Physics Data Booklet

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Physics data bookletFirst assessment 2016Annotated by Boaz V.

Diploma ProgrammePhysics data bookletPublished June 2014Revised edition published January 2016Published on behalf of the International Baccalaureate Organization, a not-for-profiteducational foundation of 15 Route des Morillons, 1218 Le Grand-Saconnex, Geneva,Switzerland by theInternational Baccalaureate Organization (UK) LtdPeterson House, Malthouse Avenue, Cardiff GateCardiff, Wales CF23 8GLUnited KingdomWebsite: www.ibo.org International Baccalaureate Organization 2014The International Baccalaureate Organization (known as the IB) offers four high-qualityand challenging educational programmes for a worldwide community of schools, aimingto create a better, more peaceful world. This publication is one of a range of materialsproduced to support these programmes.The IB may use a variety of sources in its work and checks information to verify accuracyand authenticity, particularly when using community-based knowledge sources such asWikipedia. The IB respects the principles of intellectual property and makes strenuousefforts to identify and obtain permission before publication from rights holders of allcopyright material used. The IB is grateful for permissions received for material usedin this publication and will be pleased to correct any errors or omissions at the earliestopportunity.All rights reserved. No part of this publication may be reproduced, stored in a retrievalsystem, or transmitted, in any form or by any means, without the prior written permissionof the IB, or as expressly permitted by law or by the IB’s own rules and policy. Seehttp://www.ibo.org/copyright.IB merchandise and publications can be purchased through the IB store athttp://store.ibo.org.Email: sales@ibo.orgInternational Baccalaureate, Baccalauréat International and Bachillerato Internacionalare registered trademarks of the International Baccalaureate Organization.4082

ContentsFundamental constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Metric (SI) multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Unit conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Electrical circuit symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Equations—Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Equations—AHL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Equations—Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Physics data booklet

Physics data booklet

Fundamental constantsQuantitySymbolApproximate valueAcceleration of free fall(Earth’s surface)g9.81m sGravitational constantG6.67 10 11 Nm2 kg 2Avogadro’s constantNA6.02 1023 mol 1Gas constantR8.31JK 1 molBoltzmann’s constantkB1.38 10 23 JK 115.67 10 8 W m 2 K 4Stefan–Boltzmann constantCoulomb constant2k8.99 109 Nm2 C 2Permittivity of free space08.85 10 12 C2 N 1 m 2Permeability of free space04π 10 7 T m A 1Speed of light in vacuumc3.00 108 m s 1Planck’s constanth6.63 10 34 JsElementary chargee1.60 10 19 CElectron rest massme9.110 10 31 kg 0.000549 u 0.511MeV c 2Proton rest massmp1.673 10 27 kg 1.007276 u 938 MeV c 2Neutron rest massmn1.675 10 27 kg 1.008665 u 940 MeV c 2Unified atomic mass unitu1.661 10 27 kg 931.5 MeV c 2Solar constantS1.36 103 W m 2Fermi radiusR01.20 10 15 mPhysics data booklet1

Metric (SI) 0 –1centic10 –2millim10 –310 –6micronanon10 –9picop10 –12femtof10 –15Unit conversions1 radian (rad) 180 πTemperature (K) temperature ( C) 2731 light year (ly) 9.46 1015 m1 parsec (pc)3.26 ly1 astronomical unit (AU) 1.50 1011 m1 kilowatt-hour (kWh) 3.60 106 Jhc 1.99 10 25 Jm 1.24 10 6 eV m2Physics data booklet

Electrical circuit symbolscellbatteryac supplyswitchvoltmeterVammeterresistorvariable resistorlamppotentiometerlight-dependentresistor (LDR)thermistortransformerheating elementdiodecapacitorPhysics data bookletA3

