × 10^-31 kg) but with a charge of +1.6 × 10^-19 C. It is the antiparticle of the electron. Produced during β^+ decay of proton-rich nuclei.

Physical, Biological and Effective Half-lives

• Physical half-life (TP): The time for the activity of a radioactive nuclide to decrease to half its original value due to radioactive decay alone. It is a nuclear property — fixed by the identity of the nuclide and completely unaffected by temperature, pressure, chemical bonding, or whether the nuclide is inside a patient or sitting in a lead-lined container. For example, technetium-99m has a physical half-life of approximately 6 hours.
• Biological half-life (TB): The time for the body to remove half of an administered substance through normal physiological processes — including renal filtration, hepatic metabolism, and excretion — independent of any radioactive decay. It depends on the chemical form of the tracer, the organ it targets, and the patient's own physiology. For example, iodine administered as iodide is taken up and retained by the thyroid, giving it a long biological half-life in that organ.

Engineering physics (A-level only)

23 cards from 15 lessons. Each term links to the lesson it comes from.

Moment of Inertia: Point Masses and Extended Objects

• Perpendicular distance r: The shortest distance from the axis of rotation to the mass element, measured at right angles to the axis. It is not the distance along the rod or the distance to the nearest point of the object — it is always the perpendicular (normal) distance. Using the wrong distance is the most common calculation error in this topic.

Angular Kinematics: Displacement, Speed & Acceleration

• Angular displacement (θ): The angle through which a body rotates about a fixed axis, measured in radians (rad). A full revolution corresponds to θ = 2π rad ≈ 6.28 rad. Angular displacement is a vector quantity: the sign indicates the direction of rotation (conventionally, anticlockwise is positive).
• Angular speed and angular velocity (ω): Angular speed is the magnitude of the rate of change of angular displacement: |ω| = |Δθ / Δ t|, measured in rad s⁻¹. Angular velocity is the vector form — it carries a sign (or direction along the rotation axis) to indicate the sense of rotation. At A-level, AQA uses ω for both, with sign convention applied where direction matters.
• Angular acceleration (α): The rate of change of angular velocity with respect to time: α = Δω / Δ t, measured in rad s⁻². A positive α means the angular velocity is increasing (speeding up in the positive direction); a negative α means it is decreasing (slowing down or accelerating in the negative direction).

Equations of Motion for Rotational Kinematics

• Uniform angular acceleration: A condition in which the angular acceleration α of a rotating body remains constant over the time interval considered. Under this condition, the four rotational equations of motion are valid. If α changes with time, these equations cannot be applied directly.

Rotational Kinetic Energy

• Moment of Inertia (I): The rotational equivalent of mass. For a system of point masses, I = mi ri^2, where ri is the perpendicular distance of each mass element from the axis of rotation. Measured in kg m². A larger I means more energy is stored for the same ω.

Flywheel Energy Storage

• Moment of inertia (I): The rotational equivalent of mass. Defined as I = mr^2, where each element of mass m is at distance r from the rotation axis. A larger moment of inertia means more energy is stored at a given angular velocity, and more torque is required to change the angular velocity. Units: kg m².
• Torque smoothing: The process by which a flywheel's large moment of inertia resists rapid changes in angular velocity, absorbing energy during high-torque phases and releasing it during low-torque phases. The result is a more uniform angular velocity and a steadier output torque from the machine.

Angular Momentum: Definition and Conservation

• Angular momentum (L): The product of a body's moment of inertia and its angular velocity about a given axis. L = Iω. The SI unit is kg m² s⁻¹.
• Conservation of angular momentum: The total angular momentum of a system is constant provided no resultant external torque acts on the system. If net = 0, then Ltotal = constant, so I1ω1 = I2ω2.

Angular Impulse and Real-World Applications

• Angular Impulse: The product of a constant torque T and the time interval Δ t over which it acts. Angular impulse equals the change in angular momentum of the body: TΔ t = Δ(Iω). Measured in N m s (equivalent to kg m² s⁻¹).

Four-Stroke Engine Cycles and Indicator Diagrams

• Net work per cycle: The net work done by the working gas per cycle equals the area enclosed by the indicator diagram on a p-V graph. Mathematically, Wnet = ∫ p dV, where the integral is taken around the complete loop.

