A-level Physics Specimen data booklet Physics

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 Symbol Value Units 𝑐 3.00 × 108 m s –1 µ0 permeability of free space permittivity of free space magnitude of the charge of electron the Planck constant molar gas constant the Boltzmann constant 1.60 × 10–19 C 8.85 × 10–12 ℎ 6.63 × 10–34 6.67 × 10–11 N m2 kg –2 𝑅 8.31 J K –1 mol–1 𝑒 𝑁A the Avogadro constant H m–1 ε0 𝐺 gravitational constant 4π × 10–7 6.02 × 1023 W m–2 K –4 kg the Wien constant α 5.67 × 10–8 electron rest mass (equivalent to 5.5 × 10–4 u) electron charge/mass ratio 𝑚e 9.11 × 10–31 proton rest mass (equivalent to 1.00728 u) 𝑚p 1.67(3) × 10–27 neutron rest mass (equivalent to 1.00867 u) 𝑚n 1.67(5) × 10–27 𝑔 9.81 𝑒 𝑚e 𝑒 𝑚p 𝑔 acceleration due to gravity atomic mass unit (1u is equivalent to 931.5 MeV) ALGEBRAIC EQUATION quadratic equation − b ± �b2 − 4ac x= 2a ASTRONOMICAL DATA Body Mass/kg Mean radius/m Sun 1.99 × 1030 6.96 × 108 Earth Version 1.2 5.97 × 1024 6.37 × 106 mol–1 1.38 × 10–23 σ gravitational field strength Js 𝑘 the Stefan constant proton charge/mass ratio F m–1 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 arc length = rθ circumference of circle = 2πr area of circle = πr2 curved surface area of cylinder = 2πrh area of sphere = 4πr2 volume of sphere = 4 3 πr3 1 Waves Particle Physics Class Name Symbol Rest energy/MeV wave speed photon photon γ lepton neutrino ve 0 first harmonic 0 fringe spacing 0 vµ mesons electron e± muon µ± 0.510999 π± π meson π ± K meson baryons Properties of quarks antiquarks have opposite signs Type Charge u 1 3 1 e 3 + 1 3 0 1 e 3 + 1 3 −1 2 3 − s − Strangeness + + d Baryon number e 0 critical angle sin 𝜃c = velocity and acceleration 𝑣 = equations of motion Antiparticles: −1 Photons and energy levels 𝐹 = 𝑚𝑚 force 𝐹 = force photon energy photoelectricity energy levels de Broglie wavelength 2 𝐸 = ℎ𝑓 = ℎ𝑐 /λ ℎ𝑓 = φ + 𝐸k (max) ℎ𝑓 = 𝐸1 – 𝐸2 𝜆 = ℎ ℎ = 𝑝 𝑚𝑚 𝑠 =� 𝑢+𝑣 �𝑡 2 𝑠 = 𝑢𝑢 + ∆(𝑚𝑚) ∆𝑡 𝑊 = 