Equations—CoreNote: All equations relate to the magnitude of the quantities only. Vector notation hasnot been used.Sub-topic 1.2 – Uncertainties and errorsSub-topic 1.3 – Vectors and scalarsIf: y a bthen: y y Result.a, b, c Quantities.then: y yAAVAH Horizontalcomponent.Multiplying/dividing quantities: %uncertainties of quantities are addedtogether to obtain % uncertainty in result.abcIf: yΔ Uncertainty.Adding/subtracting quantities:uncertainty in result will be sum a b of uncertainties of quantities.AV Verticalcomponent. a b c abcAHanIf: ythen:Powers of quantities: % uncertainty ofquantity is multiplied by power to obtain% uncertainty in result. y nyv Final velocity. aaAH A cos θA V A sin θF Resultant force.Sub-topic 2.1 – Motionu Initial velocity.v u atSub-topic 2.2 – ForcesF1 2at2a Acceleration (‘g’for gravitational).s ut s Displacement.v 2 u 2 2ast Time elapsed.s Equations applied touniform motion (known as‘suvat’ equations).Ff µdRFrictional force on a static object.Frictional force on a dynamic object.s Displacement.EK1mv 22Work done.Kinetic energy.m Mass.1Ep k x 22v Velocity. Ep mg hGravitational potential energy.EP Potential energy.powerPower.k Spring constantefficiencyFvElastic potential energy (in a spring).Sub-topic 2.4 – Momentumand impulsepmvF p tμs Coefficient ofstatic friction.μd “ dynamic “.EKp22mR Normal reactionforce.p Momentum.Resultant force due to momentum.m Mass.v Velocity.Kinetic energy.F Force.impulse F t pt Time.useful work outtotal work inEK Kinetic energy.h Height.4a Acceleration.Momentum.useful power outtotal power ing Earth’s gravity.m Mass.Ff Frictional force.W Fs cos θx Extension.Acceleration due to resultant force(Newton’s 2nd law of motion).(v u ) t2F Force.EK Kinetic energy.maFf µsRSub-topic 2.3 – Work, energyand powerW Work done.Trigonometric rules of triangles areapplied when taking components ofvector quantities.Physics data booklet

p Pressure.F Force.A Area.Q Energy/heat.m Mass.c Specific heatcapacity.Sub-topic 3.1 – Thermal conceptsEnergy/heat given/received in changingan object’s temperature.Q mc TQmLEnergy/heat given/received in changingan object’s phase.T Temperature.L Specific latentheat.f Frequency.Tλ Wavelength.1fPeriod (time taken to complete 1oscillation).Sub-topic 4.2 – Travelling wavesc Velocity.f Frequency.pnc fλSpeed of a wave.Sub-topic 4.3 – Wave characteristicsNNAN Number ofatoms.Pressure.NA Avogadro’sconstant.Number of moles of a substance.nRTEK3kBT2IA Amplitude.I x 2x Distance fromsource.I I 0 cos2Intensity of a wave’s radiation at a certaindistance from the source.Transmitted intensity of light incidenton a polariser (Malus’s law).V Volume.R Gas constant.Ideal gas law.3 RT2 NAT Temperature.Average kinetic energy permolecule of a gas.EK Kinetic energy.kb Boltzmann’sconstant.Sub-topic 4.4 – Wave behaviourn1 sin θ 2 v 2 n2 sin θ1 v1s λDdRefraction when a wave crosses aboundary between 2 media(Snell’s law).n1/n2 Index ofrefraction.θ Angle ofincidence/refraction.Fringe spacing in double slit diffraction.v Wave velocity.Constructive interference:path difference nλIntensity of a wave vs. amplitude.I Intensity.A2FApVSub-topic 4.1 – OscillationsT Period.n Number of moles.Sub-topic 3.2 – Modelling a gasDestructive interference: s Fringe spacing.Maxima/minima onscreen in double slitdiffraction.λ Wavelength.1 D Distance toscreen.path difference n λ2 d Slit spacing.I0 Originalintensity.n Any integer (orderof minimum/maximum).θ Angle ofpolarizer.Physics data booklet5

