Question Pages500
Dense answer pages linked by topic.
Formula Pages53
Concept explainers and deep dives.
Total Topic Pages553
Indexed study content in one hub.
Astrophysics & Cosmology
65
Question explainer pages
Biophysics & Medical Physics
35
Question explainer pages
Classical Mechanics
70
Question explainer pages
Electromagnetism
65
Question explainer pages
Nuclear & Particle Physics
45
Question explainer pages
Quantum Physics
66
Question explainer pages
Relativity
48
Question explainer pages
Thermodynamics
56
Question explainer pages
Waves & Optics
50
Question explainer pages
Formula Explainers
These pages answer the fastest conceptual version of each equation, then send the reader into the full multi-level deep dive and topic quiz.
- Ampere's Law (Electromagnetism)
- Angular Momentum (Mechanics)
- Archimedes' Principle (Fluids)
- Bernoulli's Equation (Fluids)
- Capacitance (Electromagnetism)
- Carnot Efficiency (Thermodynamics)
- Centripetal Force (Mechanics)
- Conservation of Mechanical Energy (Mechanics)
- Continuity Equation (Fluids)
- Coulomb Constant (Electromagnetism)
- Coulomb's Law (Electromagnetism)
- Diffraction Grating (Waves & Optics)
- Electric Field of a Point Charge (Electromagnetism)
- Electric Power (Electromagnetism)
- Energy Stored in a Capacitor (Electromagnetism)
- Faraday's Law of Induction (Electromagnetism)
- First Law of Thermodynamics (Thermodynamics)
- Gauss's Law (Electromagnetism)
- Gauss's Law for Magnetism (Electromagnetism)
- Gravitational Potential Energy (Mechanics)
- Half-Life Decay (Quantum)
- Heisenberg Uncertainty Principle (Quantum)
- Hooke's Law (Mechanics)
- Ideal Gas Law (Thermodynamics)
- Kinetic Energy (Mechanics)
- Larmor (Cyclotron) Frequency (Electromagnetism)
- Lens Formula (Waves & Optics)
- Lorentz Force (Electromagnetism)
- Magnetic Field Around a Wire (Electromagnetism)
- Magnetic Flux (Electromagnetism)
- Magnetic Force on a Moving Charge (Electromagnetism)
- Mass–Energy Equivalence (Relativity)
- Momentum (Mechanics)
- Newton's Law of Gravitation (Mechanics)
- Newton's Second Law (Mechanics)
- Ohm's Law (Electromagnetism)
- Photon Energy (Quantum)
- Planck's Relation (Quantum)
- Poiseuille's Law (Mechanics)
- Power (Mechanics)
- Pressure (Fluids)
- Resistivity (Electromagnetism)
- Rotational Kinetic Energy (Mechanics)
- Series Combination of Focal Lengths (Waves & Optics)
- Snell's Law of Refraction (Waves & Optics)
- Stefan–Boltzmann Law (Thermodynamics)
- Time-Dependent Schrödinger Equation (Quantum)
- Torque (Mechanics)
- Transformer Law (Electromagnetism)
- Wave Speed (Waves & Optics)
- Wave Speed on a String (Waves & Optics)
- Work (Mechanics)
- de Broglie Wavelength (Quantum)
Astrophysics & Cosmology (65 pages)
- A quasar is:
- Baryogenesis explains why the universe contains matter rather than equal matter–antimatter. The Sakharov conditions require:
- Baryon acoustic oscillations (BAOs) are used as:
- Cepheid variable stars are used to measure distance because:
- Dark matter was first inferred from:
- Gravitational lensing is caused by:
- Hawking radiation predicts that black holes:
- Hubble's law states that the recessional velocity of a galaxy is proportional to:
- In stellar structure, the virial theorem implies that for a contracting protostar:
- LIGO detected gravitational waves from:
- Magnetars are neutron stars with:
- Neutron stars are supported against collapse by:
- Primordial nucleosynthesis (BBN) predicts a helium mass fraction of approximately:
- Pulsar timing arrays (PTAs) are sensitive to gravitational waves with:
- Solar flares are associated with:
- Synchrotron radiation is produced when:
- The Birkhoff theorem in general relativity states:
- The Chandrasekhar–Friedman–Schutz instability concerns:
- The H–R diagram plots stars by:
- The Jeans instability determines:
- The Oort Cloud is:
- The Penrose process extracts energy from:
- The Schwarzschild radius of a black hole is:
- The Sunyaev–Zel'dovich effect describes:
- The Tolman–Oppenheimer–Volkoff limit determines:
- The age of stars can be estimated from:
- The characteristic frequency of gravitational wave emission from a binary system depends on:
- The cosmic inflation epoch occurred:
- The cosmic microwave background radiation is evidence for:
- The flatness problem in cosmology refers to:
- The horizon problem in cosmology refers to:
- The main sequence on the H–R diagram corresponds to:
- The observable universe has a radius of approximately:
- The proton–proton chain in the Sun primarily produces:
- The solar wind is composed of:
- The spectral index n_s ≈ 0.96 measured from CMB anisotropies is evidence for:
- The unit parsec equals approximately:
- The ΛCDM model of cosmology includes:
- Type Ia supernovae are used as standard candles because:
- What are pulsars?