Engine Power and Efficiency Calculations

• Friction Power: The power lost to internal mechanical friction within the engine. It equals the difference between indicated power and brake power: friction power = indicated power − brake power. Measured in watts (W).

Reversed Heat Engines: Principles and Uses

• First law applied to a reversed heat engine: Energy conservation requires that the heat delivered to the hot reservoir equals the heat extracted from the cold reservoir plus the work supplied: QH = QC + W. No energy is created or destroyed.
• Coefficient of performance of a refrigerator (COPref): The ratio of the thermal energy extracted from the cold reservoir to the work input: COPref = QCW. A higher value means more cooling per joule of work supplied.
• Coefficient of performance of a heat pump (COPHP): The ratio of the thermal energy delivered to the hot reservoir to the work input: COPHP = QHW. Because QH = QC + W, the COP of a heat pump is always greater than 1.

Coefficient of Performance: Refrigerators and Heat Pumps

• Ideal (Carnot) COP: The maximum possible COP for a device operating between temperatures TC and TH, derived from the Carnot efficiency. It sets an upper bound; real devices fall below it due to irreversibilities such as friction and heat losses.

The Second Law and Engine Efficiency

• First Law of Thermodynamics: Energy cannot be created or destroyed; the total energy of an isolated system is constant. For a heat engine: QH = W + QC, where QH is heat absorbed from the hot source, W is work done by the engine, and QC is heat rejected to the cold sink.
• Second Law of Thermodynamics (engine statement): It is impossible for a heat engine operating in a complete cycle to convert all of the heat absorbed from a hot source into work. Some heat QC must always be rejected to a cold sink at a lower temperature TC < TH.

Understanding p-V Diagrams

• Isothermal process: A process in which the temperature of the gas remains constant throughout. On a p–V diagram, an isothermal process appears as a hyperbolic curve (since pV = nRT = constant when T is fixed). The curve is steeper at low volumes and flatter at high volumes.
• Adiabatic process: A process in which no heat is exchanged between the gas and its surroundings. On a p–V diagram, an adiabatic curve is steeper than an isothermal curve passing through the same point, because the gas cools as it expands (losing internal energy) and heats as it is compressed.

Cyclic Processes and Work Done

• Work done by a gas (general): For any process on a p-V diagram, the work done by the gas equals the area under the curve between the initial and final volumes. For a constant-pressure process specifically, this simplifies to W = pΔ V, where Δ V = Vfinal - Vinitial.

The First Law of Thermodynamics

• First Law of Thermodynamics: Q = Δ U + W: Q is the energy transferred to the system by heating (in joules). Δ U is the increase in internal energy of the system (in joules). W is the work done by the system on its surroundings (in joules). The equation expresses conservation of energy: all heat supplied either raises internal energy or is used to do work.

Turning points in physics (A-level only)

24 cards from 17 lessons. Each term links to the lesson it comes from.

Cathode Ray Production

• Discharge tube: A sealed glass tube containing gas at very low pressure (typically around 10^-3 Pa), fitted with a cathode and anode. When a high voltage (several kV) is applied across the electrodes, cathode rays are produced at the cathode and travel towards the anode.
• Thermionic emission: The emission of electrons from a heated metal cathode. Heating the metal gives conduction electrons sufficient thermal energy to overcome the work function and escape from the surface. This produces a more intense and controllable beam of cathode rays than field emission alone.

Millikan's Oil Drop Experiment: Equilibrium and Forces

• Condition for a stationary charged droplet: A droplet of charge Q is held stationary when the upward electric force equals the downward weight: QE = mg, where E is the electric field strength between the plates.

Stokes' Law and Significance of Millikan's Results

• Dynamic viscosity (): A measure of a fluid's resistance to flow, in units of Pa s (pascal-seconds). A higher value of means a thicker, more resistive fluid. Air has ≈ 1.8 × 10^-5 Pa s at room temperature.
• Quantisation of electric charge: Electric charge does not vary continuously. It only exists in discrete integer multiples of the elementary charge e = 1.6 × 10^-19 C. Any measured charge Q satisfies Q = ne where n is a positive or negative integer.