𝐹 𝑠 cos 𝜃 𝑃 = ∆𝑊 ∆𝑡 1 𝑚 𝑣2 2 , 𝑃 = 𝐹𝐹 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 = Materials 𝑚 𝑎𝑎 2 2 Δ𝐸p = 𝑚𝑚Δℎ 𝑢𝑢𝑢𝑢𝑢𝑢 𝑜𝑜𝑜𝑜𝑜𝑜 𝑝𝑝𝑝𝑝𝑝 𝑖𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝𝑝 Hooke’s law 𝐹 = 𝑘 Δ𝐿 𝑉 Young modulus = energy stored ∆𝑣 ∆𝑡 𝐹 Δ𝑡 = Δ(𝑚𝑚) work, energy and power density 𝜌 = 𝑎 = 𝑣 2 = 𝑢2 + 2𝑎𝑎 +1 e+ , ν e , µ + , ν µ for 𝑛1 > 𝑛2 ∆𝑠 ∆𝑡 𝐸k = e , νe ; µ , νµ 𝑛1 𝑣 = 𝑢 + 𝑎𝑎 Lepton number Particles: 𝑛2 moment = 𝐹𝐹 moments impulse − 𝑐 𝑐s for two different substances of refractive indices n1 and n2, Properties of Leptons − 𝑑 sin 𝜃 = 𝑛𝑛 Mechanics 939.551 n 𝑠 diffraction grating 497.762 938.257 neutron λ𝐷 law of refraction 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2 p proton 𝑤 = 134.972 K 0 1 𝑇 � 2𝑙 𝜇 𝑓 = refractive index of a substance s, 𝑛 = 493.821 K 𝑓 = 1 𝑇 period 105.659 139.576 0 𝑐 = 𝑓𝑓 𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠 𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠 1 𝐸 = 2 𝐹Δ𝐿 tensile stress = tensile strain = 𝐹 𝐴 ∆𝐿 𝐿 Version 1.2 AQA GCE PHYSICS DATA AND FORMULAE Electricity Gravitational fields 𝐼 = current and pd resistivity resistors in series resistors in parallel power emf Circular motion 𝜌= ∆𝑄 ∆𝑡 𝑉 = 𝑅𝑅 𝐿 𝑊 𝑄 𝑅 = 𝑉 𝐼 magnitude of gravitational field strength in a radial field 𝑅T work done 1 = 𝑅1 + 1 𝑅2 + 1 +⋯ 𝑅3 𝑉 𝑅 𝑃 = 𝑉𝑉 = 𝐼 2 𝑅 = 𝜀 = magnitude of angular speed 𝐸 𝑄 ω = 2 𝜀 = 𝐼(𝑅 + 𝑟) centripetal acceleration 𝑚𝑚 2 𝐹 = = 𝑚ω2 𝑟 𝑟 centripetal force Simple harmonic motion 𝑎 = − 𝜔2 𝑥 acceleration 𝑥 = 𝐴 𝑐𝑐𝑐 (𝜔 𝑡) displacement 𝑣 = ±𝜔 speed 𝑣𝑚𝑚𝑚 = 𝜔 𝐴 maximum speed 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 1.2 �(𝐴2 2 − 𝑥 2) 𝑚 𝑘 𝑙 𝑇 = 2𝜋 � 𝑔 𝐺𝐺 𝑟 Δ𝑉 𝑔 =– Δ𝑟 𝐹 = 1 𝑄1 𝑄2 4𝜋𝜀0 𝑟 2 𝐹 = 𝐸𝐸 electric potential 𝐸 = 1 𝑄 4𝜋𝜀0 𝑟 2 capacitance 𝐸 = work done field strength for a radial field capacitor energy stored capacitor charging decay of charge time constant 𝑄 = 𝑚𝑚Δ𝜃 𝐺𝐺 𝑟2 𝑉 =– 𝑉 𝑑 𝑎𝑚𝑚𝑚 = 𝜔 𝐴 𝑇 = 2𝜋 � 𝐹 𝑚 Δ𝑊 = 𝑚Δ𝑉 𝐸 = field strength for a uniform field 𝑣2 𝑎 = = ω2 𝑟 𝑟 