- What determines the colour of a star?
- What is a light-year?
- What is a nebula?
- What is a supernova?
- What is an astronomical unit (AU)?
- What is dark energy thought to cause?
- What is nucleosynthesis?
- What is stellar parallax used for?
- What is the Big Bang?
- What is the Chandrasekhar limit?
- What is the approximate age of the universe?
- What is the cause of galactic rotation curves being flat?
- What is the closest star to Earth after the Sun?
- What is the equation of state parameter w for dark energy if it behaves as a cosmological constant?
- What is the galactic centre of the Milky Way likely to contain?
- What is the name for the apparent change in frequency of a wave as the source moves?
- What is the name of our galaxy?
- What is the r-process in stellar nucleosynthesis?
- What is the significance of the photon sphere around a black hole?
- What powers the Sun?
- What type of star will the Sun eventually become?
- Which formula gives the luminosity–temperature relation for stars?
- Which layer of the Sun is visible to the naked eye?
- Which observational evidence best supports the Big Bang model?
- Which observational technique reveals the mass of exoplanets via host star wobble?
Biophysics & Medical Physics (35 pages)
- Acoustic impedance Z of a medium is defined as:
- Bremsstrahlung radiation in an X-ray tube is produced when:
- Diffusion MRI measures:
- Electrocardiography (ECG) measures:
- Fractal geometry in physiology is most prominently seen in:
- In CT imaging, Hounsfield units define:
- In MRI, the signal-to-noise ratio (SNR) scales with B₀ as approximately:
- Laplace's law for a spherical alveolus with surface tension γ and radius r gives transmural pressure:
- Magnetic susceptibility artefacts in MRI occur near:
- Medical ultrasound typically uses frequencies in:
- Nuclear medicine SPECT uses:
- Oxygen delivery to tissues depends on Fick's law of diffusion, with flux proportional to:
- PET scanning detects:
- Poiseuille's law gives blood flow Q through a vessel as:
- Proton therapy has clinical advantage over conventional photon therapy because:
- Radiation therapy uses high-energy photons or particles to:
- Surface tension in the lungs is reduced by:
- The ALARA principle in radiation protection stands for:
- The Bernoulli effect in haemodynamics implies that in a stenosis (narrowed vessel):
- The Frank–Starling mechanism relates cardiac output to:
- The Goldman–Hodgkin–Katz equation extends the Nernst equation to:
- The Hodgkin–Huxley model describes the action potential using:
- The Nernst potential determines:
- The Reynolds number determines whether blood flow is laminar or turbulent. Turbulence occurs above Re ≈:
- The action potential velocity in a myelinated nerve fibre is increased by:
- The conductance-based neural network model extends Hodgkin–Huxley to networks and reveals:
- The effective dose in radiation physics is measured in:
- The impedance of a cell membrane arises primarily from:
- The specific absorption rate (SAR) in MRI represents:
- The threshold for tissue damage from ultrasound is primarily driven by:
- What does a sphygmomanometer measure?