Determining Specific Charge

• Specific charge: The ratio of the charge of a particle to its mass. For the electron: e/me, where e = 1.60 × 10^-19 C and me = 9.11 × 10^-31 kg, giving e/me ≈ 1.76 × 10^11 C kg^-1.

Young's Double Slits: Unveiling Light's True Nature

• Corpuscular theory: Newton's model treating light as a stream of tiny particles (corpuscles). It explained reflection and offered a particle-based account of refraction, but could not explain interference or diffraction.

Black-Body Radiation and Planck's Quanta

• Black-body radiation: The electromagnetic radiation emitted by a perfect absorber (black-body) at thermal equilibrium. The spectrum of emitted radiation depends only on the temperature of the body, not on its material or shape.
• The ultraviolet catastrophe: The prediction of classical wave theory (Rayleigh-Jeans law) that a black-body should emit radiation of ever-increasing intensity at higher frequencies, leading to an infinite total radiated power. This directly contradicts experimental observation, where intensity falls sharply at high frequencies.

Einstein's Photoelectric Explanation

• Photon energy: The energy carried by a single photon is E = hf, where h = 6.63 × 10^-34 J s (the Planck constant) and f is the frequency of the radiation in hertz. Equivalently, E = hc/λ where c is the speed of light and λ is the wavelength.

Scanning Tunnelling Microscopes (STM)

• Quantum tunnelling: The passage of a quantum particle through a potential energy barrier that it could not overcome classically. The probability of tunnelling depends exponentially on the width of the barrier and on the particle's mass and the barrier height.

De Broglie's Hypothesis

• De Broglie's hypothesis: The proposal that any particle with momentum p has an associated wavelength given by λ = h/p, where h is the Planck constant. It extends wave-particle duality from radiation to all matter.

Inertial Frames and the Laws of Physics

• Frame of reference: A coordinate system attached to an observer, used to measure the positions, velocities, and times of physical events. Different frames can assign different numerical values to the same event.
• Inertial frame of reference: A frame of reference that is not accelerating — one that moves at constant velocity (including being at rest). In an inertial frame, Newton's first law holds: an object with no net force acting on it remains at rest or moves with constant velocity.
• Principle of relativity (Einstein's first postulate): The laws of physics have the same form in all inertial frames of reference. No experiment performed entirely within an inertial frame can determine whether that frame is at rest or moving at constant velocity.

Einstein's Postulates: The Foundation of Special Relativity

• First Postulate: Principle of Relativity: The laws of physics are the same in all inertial frames of reference. No experiment performed entirely within a uniformly moving laboratory can detect that laboratory's motion through space.
• Second Postulate: Invariance of the Speed of Light: The speed of light in free space, c = 3.0 × 10^8 m/s, is the same for all observers in all inertial frames of reference, regardless of the motion of the light source or the observer.

Understanding Length Contraction

• Length contraction: The phenomenon whereby the measured length of an object moving at speed v relative to an observer is less than its proper length l0. The contracted length l is given by l = l0√(1 - v^2/c^2). Contraction occurs only along the direction of motion.

Time Dilation: Introduction

• Proper time (t0): The time interval between two events as measured by a clock that is present at both events — that is, a clock at rest relative to the process being timed. Proper time is always the minimum time interval any observer can measure between those two events.

Experimental Evidence: Muon Decay

• Time Dilation Equation: The dilated time interval t measured by a stationary observer is related to the proper time t0 (measured in the moving frame) by t = γ t0, where γ = 1/√(1 - v^2/c^2) is the Lorentz factor. Since γ ≥ 1, the observed lifetime is always greater than or equal to the proper lifetime.

Mass-Energy Equivalence and Relativistic Kinetic Energy

• Mass-energy equivalence: The principle that mass and energy are equivalent and interconvertible, quantified by E0 = m0 c^2, where m0 is the rest mass (kg), c is the speed of light in a vacuum (3.0 × 10^8 m/s), and E0 is the rest energy (J).