I Current.q Charge.t Time.Sub-topic 5.2 – Heating effect ofelectric currentsSub-topic 5.1 – Electric fieldsF Force.I q tr Separationdistance.Fqqk 122rε0 Permittivity offree space.kk Coulombconstant.V Potential.W Work done.E Electric fieldstrength.n Number ofcharges per unitvolume.Coulomb constant.WqPotential difference.EFqElectric field strength.nAvqCurrent in a wire.VRPv Drift velocity.ε I (R r )I Current.Emf of a cell. 11 .R1 R2RALPower supplied/dissipated.L Length.Total resistance of resistorsin series.Total resistance of resistorsin parallel.Resistivity of material of a wire.F Force.F qvB sin θF B IL sin θR Resistance.VRSub-topic 5.4 – Magnetic effects ofelectric currentsSub-topic 5.3 – Electric cellsε Emf.I 2R2Rtotal R1 R2 .Rtotalρ Resistivity.A X-sectional area.VI1P Power.Resistance.Iρ A X-sectional area.R Resistance.ΣI 0 (junction)0VII Current.ΣV 0 (loop)Force experienced by 2 charges(Coulomb’s law).14Kirchhoff’s circuit laws:Current.V Potential.Force on a charge moving through amagnetic field.Force on a current-carrying wire in amagnetic field.q Charge.v Velocity of charge.B Magnitude ofmagnetic field.θ Angle with field.r Internal resistance.Sub-topic 6.2 – Newton’s law ofgravitationSub-topic 6.1 – Circular motionv Velocity.v ωrω Angular velocity.r Radius of circle.Velocity of body travelling in circle.v 2 4 π2 ra 2rTa Acceleration.T Period ofrotation.F F Force.Centripetal acceleration.mv 2 mω 2 rrCentripetal force.FGgFmgGMmr2Force experienced by 2 masses(Newton’s law of gravitation).Field strength as experienced by amass in the field.Mr2Field strength at a certaindistance from body.F Force.G Gravitationalconstant.M Mass of body.m Mass of body (ina field).r Separationdistance of bodies.g Gravitationalfield strengthm Mass.6Physics data booklet

E Energy.Sub-topic 7.1 – Discrete energy andradioactivityh Planck’s constant.f Frequency.λ Wavelength.c Speed of light.Ehfλ hcE E mc 2Energy of a photon.E Energy.Sub-topic 7.2 – Nuclear reactionsm Mass.Energy released when nucleons areassembled into nucleus.c Speed of light.Wavelength of a photon.Sub-topic 7.3 – The structure of mattere Elementarycharge.u Up.d Down.c Charm.s Strange.t 130Leptonse Electron.eeνµu Muon.νττ Tau.All leptons have a lepton numberof 1 and antileptons have a leptonnumber of –113ν Neutrino.All quarks have a strangeness numberof 0 except the strange quark that hasa strangeness number of –1b sChargedQuarks,gluonsGravitonW , W , Z0Sub-topic 8.2 – Thermal energytransferSub-topic 8.1 – Energy sourcesA Area swept outby turbine blades.ρ Air density.v Wind speed.powerenergytime1power Aρv 32P eσ AT 4Power available from a windturbine.powerAalbedoP Power.Power radiated by a body.2.90 10 3λmax (metres) T (kelvin)IPhysics data bookletGluonse Emissivity.σ Stefan-Boltzmannconstant.Wavelength atwhich intensity ofradiation is at amaximum.A Area.Intensity of radiation.T Temperature.λ Wavelength.total scattered powertotal incident powerI Intensity.7

Equations—AHLSub-topic 9.1 – Simple harmonicmotionω Angularfrequency.ω T Period.2πTAngular frequency of oscillation.a ω 2 xa Acceleration.Displacement ofobject in SHM.x0 Maximumdisplacement.v ω x0 cos ω t ; v ω x0 sin ω tt Time elapsed.v ω ( x0 2 x 2 )Velocity ofobject inSHM.Velocity of object in SHM.EK Kinetic energy.EK ET Total energy.l Length ofpendulum.1mω 2 ( x0 2 x 2 )21ET mω 2 x0 22g Gravitational fieldstrength.Kinetic energy of object inSHM.lgθ 1.22b Slit width/diameter.R R ResolvanceΔλ Smallestpossible resolvablewavelengthdifference.λbλ Wavelength.b Slit width.nλ d sin θPath difference between slits for adiffraction grating (constructive/destructive interference).1 Constructive interference: 2dn m λ2 Destructive interference: 2dn mλInterference patterns for thin-filminterference.n Any integer (fordiffraction grating).λ Wavelength.d Slit spacing (fordiffraction grating).θ Angle.d Thickness ofmedium (for TFI).n Refractive indexof medium (for TFI).m Any integer (forTFI).Period of oscillation ofa mass on a spring inSHM.First minimum for diffraction in a circularaperture.λ mN λθ Angle.Sub-topic 9.3 – InterferenceSub-topic 9.4 – Resolutionλ Wavelength.bAngle at which first minimum occursin single-slit diffraction.Period of oscillation ofa pendulum in SHM.mmass-spring:T 2πkθ Angle.λTotal energy of object in SHM.pendulum: T 2πk Spring constant.θ Acceleration of object in SHM.x x0 sin ω t ; x x0 cos ω tx Displacementfrom equilibrium.Sub-topic 9.2 – Single-slit diffractionResolvance of a diffraction grating.Sub-topic 9.5 – Doppler effect v Moving source: f ′ f v us v uo Moving observer: f ′ f v f λv fλ cDoppler effect for light.f’ Perceivedfrequency.f Actual frequency.v Wave speed.us Velocity ofsource.uo Velocity ofobserver.λ Wavelength.m Diffractionorder.v Relative speed ofobserver and source.N Number of slitsilluminated.c Speed of light.8Physics data booklet