- What unit is used for absorbed radiation dose?
- Which imaging modality uses no ionising radiation?
- Which physics principle underlies MRI imaging?
- X-ray contrast agents increase visibility of blood vessels because they:
Classical Mechanics (70 pages)
- A 10 N force acts over 5 m in the direction of motion. Work done is:
- A 2 kg object accelerates at 3 m/s². What is the net force?
- A 3 kg object moving at 4 m/s has momentum of:
- A 4 kg object experiences a net force of 12 N. Its acceleration is:
- A 5 kg block slides 10 m on a surface with μk = 0.3. Work done by friction is:
- A ball is thrown horizontally from a cliff. Which graph best describes its vertical displacement?
- A ball is thrown upward. At its highest point, its velocity is:
- A car rounds a flat curve of radius 50 m at 20 m/s. Required centripetal force for 1000 kg is:
- A driven oscillator at resonance is characterised by:
- A gyroscope precesses because:
- A projectile's horizontal velocity (ignoring air resistance):
- A rigid body's rotational kinetic energy is:
- A satellite in a lower orbit compared to one in a higher orbit will move:
- A spring with k = 200 N/m is compressed 0.05 m. Elastic PE stored is:
- An athlete exerts a force over 0.2 s to accelerate a 0.5 kg ball from rest to 20 m/s. Impulse is:
- An object in uniform circular motion has constant:
- Buoyancy force on a submerged object equals:
- Centre of mass of a uniform rod is located at:
- Centripetal acceleration for circular motion is:
- Coriolis acceleration for a particle moving with velocity v in a rotating frame (angular velocity Ω) is:
- Escape velocity from Earth (radius R, mass M) is given by:
- For a rigid body rolling without slipping on a surface, total KE is:
- For an elastic collision between a heavy ball (mass M) and a light ball (mass m, M≫m), the lighter ball's final speed is approximately:
- For simple harmonic motion, acceleration is proportional to:
- If no net torque acts on a rotating body, what is conserved?
- If speed doubles while mass stays fixed, kinetic energy changes by a factor of:
- Impulse is defined as:
- In Lagrangian mechanics, the Euler–Lagrange equation is:
- In a completely inelastic collision between equal masses, fraction of kinetic energy lost is:
- Kepler's third law states that orbital period T and semi-major axis a satisfy:
- Lissajous figures are produced when:
- Noether's theorem connects continuous symmetries with:
- Phase space in classical mechanics is spanned by:
- Power delivered by a constant force F on an object moving at velocity v is:
- The Hamilton–Jacobi equation is used to:
- The Poincaré recurrence theorem states that a bounded Hamiltonian system will:
- The SI unit of power is:
- The area under a force–displacement graph gives:
- The canonical momentum conjugate to a coordinate q in Lagrangian mechanics is:
- The condition for an elastic collision conserves:
- The equation of motion for damped SHM is: mẍ + bẋ + kx = 0. Critical damping occurs when:
- The law of conservation of energy states that in a closed system:
- The moment of inertia of a point mass m at radius r is:
- The moment of inertia of a solid sphere of mass M and radius R about its diameter is:
- The period of a simple pendulum depends primarily on:
- The virial theorem for a bound gravitational system states <KE> =:
- Torque is maximized when force is applied:
- Two objects collide and stick together. What type of collision is this?
- What does Newton's first law state?
- What does the slope of a velocity–time graph represent?
- What happens to acceleration as mass increases (constant force)?
- What is the SI unit of force?
- What is the acceleration due to gravity at Earth's surface (approx)?
- What is the formula for gravitational potential energy near Earth's surface?
- What is the relationship between weight and mass?
- What is the unit of work?
- What type of friction acts on a sliding object?
- Which conserved quantity is associated with translational symmetry in Noether's theorem?
- Which formula correctly expresses kinetic energy?
- Which law describes how springs behave?
- Which mathematical technique is used to switch between Lagrangian and Hamiltonian mechanics?
- Which of the following is an example of a non-inertial reference frame?
- Which of these is a contact force?
- Which of these quantities is a scalar?