Bertozzi's Experiment: Evidence for Relativistic Kinetic Energy

• Time-of-flight measurement: A technique for measuring particle speed by timing how long a particle takes to travel a known, fixed distance. Speed is then calculated as v = d/t. In Bertozzi's experiment, the flight path was 8.4 m.

Michelson-Morley Experiment: Unveiling the Invariance of Light

• Interference fringe shift: A displacement of the bright and dark bands in an interference pattern, caused by a change in the path difference between two recombined beams of light. In the Michelson-Morley experiment, a fringe shift would indicate that light travelled at different speeds along the two perpendicular arms.
• Invariance of the speed of light: The speed of light in a vacuum, c = 3.0 × 10^8 m/s, has the same measured value for all observers in inertial (non-accelerating) reference frames, irrespective of the relative motion between the observer and the light source. This is the second postulate of Einstein's special theory of relativity.

Electronics (A-level only)

65 cards from 32 lessons. Each term links to the lesson it comes from.

Zener Diode Characteristics and Operation

• Anode: The p-type terminal of a zener diode. Conventional current enters the anode when the diode is forward biased. In a voltage-regulator circuit, the anode is connected to the lower potential (negative supply rail or ground side).
• Cathode: The n-type terminal of a zener diode, marked by a band on the component body. In reverse-bias voltage regulation, the cathode is connected to the more positive potential. The zener symbol shows a bent-ended bar at the cathode to distinguish it from a standard diode.

Zener Diodes as Voltage References and Stabilizers

• Zener breakdown voltage (VZ): The reverse voltage at which a Zener diode enters controlled conduction, holding the voltage across its terminals approximately constant. Values are typically in the range 2.4 V to 200 V and are specified on the component datasheet.

Photodiode Characteristics and Operation

• Photocurrent (Iph): The current produced in a photodiode as a direct result of photon absorption generating electron-hole pairs in or near the depletion region. It is proportional to the incident light intensity (irradiance) for a given wavelength.
• Long-wavelength cut-off: The maximum wavelength at which a photodiode can respond, determined by the condition hf = Eg. Photons with wavelength longer than this cut-off have insufficient energy to excite electrons across the band gap, so no photocurrent is generated.

Photodiodes and Scintillation

• Photodiode: A p-n junction semiconductor device that generates a current when photons are absorbed in or near the depletion region. Each absorbed photon with sufficient energy creates one electron-hole pair; these carriers are swept apart by the electric field, producing a photocurrent.
• Scintillator: A material that absorbs ionising radiation and re-emits the energy as photons of visible or near-visible light. The number of photons produced is proportional to the energy deposited by the incident particle, making scintillators useful for both detecting and measuring the energy of atomic particles.

MOSFET Structure and Characteristics

• Gate: The control terminal of a MOSFET, separated from the semiconductor body by a thin insulating oxide layer. Because the gate is insulated, it draws negligible steady-state current, giving the MOSFET an extremely high input impedance.
• Threshold voltage (Vth): The minimum gate-source voltage (VGS) at which a conducting inversion channel forms between source and drain, allowing significant drain current (ID) to flow. Typical values for enhancement MOSFETs range from 1 V to 4 V.

MOSFET Applications: Switch and High Input Resistance Device

• N-channel enhancement mode MOSFET: A three-terminal semiconductor device (gate, drain, source) in which a positive gate-source voltage above the threshold value induces an N-type conducting channel, allowing current to flow from drain to source. With no gate voltage applied, the device is off.

Hall Effect Sensor Applications

• Attitude (in sensing contexts): The angular orientation of an object relative to a fixed reference frame. Monitoring attitude means continuously measuring how the object's orientation changes over time.

Analogue to Digital Conversion: The Basics

• Analogue signal: A signal whose amplitude varies continuously with time, capable of taking any value within a given range. Real-world examples include audio waveforms and temperature sensor outputs.
• Quantisation: The process of assigning each sampled voltage value to the nearest available discrete level. The number of levels available is determined by the number of bits used per sample.