𝐺𝑚1 𝑚2 𝑟2 Electric fields and capacitors force on a charge ω = 2𝜋𝜋 𝑔 = gravitational potential force between two point charges 𝑣 𝑟 𝑔 = gravitational field strength 𝑅T = 𝑅1 + 𝑅2 + 𝑅3 + … 1 𝐹 = force between two masses Δ𝑊 = 𝑄Δ𝑉 𝑉 = 1 𝑄 4𝜋𝜀0 𝑟 𝐸 = 1 1 1 𝑄2 𝑄𝑄 = 𝐶𝑉 2 = 2 2 2 𝐶 Δ𝑉 Δ𝑟 𝑄 𝐶 = 𝑉 𝐴𝜀0 𝜀r 𝐶 = 𝑑 𝑄 = 𝑄0 (1 − e–𝑡/𝑅𝑅 ) 𝑄 = 𝑄0 e–𝑡/𝑅𝑅 𝑅𝑅 𝑄 = 𝑚𝑙 𝑝𝑝 = 𝑛𝑛𝑛 𝑝𝑝 = 𝑁𝑁𝑁 1 𝑁 𝑚 (𝑐rms )2 3 1 3 3𝑅𝑅 𝑚 (𝑐rms )2 = 𝑘𝑘 = 2 2 2𝑁A 𝑝𝑝 = 3 Magnetic fields Ф = 𝐵𝐵 magnetic flux 𝑁Ф = 𝐵𝐵𝐵 cos 𝜃 magnetic flux linkage 𝜀 = 𝑁 magnitude of induced emf 𝜀 = 𝐵𝐵𝐵ω sin ω t 𝐼rms = 𝑁s 𝐼0 √2 𝑁p = the inverse square law for γ radiation activity half-life nuclear radius energy-mass equation 𝑉s 𝑉rms = 𝑉p 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 = Nuclear physics radioactive decay ΔФ Δ𝑡 𝑁Ф = 𝐵𝐵𝐵 cos 𝜃 emf induced in a rotating coil transformer equations Astrophysics 𝐹 = 𝐵𝐵𝐵 force on a moving charge alternating current OPTIONS 𝐹 = 𝐵𝐵𝐵 force on a current Δ𝑁 Δ𝑡 𝐼 = 𝑘 𝑥2 𝑉0 √2 𝐼s 𝑉s 𝐼p 𝑉p = – 𝜆 𝑁, 𝑁 = 𝑁o e−λ𝑡 𝐴 = 𝜆𝜆 𝑇½ = ln 2 𝜆 𝑅 = 𝑅0 𝐴1/3 𝐸 = 𝑚𝑚 2 1 astronomical unit = 1.50 × 1011 m 1 light year = 9.46 × 1015 m 1 parsec = 206265 AU = 3.08 × 1016 m = 3.26 light year Hubble constant, 𝐻 = 65 km s–1 Mpc–1 𝑀 = 𝑎𝑎𝑎𝑎𝑎 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑏𝑏 𝑖𝑖𝑖𝑖𝑖 𝑎𝑎 𝑒𝑒𝑒 𝑎𝑎𝑎𝑎𝑎 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑏𝑏 𝑜𝑜𝑜𝑜𝑜𝑜 𝑎𝑎 𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑒𝑒𝑒 in normal adjustment Rayleigh criterion magnitude equation Wien’s law Stefan’s law Schwarzschild radius Doppler shift for v << c red shift Hubble’s law Medical physics lens equations 𝑀 = 𝜃 ≈ intensity level absorption ultrasound imaging 4 𝑑 10 𝜆max 𝑇 = 2.9 × 10−3 m K 𝑃 = 𝜎𝜎𝑇 4 𝑅s ≈ 2GM c2 Δ𝑓 Δ𝜆 𝑣 =– = 𝑓 𝜆 𝑐 𝑣 𝑧= − 𝑐 𝑣 = 𝐻𝐻 1 𝑓 𝑣 𝑚 = 𝑢 𝑃 = 𝑓 = 1 𝑢 + 1 𝑣 𝐼0 = 1.0 × 10−12 W m−2 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑙𝑙𝑙𝑙𝑙 = 10 log 𝐼 = 𝐼0 𝑒 –𝜇𝜇 𝜇 𝜇m = 𝜌 𝑍 = 𝑝𝑐 𝐼𝑟 half-lives 𝜆 𝐷 𝑚 – 𝑀 = 5 log 1 threshold of hearing 𝑓0 𝑓e 𝐼𝑖 1 𝑇E = = � 𝐼 𝐼0 𝑍2 − 𝑍1 2 𝑍2 + 𝑍1 1 𝑇B + � 1 𝑇P Version 1.2 AQA GCE PHYSICS DATA AND FORMULAE Engineering physics moment of inertia angular kinetic energy equations of angular motion Turning points in physics 𝐼 = Σ𝑚𝑚 2 𝐸𝑘 = 𝐹 = electrons in fields 1 2 𝐼ω 2 𝐹 = 𝐵𝐵𝐵 𝑚𝑚 𝑟 = 𝐵𝐵 ω2 = ω1 + 𝛼 𝑡 ω2 2 = ω1 2 + 2𝛼𝛼 𝛼𝛼 2 (𝜔1 + 𝜔2 ) 𝑡 𝜃 = 2 𝑇 = 𝐼𝛼 Millikan’s experiment 𝑇Δ𝑡 = Δ(𝐼𝐼) special relativity 𝜃 = ω1 𝑡 + torque 2 ½ 𝑚𝑚 2 = 𝑒𝑒 𝑄𝑄 = 𝑚𝑚 𝑑 𝐹 = 6𝜋𝜋𝜋𝜋 𝑐 = Maxwell’s formula 𝑇 = 𝐹𝑟 𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 𝐼ω angular momentum angular impulse 𝜆 = 𝑡 = 𝑊 = 𝑇𝑇 work done 𝑃 = 𝑇ω power 𝑄 = Δ𝑈 + 𝑊 thermodynamics 𝑝𝑝 𝛾 = constant heat engines efficiency = maximum theoretical efficiency = 𝑊 𝑄H − 𝑄C = 𝑄H 𝑄H 𝑇H − 𝑇C 𝑇H resonant frequency × (𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜 𝑐𝑐𝑐𝑐𝑐𝑐 𝑝𝑝𝑝 𝑠𝑠𝑠𝑠𝑠𝑠) × (𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐) heat pumps and refrigerators summing amplifier heat pump: 𝐶𝐶𝐶hp = 𝑄C 𝑊 𝑄H 𝑊 = = 𝑄C 𝑄H − 𝑄C 𝑄H 𝑄H − 𝑄C difference amplifier Version 1.2 Copyright © 2016 AQA and its licensors. All rights reserved. 2 �1 − 𝑣2 𝑐 1 𝑉out 𝑅f =− 𝑉in 𝑅in 𝑉out 𝑅f =1+ 𝑉in 𝑅l 𝑉out = −𝑅f � 𝑉1 𝑉2 𝑉3 + + + ⋯� 𝑅1 𝑅2 𝑅3 𝑉out = (𝑉+ − 𝑉− ) Bandwidth requirement: for AM for FM 𝑚0 𝑐 2 𝑉out = 𝐴OL (𝑉+ − 𝑉− ) inverting amplifier non-inverting amplifier refrigerator: 𝐶𝐶𝐶ref = 𝑣2 𝑐2 2𝜋 √𝐿𝐿 𝑓0 𝑄= 𝑓B operational amplifiers: open loop output or brake power 𝑃 = 𝑇ω friction power = 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑝𝑝𝑝𝑝𝑝 – 𝑏𝑏𝑏𝑏𝑏 𝑝𝑝𝑝𝑝𝑝 2 �1 − 𝑣2 𝑐 𝑓0 = input power = calorific value × fuel flow rate indicated power = (𝑎𝑎𝑎𝑎 𝑜𝑜 𝑝 − 𝑉 𝑙𝑙𝑙𝑙) ℎ ℎ = 𝑝 √2𝑚𝑚𝑚 𝑡0 Electronics Q-factor work done per cycle = area of loop �𝜇0 𝜀0 𝐸 = 𝑚 𝑐2 = 𝑝𝑝 = constant isothermal change 1 𝑙 = 𝑙0 �1 − 𝑊 = 𝑝Δ𝑉 adiabatic change 𝑒𝑒 𝑑 𝑅f 𝑅l 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ = 2𝑓M 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ = 2(∆𝑓 + 𝑓M ) 5

A-level Physics Specimen data booklet Physics

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