- Which quantity has both magnitude and direction?
- Which statement best describes a constraint in the Lagrangian formalism?
- Which stays constant for an isolated system with no external forces?
- Which theorem links net force over time to change in momentum?
- Work done against gravity lifting a 2 kg mass 5 m is:
- Work is done only when:
Electromagnetism (65 pages)
- A charge q at rest in an electric field E experiences force:
- A magnetic field exerts force on:
- A parallel-plate capacitor with plate separation d and area A has capacitance:
- A transformer changes:
- An EMF of 10 V drives a current of 2 A through a resistor. Power dissipated is:
- An electric field exists around:
- An induction motor operates on the principle of:
- Capacitance is the ability of a component to:
- Electric field lines point:
- Electromagnetic waves are transverse because:
- Faraday's law states that an EMF is induced when:
- Gauge invariance in electromagnetism means:
- Gauss's law for electricity states that the electric flux through a closed surface equals:
- In an RL circuit, time constant τ = L/R means:
- In resonance of an LC circuit, what is the resonant frequency?
- In series circuits, the current through each component:
- In the Drude model of a metal, conductivity σ is given by:
- In waveguides, the cutoff frequency depends on:
- Johnson–Nyquist (thermal) noise in a resistor has power spectral density:
- Lenz's law states that induced current:
- Like charges:
- Magnetic flux Φ through an area A with field B at angle θ is:
- Maxwell added the displacement current term because:
- Multipole expansion of radiation shows that electric dipole radiation scales with:
- Negative group velocity of a wave means:
- Ohm's law states V = IR. What does R represent?
- Self-inductance opposes changes in current because:
- Skin depth in a conductor decreases as:
- The Abraham–Lorentz force is the radiation reaction force on:
- The Aharonov–Bohm effect demonstrates:
- The Biot–Savart law gives the magnetic field produced by:
- The Hall effect is used to measure:
- The Jeans–Maxwell stress tensor describes:
- The Kramers–Kronig relations connect:
- The Larmor formula gives the power radiated by an accelerating charge as:
- The London equations describe:
- The Poynting vector S represents:
- The QED prediction of the electron's anomalous magnetic moment agrees with experiment to:
- The SI unit of magnetic field strength (B) is:
- The classical electron radius r_e arises when:
- The cyclotron frequency of a charge q in field B is:
- The electric force between two point charges is described by:
- The electric potential V at distance r from a point charge q is:
- The energy density of an electric field E is:
- The energy stored in a capacitor with capacitance C and voltage V is:
- The force on a charge q moving at velocity v in field B is:
- The impedance of a series RLC circuit at angular frequency ω is:
- The phase difference between voltage and current in a pure inductor is:
- The retarded potentials in electrodynamics are:
- The speed of light in vacuum c is approximately:
- The vector potential A is related to B by:
- The wave equation for electromagnetic waves in vacuum comes from:
- What does a voltmeter measure?
- What does an ammeter measure?
- What is the direction of conventional current?
- What is the time constant of an RC circuit?
- What is the unit of electric charge?
- What is the unit of electrical resistance?
- Which equation of a perfect conductor implies the field inside is zero?
- Which equation shows ∇·B = 0 implies:
- Which law states that the line integral of B around a closed loop equals μ₀ times the enclosed current?
- Which material is a good electrical conductor?
- Which of Maxwell's equations embodies Faraday's law?
- Which type of electromagnetic wave has the highest frequency?
- Why is there no magnetic monopole charge (so far) in Maxwell's equations?