Sampling Rate and Quality in Digital Conversion

• Sampling rate: The number of amplitude measurements taken per second from an analogue signal. Measured in hertz (Hz). A sampling rate of 44 100 Hz means 44 100 samples are recorded every second.
• Quantisation error: The difference between the true amplitude of an analogue signal at the moment of sampling and the nearest digital level available given the bit depth. Smaller bit depth means larger quantisation error and more audible distortion.
• Pulse code modulation (PCM): A method of digitally encoding an analogue signal. The signal is sampled at regular intervals (determined by the sampling rate), each sample amplitude is rounded to the nearest available quantisation level (determined by the bit depth), and that level is encoded as a binary number. The resulting sequence of binary codes forms the digital signal.

LC Resonance: Frequency and Analogy

• Inductance as mass analogy: Inductance L plays the role of mass in the LC-to-mass-spring analogy. Just as a large mass resists changes in velocity (inertia), a large inductance resists changes in current. Both quantities represent inertia — the tendency of a system to keep doing what it is already doing.
• Capacitance as spring analogy: Capacitance C plays the role of the spring (or more precisely, 1/C maps to spring stiffness k). A capacitor stores charge and, when displaced from equilibrium, provides a restoring voltage that drives current back — just as a spring provides a restoring force that drives the mass back towards equilibrium.

Energy Response and Q Factor

• 50% energy points: The two frequencies on the energy response curve at which the energy delivered to the load falls to half (50%) of the peak value. They define the edges of the bandwidth. Because energy is proportional to V², these points correspond to the voltage falling to 1/√(2) (approximately 0.707) of its peak value — sometimes called the '–3 dB points' in wider electronics contexts, though AQA focuses on the 50% energy description.

Op-Amp Fundamentals

• Non-inverting input (+): The input terminal at which a signal applied produces an output of the same polarity. If the non-inverting input is more positive than the inverting input, the output is positive.
• Infinite open-loop voltage gain (AOL ): An ideal op-amp amplifies the differential input voltage by an infinitely large factor. In practice this means that with negative feedback, the op-amp adjusts its output to keep the differential input (V+ - V-) effectively at zero.
• Infinite input impedance (Zin ): No current flows into either input terminal of an ideal op-amp. The input terminals draw zero current from the signal source, so the source is not loaded by the amplifier.
• Zero output impedance (Zout = 0): An ideal op-amp can supply any current demanded by the load without its output voltage changing. The output behaves as a perfect voltage source with no internal resistance.
• Infinite bandwidth: An ideal op-amp amplifies all frequencies equally, from DC up to infinitely high frequencies, with no reduction in gain. Real op-amps have a gain-bandwidth product that limits high-frequency performance.

Ideal Op-Amp Properties: Gain and Resistance

• Virtual earth: In a negative-feedback op-amp circuit, the inverting input is held at the same potential as the non-inverting input by the action of the feedback. When the non-inverting input is connected to 0 V (earth), the inverting input is also at 0 V — not because it is directly connected to earth, but because infinite open-loop gain forces the differential voltage to zero. This point is called a virtual earth.
• Input resistance (op-amp): The resistance presented at the input terminals of an op-amp. For an ideal op-amp, input resistance is infinite, so zero current is drawn from the signal source connected to either input terminal.

Op-Amp Transfer Function and Comparator

• Open-loop transfer function: The relationship between the output voltage and the differential input voltage of an op-amp when no external feedback is applied: Vout = AOL(V+ - V-), where AOL is the open-loop voltage gain (dimensionless), V+ is the non-inverting input voltage (V), and V- is the inverting input voltage (V).
• Comparator: A circuit in which an op-amp is operated open-loop to compare a signal voltage applied to one input against a reference voltage applied to the other. The output switches to positive saturation when V+ > V-, and to negative saturation when V- > V+.

Inverting Amplifier: Gain and Virtual Earth

• Virtual earth (virtual ground): The inverting input of an ideal op-amp in a negative-feedback circuit is said to be at virtual earth because it sits at 0 V — the same potential as the non-inverting input — even though no wire connects it directly to earth. The condition arises from two properties of an ideal op-amp acting together: (1) the open-loop gain A is so large that the differential voltage (V+ - V-) must be essentially zero for the output to remain finite; and (2) the input impedance is infinite, so no current flows into either input terminal.