Vg Gravitationalpotential.Sub-topic 10.1 – Describing fieldsW Work done.q Charge.Ve Electricpotential.m Mass.W q VeWork done moving a chargebetween 2 points in a field.W m VgWork done moving a massbetween 2 points in a field.Potential.Field strength.Potential energy.Vg Gravitationalpotential.Force.Ve Electricpotential.Sub-topic 10.2 – Fields at workGMrVe Vg rE Vg g GMmEp mVg EprFgGMmr2FekQrG Gravitationalconstant.k Coulombconstant. Ve rqVeM Mass.kQqrQ Charge.r Separationdistance.kQqr2v esc2GMrEscape velocity of a planet.v orbitGMrVelocity of a body in circular orbitaround another body.g Gravitationalfield strength.E Electric fieldstrength.Ep Potentialenergy.m Mass.q Charge.Fg Gravitationalforce.Fe Electric force.V(esc) Escapevelocity.V(orbit) velocity oforbit.Physics data booklet9

Φ Magnetic flux.B B Magnitude ofmagnetic field.A Area of coil.Sub-topic 11.1 – ElectromagneticinductionΦ BA cos θN Number of turns. Φε N tt Time elapsed.ε Bv lMagnetic flux.Induced emf in a coil.Sub-topic 11.3 – CapacitanceCapacitance of a capacitor.Cparallel C1 C2 .Induced emf in a conductor movingthrough a field.Induced emf in a coiled wire movingthrough a field.q Charge.qVC1Cseriesε Bv l Nl Length of wire.ASub-topic 11.2 – Power generation andC εtransmissiondI0 Maximum current.V(rms) Effective pd.I0Irms2V0VrmsP(max) Maximumpower dissipated.P Power dissipated.ε Emf.N Number of turns.p/s Primary/secondary.f Frequency.Φ Work function.n State of atom.m Mass.v Velocity.I 0V0Maximum power dissipated.1I 0V02Average power dissipated.EhfEmax h f Φ13.6E 2 eVnmvr nh2πx Position.p Momentum.h4πh E t 4πKinetic energy of freed electron(photoelectric effect) ( e stopping voltage).Quantised energy of electron in thehydrogen atom.Angular momentum of the orbitingelectron in the hydrogen atom.P (r ) ψ V x p Capacitance of capacitors inseries.Capacitance of a capacitor.1CV 22τ RC V V0 eEnergy stored in a capacitor.Exponential decrease of chargestored for a discharging capacitor.τtExponential decrease of current for adischarging capacitor.τtExponential decrease of potentialdifference for a discharging capacitor.τSub-topic 12.2 – Nuclear physicsRR0 AN N0 e13 λtA λ N0 esin θ λD λtNuclear radius of an element.Number of nuclei left in a radioactivesample.Activity of a radioactive sample.d Separation ofplates.τ Time constant.R Resistance.t Time elapsed.I Current.I0 Initial maximumcurrent.V0 Initial maximumpotential difference.R Nuclear radius.R0 Fermi radius(constant).A Atomic massnumber.N Number ofnuclei.N0 Originalnumber of nuclei.First minimum of an electron diffractionpattern around a circular object.Probability that an electron will befound within a small volume ΔV.A Activity.λ Decay constant.θ Angle of firstminimum.Uncertainty in momentum andposition of a particle (Heisenberg).λ De Brogliewavelength.Uncertainty in energy and lifetime ofthe state of a particle (Heisenberg).D Diameter ofcircular object.t Time.10A Area of plates.q0 Original charge.t ε Permittivity ofdielectric material.E Energy stored.Time constant for a circuit.q q0 eI I0eCapacitance of capacitors inparallel.V Potential(difference).Ratios of emf, turns and current in atransformer.Energy of a photon.2V Volume.ESub-topic 12.1 – The interaction ofmatter with radiationr Radius.Ψ Wave function.Resistance.ε p Np I s ε s Ns I pE Energy.h Planck’s constant.I0PmaxPVrmsIrmsV0REffective (root mean square) potentialdifference in an AC generator.2V0 Maximum pd.R ResistanceEffective (root mean square) current inan AC generator.11 .C1 C2 v Speed of wire.I(rms) Effectivecurrent.C Capacitance.Physics data booklet