Nuclear & Particle Physics (45 pages)
- A neutrino is:
- A proton is composed of:
- Alpha decay emits:
- Asymptotic freedom in QCD means:
- Beta decay (β⁻) emits:
- Beta-plus (β⁺) decay emits:
- CP violation in particle physics was first observed in:
- Colour confinement in QCD explains why:
- Deep Inelastic Scattering experiments at SLAC/HERA revealed:
- Fission involves:
- Fusion involves:
- Gamma rays are:
- In the Standard Model, quarks are held together by:
- In the electroweak theory, the W and Z bosons get their mass via:
- Lattice QCD is used to:
- Nuclear isomers are nuclei with:
- Pair annihilation of an electron and positron produces:
- Proton decay (if it exists) is predicted by:
- Radiocarbon dating uses ¹⁴C because:
- The Breit-Wigner formula describes:
- The CKM matrix describes:
- The Cabibbo angle θ_C governs:
- The Feynman propagator represents:
- The Gamow factor in nuclear fusion determines:
- The Geiger–Marsden (gold foil) experiment revealed:
- The PMNS matrix describes:
- The Q-value of a nuclear reaction is:
- The Weinberg angle θ_W parameterises:
- The atomic mass unit (u) is defined as:
- The binding energy per nucleon peaks at:
- The half-life of a radioactive isotope is:
- The mass defect of a nucleus is:
- The no-go theorem for anomaly cancellation in the Standard Model requires:
- The shell model of the nucleus was developed by:
- The term 'magic numbers' in nuclear physics refers to:
- The weak nuclear force is mediated by:
- What is the nucleus of a hydrogen atom composed of?
- What is the role of a moderator in a nuclear fission reactor?
- What is the strong nuclear force responsible for?
- Which conservation law is obeyed in all nuclear reactions?
- Which decay mode involves a nucleus emitting two electrons simultaneously without neutrinos (if observed)?
- Which particle mediates the electromagnetic force?
- Which symmetry is maximally violated by the weak force?
- Which type of nuclear reaction powers thermonuclear weapons?
- cosmic ray primary particles are mostly:
Quantum Physics (66 pages)
- A phonon is the quantum of:
- A quantum harmonic oscillator has energy levels:
- Anderson localisation occurs when:
- Atomic orbitals with ℓ = 2 are called:
- Berry's phase is:
- Bohr's model of the hydrogen atom quantises:
- Bose–Einstein condensation occurs when:
- Compton scattering demonstrated that photons have:
- Cooper pairs in superconductors are:
- Density matrix formalism is used to describe:
- Energy levels in a hydrogen atom are quantised according to E ∝:
- In a particle in a box (infinite square well) of length L, the energy of the nth level is:
- In quantum mechanics, operators corresponding to observables must be:
- In second quantisation, the creation operator ←satisfies:
- Pair production occurs when:
- Path integral formulation was developed by:
- Perturbation theory in quantum mechanics is valid when:
- Planck's constant h is approximately:
- Quantum chromodynamics (QCD) describes:
- Quantum decoherence explains:
- Quantum error correction uses:
- Quantum field vacuum is not truly empty because of:
- Quantum tunnelling explains:
- Selection rules in spectroscopy arise from:
- Spontaneous symmetry breaking in quantum field theory explains:
- Stimulated emission used in lasers is described by:
- The Bell inequality violation proves:
- The Casimir effect is caused by:
- The Dirac equation (in natural units) is:
- The Heisenberg uncertainty principle limits simultaneous knowledge of:
- The Josephson effect occurs in:
- The Rabi frequency describes:
- The Schrödinger cat thought experiment highlights:
- The Stern–Gerlach experiment demonstrated:
- The WKB approximation is used when:
- The Wigner function in quantum mechanics is:
- The adiabatic theorem in quantum mechanics states:
- The commutator [x̂, p̂] equals:
- The eigenvalue of the Hamiltonian operator gives:
- The energy gap between valence and conduction bands determines whether a material is:
- The fractional quantum Hall effect arises from:
- The ground state energy of a hydrogen atom is approximately:
- The no-cloning theorem states:
- The photoelectric effect shows that light behaves as:
- The probability current in quantum mechanics describes:
- The spin quantum number of an electron can be:
- The spin–statistics theorem states that:
- The uncertainty in energy and time satisfies:
- The wavefunction ψ in quantum mechanics is related to probability by:
- What did the double-slit experiment with electrons demonstrate?
- What does the de Broglie hypothesis state?
- What is a quantum of light called?
- What is a wave packet?
- What is quantum entanglement?
- What is zero-point energy?
- What principle forbids two fermions from occupying the same quantum state?
- Which effect describes quantised energy levels in a magnetic field?