Non-Inverting Amplifier Gain

• Negative feedback: A fraction of the output signal is fed back to the inverting input, opposing changes in the output. This stabilises the gain and makes it dependent on the external resistor ratio rather than the op-amp's open-loop gain.

Difference Amplifier Configuration

• Voltage Gain of a Difference Amplifier: The ratio Rf / R1, where Rf is the feedback resistor and R1 is the input resistor. It is dimensionless. The same ratio applies to both input paths when the resistors are matched, which is the condition required for the formula to hold.

Real Op-Amps: Limitations & Frequency Response

• Open-loop gain (AOL): The voltage amplification of an op-amp when no external feedback is applied. It is very large at DC (typically 10^5) but decreases with frequency, eventually falling to unity (1) at the unity-gain bandwidth frequency.
• Slew rate: The maximum rate of change of output voltage a real op-amp can sustain, expressed in V μs^-1. If an input signal demands a faster output change than the slew rate allows, the output waveform is distorted — steep edges become ramps.
• Unity-gain bandwidth (fT): The frequency at which the open-loop gain of an op-amp falls to exactly 1 (0 dB). It sets the upper limit of useful operation and is numerically equal to the gain-bandwidth product for a single-pole op-amp.

Gain × Bandwidth = Constant

• Gain-Bandwidth Product (GBP): For a given op-amp device, the product of the closed-loop voltage gain and the bandwidth at that gain setting is a constant. Mathematically: Av × fBW = constant. The GBP is also equal to the frequency at which the open-loop gain falls to unity (gain = 1), sometimes called the unity-gain bandwidth.

Logic Gates and Boolean Algebra

• NOT (complement): Written as A, read as 'not A'. The output is the inverse of the input: if A = 1 then A = 0, and vice versa.
• AND (conjunction): Written as A × B, read as 'A and B'. The output is 1 only when both A and B are 1; in all other cases the output is 0.
• OR (disjunction): Written as A + B, read as 'A or B'. The output is 1 when at least one of A or B is 1; the output is 0 only when both inputs are 0.

Advanced Logic Gates and Circuit Design

• NOT gate (inverter): A single-input gate that inverts its input. Output = 1 when input = 0, and output = 0 when input = 1. Boolean notation: A (A-bar). This is the simplest gate — it flips the signal.

Introduction to Astables

• Astable oscillator: A circuit with no stable output state that switches continuously between HIGH and LOW, producing a periodic square-wave clock signal. The timing is set by resistor and capacitor values in the circuit.
• Period (T): The time for one complete cycle of the waveform — one HIGH phase plus one LOW phase. Measured in seconds (s). Equal to the sum of the mark time and the space time: T = tmark + tspace.
• Pulse width: The duration of a single HIGH pulse — equivalent to the mark time tmark. Measured in seconds (s). In a 555 astable, the pulse width is determined by the values of RA, RB, and C.

Frequency Control in Astables

• Time constant (τ): The time constant τ = RC, where R is resistance in ohms (Ω) and C is capacitance in farads (F). It gives the time in seconds for the capacitor voltage to rise to approximately 63% of the supply voltage during charging, or fall to approximately 37% of its starting voltage during discharging.

Binary, BCD, and Johnson Counters

• Binary counter: A sequential logic circuit built from cascaded flip-flops that counts upward through binary states (0000, 0001, 0010,...) on successive clock pulses, resetting to 0000 after reaching its maximum count.
• BCD counter (Binary Coded Decimal counter): A 4-bit counter that cycles through only the ten states 0000 to 1001 (decimal 0 to 9), then resets to 0000. States 1010 to 1111 are unused. Used to represent individual decimal digits in binary form.
• Johnson counter (twisted ring counter): A shift-register counter in which the complemented output (Q) of the final stage feeds back to the input of the first stage. For n flip-flops, the counter produces a sequence of 2n unique states before repeating.

