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A-level Physics Data and Formulae Sheet | Constants & Equations
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A-level Physics data and formulae For use in exams from the June 2017 Series onwards DATA - FUNDAMENTAL CONSTANTS AND VALUES Quantity speed of light in vacuo permeability of free space permittivity of free space magnitude of the charge of electron the Planck constant gravitational constant the Avogadro constant Symbol Value Units π 3.00 × 108 m s –1 π0 H m–1 1.60 × 10–19 C π0 8.85 × 10–12 πΊ π F m–1 β 6.63 × 10–34 6.67 × 10–11 N m2 kg –2 π 8.31 J K –1 mol–1 πA molar gas constant 4π × 10–7 6.02 × 1023 Js mol–1 π 1.38 × 10–23 5.67 × 10–8 W m–2 K –4 electron rest mass (equivalent to 5.5 × 10–4 u) πe 9.11 × 10–31 kg proton rest mass (equivalent to 1.00728 u) πp 1.67(3) × 10–27 neutron rest mass (equivalent to 1.00867 u) πn 1.67(5) × 10–27 π 9.81 the Boltzmann constant the Stefan constant σ the Wien constant πΌ π πe electron charge/mass ratio π πp proton charge/mass ratio gravitational field strength acceleration due to gravity atomic mass unit (1u is equivalent to 931.5 MeV) ALGEBRAIC EQUATION quadratic equation − b ± b 2 − 4 ac x= 2a ASTRONOMICAL DATA Body Mass/kg Mean radius/m Sun 1.99 × 1030 6.96 × 108 Earth Version 1.5 5.97 × 1024 6.37 × 106 π u 2.90 × 10–3 J K –1 mK 1.76 × 1011 C kg –1 9.58 × 107 C kg –1 9.81 N kg –1 1.661 × 10–27 kg kg kg m s –2 GEOMETRICAL EQUATIONS circumference of circle = rπ area of circle = πr2 curved surface area of cylinder = 2πrh area of sphere = 4πr2 volume of sphere = 4 πr3 arc length = 2πr 3 1 Particle Physics Waves Class Name Symbol Rest energy/MeV wave speed photon photon lepton neutrino πΎ 0 vµ 0 first harmonic mesons ve electron e± muon µ± π meson π± 0 0.510999 π ± K meson baryons K proton neutron Properties of quarks Charge p 938.257 939.551 Baryon number Strangeness 0 d − 1e 3 + 1 3 0 − 1e + 1 −1 3 moments velocity and acceleration π£ = equations of motion −1 Photons and energy levels photon energy photoelectricity energy levels de Broglie wavelength 2 βπ π βπ = Ο + πΈk (max) πΈ = βπ = βπ = πΈ1 – πΈ2 π = β β = π ππ πΉ = ππ force πΉ = βπ£ βπ‘ π =οΏ½ π’+π£ οΏ½π‘ 2 π = π’π’ + β(ππ) βπ‘ ππ 2 2 πΉ Δπ‘ = Δ(ππ) work, energy and power π = πΉ π cos π π = 1 π π£2 2 βπ ,π βπ‘ = πΉπΉ ππππππππππ = Materials π ΔπΈp = ππΔβ π’π’π’π’π’π’ ππππππ πππππ πππππ πππππ Hooke’s law πΉ = π ΔπΏ π Young modulus = energy stored π = π£ 2 = π’2 + 2ππ force density π = for π1 > π2 π£ = π’ + ππ +1 e+ , ν e , µ + , ν µ π1 βπ βπ‘ πΈk = e− , νe ; µ− , νµ π2 moment = πΉπΉ Lepton number Antiparticles: s critical angle sin πc = Properties of Leptons Particles: π for two different substances of refractive indices n1 and n2, impulse 3 1 π π sin π = ππ Mechanics K + 1 3 diffraction grating 497.762 0 + 2e s ππ π law of refraction π1 sin π1 = π2 sin π2 u 3 π€ = 134.972 antiquarks have opposite signs Type 1 π οΏ½ 2π π refractive index of a substance s, π = π 493.821 n π = π = 105.659 139.576 0 fringe spacing period π = ππ π‘π‘π‘π‘π‘π‘π‘ π π π π π π π‘π‘π‘π‘π‘π‘π‘ π π π π π π 1 πΈ = 2 πΉΔπΏ tensile stress = tensile strain = πΉ π΄ βπΏ πΏ Version 1.5 AQA A-LEVEL PHYSICS DATA AND FORMULAE Electricity Gravitational fields current and pd resistivity resistors in series resistors in parallel power emf Circular motion πΌ = π= βπ βπ‘ π = π π πΏ π π π = π πΌ π T = π 1 + π 2 + π 3 + … 1 π T 1 1 1 = π + π + π +β― 1 2 3 π = ππ = πΌ 2 π = π = magnitude of angular speed πΈ π π π 2 π = πΌ(π + π) π = π£ π centripetal force Simple harmonic motion acceleration displacement π₯ = π΄ cos (ππ) speed π£ maximum speed π£max = ππ maximum acceleration for a mass-spring system for a simple pendulum Thermal physics energy to change temperature energy to change state gas law kinetic theory model kinetic energy of gas molecule Version 1.5 = ± π οΏ½(π΄2 2 − π₯ 2) πmax = π π΄ π π π = 2π οΏ½ π π = 2π οΏ½ π π = ππΔπ π = ππ πΊπ1 π2 π2 πΉ π πΊπΊ π2 Δπ = πΔπ πΊπΊ π Δπ π =– Δπ gravitational potential π =– Electric fields and capacitors work done field strength for a radial field electric potential π = − π2 π₯ π = work done field strength for a uniform field ππ 2 πΉ = = ππ2 π π π = magnitude of gravitational field strength in a radial field force on a charge π£2 π = = π2 π π πΉ = gravitational field strength force between two point charges π = 2ππ centripetal acceleration force between two masses field strength capacitance capacitor energy stored capacitor charging decay of charge time constant πΉ = 1 π1 π2 4ππ0 π 2 πΉ = πΈπΈ πΈ = π π πΈ = 1 π 4ππ0 π 2 Δπ = πΔπ π = 1 π 4ππ0 π πΈ = 1 1 1 π2 ππ = πΆπ 2 = 2 2 2 πΆ Δπ Δπ π πΆ = π π΄π0 πr πΆ = π πΈ = π‘ π = π0 (1 − e– π π ) π‘ π = π0 e– π π π π ππ = πππ ππ = πππ 1 ππ (πrms )2 3 1 3 3π π π (πrms )2 = ππ = 2 2 2πA ππ = 3 Magnetic fields force on a current OPTIONS πΉ = π΅π΅π΅ force on a moving charge Astrophysics πΉ = π΅π΅π΅ magnetic flux magnetic flux linkage Π€ = π΅π΅ 1 astronomical unit = 1.50 × 1011 m π = π = 3.26 ly magnitude of induced emf πΠ€ = π΅π΅π΅ cos π emf induced in a rotating coil πΠ€ = π΅π΅π΅ cos π alternating current transformer equations π = π΅π΅π΅π΅ sin π t πΌrms = πs πΌ0 √2 πp inverse square law for γ radiation activity half-life nuclear radius energy-mass equation π = s πrms = πp efficiency = Nuclear physics radioactive decay ΔΠ€ Δπ‘ Δπ Δπ‘ πΌ = π½ = ln 2 π π = π 0 π΄1/3 πΈ = ππ 2 √2 πΌs πs πΌp πp π π₯2 1 parsec = 2.06 × 105 AU = 3.08 × 1016 m Hubble constant, π» = 65 km s–1 Mpc–1 π = πππππ π π π π π π π π π ππ πππππ ππ πππ πππππ π π π π π π π π π ππ ππππππ ππ π’π’π’π’π’π’π’ πππ telescope in normal adjustment Rayleigh criterion magnitude equation Wien’s law Stefan’s law = – π π, π = πo e π΄ = ππ π0 1 light year = 9.46 × 1015 m −ππ Schwarzschild radius Doppler shift for v << c red shift Hubble’s law Medical physics lens equations threshold of hearing intensity level absorption ultrasound imaging π = π ≈ 4 π π· π – π = 5 log π 10 πmax π = 2.9 × 10−3 m K π = πππ 4 π s ≈ 2GM c2 Δπ Δπ π£ =– = π π π π£ π§= − π π£ = π»π» 1 π π£ π = π’ π = 1 π = 1 π’ + 1 π£ πΌ0 = 1.0 × 10−12 W m−2 πππππππππ πππππ = 10 log πΌ = πΌ0 π –ππ π πm = π π = ππ πΌr half-lives π0 πe πΌi 1 πE =οΏ½ = πΌ πΌ0 π2 − π1 2 π2 + π1 οΏ½ 1 1 + πB πP Version 1.5 AQA A-LEVEL PHYSICS DATA AND FORMULAE Engineering physics moment of inertia angular kinetic energy equations of angular motion Turning points in physics πΌ = Σππ 2 πΈπ = electrons in fields 1 2 πΌπΌ 2 2 πΌπΌ 2 (π1 + π2 ) π‘ π = 2 π = π1 π‘ + torque ½ ππ 2 = ππ ππ = ππ π Millikan’s experiment πΉ = 6ππππ π = Maxwell’s formula π = πΌπΌ π = πΉπ angular momentum πππππππ ππππππππ = πΌπΌ angular impulse πΔπ‘ = Δ(πΌπΌ) work done π = π‘ = special relativity π = ππ power π = ππ thermodynamics π = Δπ + π ππ πΎ = constant isothermal change efficiency = maximum theoretical efficiency = π πH − πC = πH πH πH − πC πH input power = calorific value × fuel flow rate indicated power = (ππππ ππ π − π ππππ) × (ππππππ ππ ππππππ πππ π π π π π π ) × (ππππππ ππ πππππππππ) resonant frequency heat pumps and refrigerators summing amplifier heat pump: πΆπΆπΆhp = πC π = π −Cπ π πH π H C H C π = π −Hπ 2 οΏ½1 − π£ 2 π π£2 π2 difference amplifier 2 οΏ½1 − π£ 2 π 1 πout = π΄OL (π+ − π− ) πout π f =− πin π in πout π f =1+ πin π l πout = −π f οΏ½ π1 π2 π3 + + + β―οΏ½ π 1 π 2 π 3 πout = (π+ − π− ) Bandwidth requirement: for AM for FM π0 π 2 2π √πΏπΏ π0 π= πB inverting amplifier non-inverting amplifier refrigerator: πΆπΆπΆref = π‘0 π0 = operational amplifiers: open loop output or brake power π = ππ friction power = πππππππππ πππππ – πππππ πππππ β β = π √2πππ Electronics Q-factor work done per cycle = area of loop οΏ½π0 π0 πΈ = π π2 = ππ = constant heat engines 1 π = π0 οΏ½1 − π = πΔπ adiabatic change ππ π πΉ = π΅π΅π΅ ππ π = π΅π΅ π2 = π1 + πΌ π‘ π2 2 = π1 2 + 2πΌπΌ Version 1.5 πΉ = π f π l ππππππππβ = 2πM ππππππππβ = 2(βπ + πM ) 5 6 Version 1.5 AQA A-LEVEL PHYSICS DATA AND FORMULAE Version 1.5 7 8 Copyright © 2017 AQA and its licensors. All rights reserved. Version 1.5
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