- Which experiment proved the quantisation of atomic energy levels?
- Which interpretation of quantum mechanics holds that the universe splits at each measurement?
- Which of the following has the highest energy for a given wavelength?
- Which of the following is a boson?
- Which physicist formulated the wave equation for quantum mechanics?
- Which postulate of quantum mechanics states the state of a system is fully described by its wavefunction?
- Which quantum number describes the shape of an atomic orbital?
- Which scientist explained the photoelectric effect using photons?
- Which symbol represents the reduced Planck constant?
Relativity (48 pages)
- A Minkowski diagram is used to:
- A beam of light crossing an accelerating elevator appears to bend because:
- A black hole's event horizon is the boundary where:
- A geodesic in general relativity is:
- A positive cosmological constant is associated with:
- According to relativity, a massive object can reach the speed of light if:
- At v = 0.8c, the Lorentz factor gamma is approximately:
- Clocks deeper in a gravitational field compared with clocks farther away will:
- Einstein's equation E = mc^2 states that:
- Einstein's field equations connect spacetime curvature to:
- For light travelling in vacuum, the spacetime interval along its worldline is:
- For timelike-separated events, which path maximises proper time?
- Frame dragging refers to:
- Free fall in general relativity is best described as:
- General relativity describes gravity as:
- Gravitational waves are produced primarily by:
- If 5 years pass on board a spacecraft moving at 0.8c, approximately how much time passes in Earth's frame?
- If L0 is proper length, the observed length of an object moving at speed v is:
- In flat spacetime, which curvature object vanishes everywhere?
- In special relativity, simultaneity is:
- In the weak-field limit, gravitational waves are:
- Length contraction affects an object's dimension:
- Light climbing out of a gravitational field is observed to:
- Light passing near a massive object is bent because:
- Nuclear reactions release energy because:
- Proper time is the time measured:
- Relativistic effects become most noticeable when an object's speed is:
- Relativistic momentum is:
- Relativistic velocity addition ensures that:
- Rest mass is also called:
- Special relativity predicts that a moving clock compared with a stationary one will:
- The Schwarzschild event horizon at r = 2GM/c^2 is:
- The Schwarzschild radius of a non-rotating black hole is:
- The equivalence principle says that locally:
- The invariant magnitude of the four-momentum satisfies:
- The spacetime interval is encoded by the:
- The stress-energy tensor includes:
- The twin paradox is resolved because one twin:
- The weak equivalence principle states that:
- What is the Lorentz factor gamma?
- What is the speed of light in vacuum?
- Which Lorentz transformation for the x-coordinate is correct for motion along x?
- Which quantity stays the same for all inertial observers?
- Which relation connects total energy, momentum, and rest mass?
- Which solar-system observation was famously explained by general relativity?
- Which statement about GPS satellite clocks is correct overall?
- Which statement about gravitational redshift near a Schwarzschild mass is correct?
- Why do GPS satellites need relativity corrections?
Thermodynamics (56 pages)
- A refrigerator works by:
- An adiabatic process involves:
- An ideal gas undergoes isothermal expansion from V₁ to V₂. Work done by gas is:
- At the triple point, a substance:
- Bose–Einstein and Fermi–Dirac statistics differ from Maxwell–Boltzmann because:
- Boyle's law states that for a fixed amount of gas at constant temperature:
- Conduction of heat requires:
- Enthalpy H is defined as:
- Entropy is a measure of:
- For a blackbody, spectral radiance is given by:
- For a reversible process, total entropy change of universe is:
- Fourier's law of heat conduction is:
- Heat flows naturally from:
- In a phase transition of second order, which quantity diverges at the critical point?
- In an ideal gas, internal energy U depends only on:
- In an isochoric process, which quantity remains constant?