Counting Circuit Basics: Inputs and Outputs

• Clock input (CLK): The clock input is the timing signal that drives the counter forward. On each active clock edge — usually the rising edge, where the signal transitions from 0 to 1 — the counter advances its count by one step. The frequency of the clock signal therefore determines how rapidly the count changes.
• Reset input: The reset input forces all output bits simultaneously to logic 0, returning the counter to the state 0000 regardless of its current count. On most counters this is an asynchronous reset, meaning it takes effect immediately when asserted, without waiting for the next clock edge.
• Up/Down input: The up/down input selects the direction of counting. When set to logic 1 (up mode), the counter increments by one on each clock edge. When set to logic 0 (down mode), the counter decrements by one on each clock edge. This allows the same circuit to count upwards or downwards depending on the control signal applied.

Modulo-n Counters and Gate Building Blocks

• Reset pin: An input on a counter IC that forces all flip-flop outputs to zero when driven to its active level (often active-LOW, meaning a logic 0 triggers the reset). Once the reset signal is removed, the counter resumes counting from zero.

AM and FM Modulation: Principles and Bandwidth

• Carrier wave: A sinusoidal wave of constant, high frequency and constant amplitude, used as the medium for transmitting information. It carries no useful information on its own — it is modified by the information signal during modulation.
• Frequency deviation (Δf): The maximum shift in the carrier frequency above or below its unmodulated (rest) frequency, caused by the information signal. Measured in Hz. A larger information signal amplitude produces a larger frequency deviation.

Analyzing AM and FM Signals: Frequency and Data Capacity

• Carrier frequency: The number of complete oscillations per second of the unmodulated carrier wave, read from a voltage-time graph as the frequency of the rapid oscillation. Measured in hertz (Hz).
• Information frequency: The frequency of the modulating (audio) signal that carries the actual data or sound. It is read from a voltage-time graph as the frequency of the slow envelope variation in AM, or the slow variation in carrier spacing in FM. Measured in hertz (Hz).
• Bandwidth (of a signal): The range of frequencies occupied by a modulated signal, equal to the difference between its highest and lowest frequency components. Measured in hertz (Hz). For an AM signal carrying audio up to frequency finfo, the bandwidth is 2finfo.

Introduction to Communication Systems

• Input transducer: A device that converts a non-electrical input signal — such as sound, light, or temperature — into an electrical signal that the rest of the system can process. A microphone is the classic example: it converts pressure variations in air (sound waves) into a varying voltage.
• Transmitter-side signal processor: The stage that prepares the electrical signal for transmission. Its purposes include amplification (increasing signal strength), filtering (removing unwanted frequencies), and modulation (encoding the signal onto a carrier wave suitable for the chosen transmission medium).
• Transmission medium: The physical channel through which the processed signal travels from transmitter to receiver. Examples include copper wire (electrical signals), optical fibre (light pulses), and free space (electromagnetic waves). The medium introduces attenuation (reduction in signal strength) and noise.
• Receiver-side signal processor: The stage that recovers the original information signal from the received (degraded) signal. Its purposes include amplification (restoring signal strength lost to attenuation), filtering (removing noise), and demodulation (extracting the original information from the carrier wave).
• Output transducer: A device that converts the recovered electrical signal back into a physical form useful to the recipient. A loudspeaker is the standard example: it converts a varying electrical current into pressure variations in air, reproducing the original sound.

Time-Division Multiplexing: Basic Principles

• Time-Division Multiplexing (TDM): A method of transmitting multiple digital signals over a single channel by allocating each signal a dedicated, repeating time slot within a continuous frame structure. The channel carries only one signal's data at any instant, but cycles through all signals so rapidly that each appears to have continuous access.

Transmission Media: Wires, Fibres & Radio

• Attenuation: The loss of signal power as it propagates through a medium. In metal wire, attenuation increases with frequency and distance, limiting the usable data rate over long runs.
• Total internal reflection: The complete reflection of a light ray at the boundary between two media when the angle of incidence exceeds the critical angle. This is the mechanism that confines light within an optic fibre.

Satellite Systems and Frequencies

• Rain fade: The attenuation (weakening) of a microwave or millimetre-wave signal caused by absorption and scattering by water droplets in heavy rainfall. More severe at higher frequencies, particularly above 10 GHz.
• De-sensitisation: The reduction in a receiver's sensitivity caused by a strong signal — often the receiver's own transmitted signal — on the same or a nearby frequency. The receiver is effectively blinded to the weak signal it is trying to detect.