Equations—OptionsSub-topic A.1 – The beginnings ofrelativityx′ x v tSub-topic A.2 – Lorentztransformations1γ 1 u′ u vSub-topic A.3 – Spacetime diagrams v θ tan 1 c v2c2x′ γ ( x vt ); x′ γ ( x v t )vx ; t ′ γc 2 t′ γ t v x t c 2 u vuv1 2cu′ t γ t0L L0γ(ct ′)2 ( x′)2 (ct )2 ( x )2Sub-topic A.4 – Relativistic mechanics(HL only)E γ m0 c 2E0m0 c 2EK (γ 1) m0 c 2p γ m0vE 2 p 2c 2 m0 2c 4Sub-topic A.5 – General relativity(HL only) ff Rs t g hc22GMc2 t01 RsrqV EKPhysics data booklet11

Sub-topic B.1 – Rigid bodiesand rotational dynamicsΓ Fr sin θI mr 2Γ Iαω 2πfωf ωi α tω f2 ω 2i 2αθ1θ ωi t α t 22L IωEKrot 1 2Iω2Sub-topic B.3 – Fluids and fluiddynamics (HL only)Sub-topic B.2 – ThermodynamicsQ U W3nRT2U S QT5pV 3constant (for monatomic gases)W p Vη useful work doneenergy inputηCarnot 1 TcoldThotSub-topic B.4 – Forced vibrations andresonance (HL only)energy storedenergy dissipated per cycleB ρ fVf gQ 2πP P0 ρ f gdQ 2π resonant frequency Avenergy storedpower lossconstant1 2ρv ρ gz p constant2FD 6πη rvR 12vr ρηPhysics data booklet

Sub-topic C.1 – Introduction toimaging1f 1 1 v uSub-topic C.2 – ImaginginstrumentationfofeM1PSub-topic C.3 – Fibre opticsfM attenuation 10 logθiθoMnear point 1sin cnhvm i houDf 1; Minfinity II0Sub-topic C.4 – Medical imaging(HL only)Df10 logLII1I0I I0e µ xµ x 1 In22d Distance fromEarth to a star.Z ρcp Parallax angle.L Luminosity.σ StefanBoltzmann constant.Sub-topic D.1 – Stellar quantitiesd (parsec)1p (arc-second)T Temperature.L σ AT 4Luminosity of a star.b Apparentbrightness.Lb 4πd 2A Area.d Distance to star.z λ v λ0 cv Relative velocityof light source.z R 1R0c Speed of light.vH0 dT1H0R Cosmic scalefactor.R(0) λmaxT 2.9 10 3 mKLM 3 .5Apparent brightness of a star.Sub-topic D.3 – Cosmologyz Red shift.λ(0) Emittedwavelength.Distance to astar in parsec.Sub-topic D.2 – Stellar characteristicsand stellar evolutionRed shift of a star/galaxy movingaway from us.Red shift depending on cosmicscale factor.Relation betweenwavelength of maximumintensity radiation of astar and its temperature.T Temperature.L Luminosity.Mass-luminosity relation for mainsequence stars.M Mass.Sub-topic D.5 – Further cosmology(HL only)v 4πG ρr3ρc 3H 28πGH(0) Hubbleconstant.d Distance fromEarth.Physics data bookletλ Wavelength.13

4 Physics data booklet. Adding/subtracting quantities: uncertainty in result will be sum of uncertainties of quantities. Multiplying/dividing quantities: % uncertainties of quantities are added together to obtain % uncertainty in result. Powers of quantities: % uncertainty of quantity is multiplied by power to obtain % uncertainty in result.

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