- In statistical mechanics, the partition function Z is defined as:
- Landauer's principle states:
- Renormalisation group theory in statistical mechanics was used to explain:
- Specific heat capacity describes:
- The Carnot efficiency of a heat engine operating between 300 K and 600 K is:
- The Clausius inequality states:
- The Gibbs phase rule relating phases P, components C, and degrees of freedom F is:
- The Helmholtz free energy is F = U − TS. For a system at constant T and V, equilibrium minimises:
- The Jarzynski equality relates:
- The Joule–Thomson effect describes:
- The Kelvin temperature scale starts at:
- The Maxwell–Boltzmann distribution describes:
- The Onsager reciprocal relations state:
- The Prandtl number Pr = ν/α in fluid mechanics represents:
- The Sackur–Tetrode equation gives:
- The Stefan–Boltzmann law relates radiated power to:
- The adiabatic index γ = Cₚ/Cᵥ for a monatomic ideal gas is:
- The coefficient of performance (COP) of a Carnot refrigerator is:
- The critical exponent β describes:
- The efficiency of a heat engine is maximised by:
- The equipartition theorem assigns ½k_BT of energy per:
- The first law of thermodynamics is a statement of:
- The fluctuation-dissipation theorem connects:
- The ideal gas law is PV = nRT. What does n represent?
- The non-equilibrium steady state in driven systems is characterised by:
- The second law of thermodynamics states:
- The specific heat of a Debye solid at very low temperature varies as:
- The third law of thermodynamics (Nernst theorem) states:
- The zeroth law of thermodynamics states:
- Van der Waals equation modifies the ideal gas law to account for:
- What is absolute zero?
- What is latent heat?
- Which gas behaves most like an ideal gas?
- Which model accounts for the failure of the Dulong–Petit law at low temperature?
- Which process describes a gas expanding with no heat exchange?
- Which statement describes an irreversible process?
- Which thermodynamic cycle drives most petrol engines?
- Which thermodynamic potential is minimised at constant T and P?
- Which thermodynamic process occurs at constant temperature?
- Wien's displacement law states:
Waves & Optics (50 pages)
- A concave mirror converges:
- A laser differs from ordinary light because it is:
- Beats are produced when:
- Chromatic aberration in lenses occurs because:
- Coherence length of a light source is defined as:
- Huygens' principle states that:
- In a diffraction grating, constructive interference occurs when:
- Non-linear optics describes phenomena when:
- Optical tweezers work by:
- Polarisation shows that light is:
- Rayleigh scattering explains why the sky is blue because:
- Reflection follows:
- Snell's law of refraction states:
- Solitons in optical fibres maintain their shape because:
- Sound travels fastest in:
- Sound waves are:
- Speckle patterns in laser light arise from:
- Stimulated Raman scattering involves:
- The ABCD matrix (ray transfer matrix) is used to:
- The Airy disc in diffraction-limited optics has angular radius:
- The Doppler effect for sound explains why a siren sounds higher-pitched when:
- The Doppler formula for a source moving toward a stationary observer at speed v_s in medium with sound speed c is:
- The Jones calculus for polarisation uses:
- The Kramers–Kronig relations applied to optics connect:
- The Mach number is:
- The Wigner–Seitz cell in reciprocal space is called:
- The amplitude of a wave is:
- The concept of optical coherence tomography (OCT) is based on:
- The frequency of a guitar string increases if:
- The intensity of a wave is proportional to:
- The optical path difference for two coherent sources separated by d at angle θ is:
- The phase velocity and group velocity of a wave packet are equal when:
- The photonic bandgap in a photonic crystal prevents:
- The principle of superposition states:
- The refractive index n of a medium is defined as:
- The relationship between wave speed v, frequency f, and wavelength λ is:
- The resolving power of a microscope is limited by:
- The wavenumber k of a wave with wavelength λ is:
- Thin-film interference (e.g., soap bubble colours) arises from:
- Total internal reflection occurs when:
- What is a standing wave?
- What is group velocity dispersion (GVD) in a fibre?
- What is single-slit diffraction's central maximum width proportional to?
- What is the SI unit of frequency?
- What is the condition for a standing wave on a string fixed at both ends?
- What is the critical angle for glass (n = 1.5) with air?
- Which phenomenon explains why a straw appears bent in water?
- Which type of lens corrects myopia (short-sightedness)?
- Why does a diffraction grating produce sharper peaks than a double-slit?
- Young's double-slit experiment demonstrates: