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Physics data bookletFirst assessment 2016

Diploma ProgrammePhysics data bookletPublished June 2014Revised edition published November 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

ContentsMathematical equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Fundamental constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Metric (SI) multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Unit conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Electrical circuit symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Equations—Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Equations—AHL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Equations—Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Physics data booklet

Physics data booklet

Mathematical equationsArea of a circleA πr 2 , where r is the radiusCircumference of a circleC 2πr , where r is the radiusSurface area of a sphereA 4πr 2 , where r is the radiusVolume of a sphere4V πr 3 , where r is the radius3Physics data booklet1

Fundamental constantsQuantity2SymbolApproximate valueAcceleration of free fall(Earth’s surface)g9.81m s 2Gravitational constantG6.67 10 11 Nm2 kg 2Avogadro’s constantNA6.02 1023 mol 1Gas constantR8.31JK 1 mol 1Boltzmann’s constantkB1.38 10 23 JK 1Stefan–Boltzmann constantσ5.67 10 8 W m 2 K 4Coulomb constantk8.99 109 Nm2 C 2Permittivity of free spaceε08.85 10 12 C2 N 1 m 2Permeability of free spaceµ04π 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 booklet

Metric (SI) 0 –1centic10 –2millim10 –3microµ10 –6nanon10 –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 mPhysics data booklet3

Electrical circuit symbolscellbatteryac supplyswitchvoltmeter4Vammeterresistorvariable resistorlamppotentiometerlight-dependentresistor (LDR)thermistortransformerheating elementdiodecapacitorAPhysics data booklet

Equations—CoreNote: All equations relate to the magnitude of the quantities only. Vector notation hasnot been used.Sub-topic 1.2 – Uncertainties and errorsIf: y a bthen: y a bIf: y then:AAVabc yy a b c abc yyθ n aaA V A sin θSub-topic 2.1 – Motion1 2at2v 2 u 2 2ass Sub-topic 2.2 – ForcesF mav u ats ut AHAH A cos θIf: y a nthen:Sub-topic 1.3 – Vectors and scalarsFf µsRFf µdR(v u ) t2Sub-topic 2.3 – Work, energyand powerW Fs cos θSub-topic 2.4 – Momentumand impulsep mvEK 1mv 22F Ep 1k x22EK Ep mg hpower Fvefficiency p tp22mimpulse F t puseful work outtotal work inuseful power outtotal power inPhysics data booklet5

Sub-topic 3.1 – Thermal conceptsQ mc TSub-topic 3.2 – Modelling a gasp FAn NNAQ mLpV nRT EKSub-topic 4.1 – OscillationsT 1fSub-topic 4.2 – Travelling wavesc fλSub-topic 4.3 – Wave characteristicsI A2I x 2I I 0 cos2 θ633 R kBTT22 NASub-topic 4.4 – Wave behaviourn1 sin θ 2 v 2 n2 sin θ1 v1s λDdConstructive interference:path difference nλDestructive interference: 1 path difference n λ2 Physics data booklet

Sub-topic 5.2 – Heating effect ofelectric currentsSub-topic 5.1 – Electric fieldsI q tq1q2r2F kKirchhoff’s circuit laws:ΣV 0 (loop)ΣI 0 (junction)k 14πε0R V Wq P V I I 2R E FqRtotal R1 R2 .I nAvqε I (R r )I1Rtotalρ Sub-topic 5.3 – Electric cellsV V2R11 .R1 R2RALSub-topic 5.4 – Magnetic effects ofelectric currentsF qvB sin θF B IL sin θSub-topic 6.2 – Newton’s law ofgravitationSub-topic 6.1 – Circular motionv ωrF Ga v 2 4 π2 r 2rTg F mv 2 mω 2 rrg GPhysics data bookletMmr2FmMr27

Sub-topic 7.1 – Discrete energy andradioactivityE hfλ Sub-topic 7.2 – Nuclear reactions E mc 2hcESub-topic 7.3 – The structure of matterCharge2e31 τ0νeνµντAll leptons have a lepton numberof 1 and antileptons have a leptonnumber of –1All quarks have a strangeness numberof 0 except the strange quark that hasa strangeness number of argedQuarks,gluonsGravitonW , W , Z0γGluonsSub-topic 8.2 – Thermal energytransferSub-topic 8.1 – Energy sourcespower energytimeP eσ AT 4power 1Aρv 32λmax (metres) I powerAalbedo 82.90 10 3T (kelvin)total scattered powertotal incident powerPhysics data booklet

Equations—AHLSub-topic 9.1 – Simple harmonicmotionω 2πTSub-topic 9.2 – Single-slit diffractionθ λba ω 2 xSub-topic 9.3 – Interferencex x0 sin ω t ; x x0 cos ω tnλ d sin θv ω x0 cos ω t ; v ω x0 sin ω t1 Constructive interference: 2dn m λ2 v ω ( x0 2 x 2 )Destructive interference: 2dn mλEK 1mω 2 ( x0 2 x 2 )2ET 1mω 2 x0 22pendulum: T 2πlgmass-spring:T 2πmkSub-topic 9.4 – Resolutionθ 1.22R λbλ mN λSub-topic 9.5 – Doppler effect v Moving source: f ′ f v us v uo Moving observer: f ′ f v ffPhysics data booklet λλ vc9

Sub-topic 10.1 – Describing fieldsW q VeW m VgSub-topic 10.2 – Fields at workGMrVe Vg rE Vg g Ep mVg Fg 10GMmr2v esc 2GMrv orbit GMrkQr Ve rGMmkQq Ep qV errFe kQqr2Physics data booklet

Sub-topic 11.1 – ElectromagneticinductionΦ BA cos θ Φ tε Nε Bv lSub-topic 11.3 – CapacitanceC qVCparallel C1 C2 .1Cseriesε Bv l N11 .C1 C2 ASub-topic 11.2 – Power generation andC εtransmissiondI0Irms E 2V0Vrms 1CV 22τ RC2V0VR rmsI 0 Irmsq q0 ePmax I 0V0I I0e1I 0V02V V0 eP tτtτ tτε p Np I s ε s Ns I pSub-topic 12.1 – The interaction ofmatter with radiationSub-topic 12.2 – Nuclear physics1E hfR R0 A 3Emax h f ΦN N0 e λ tE 13.6eVn2mvr nh2πA λ N0 e λ tsin θ λD2P (r ) ψ V x p h4π E t h4πPhysics data booklet11

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 2E0 m0 c 2EK (γ 1) m0 c 2p γ m0vE 2 p 2c 2 m0 2c 4Sub-topic A.5 – General relativity(HL only) f g hc2Rs 2GMc2f t t01 RsrqV EK12Physics data booklet

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 3 constant (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 energy storedpower lossAv constant1 2ρv ρ gz p constant2FD 6πη rvR vr ρηPhysics data booklet13

Sub-topic C.1 – Introduction toimaging1f 1 1 v uSub-topic C.2 – ImaginginstrumentationfofeM 1P Sub-topic C.3 – Fibre opticsfn hvm i houM attenuation 10 logθiθoMnear point 1sin cDf 1; Minfinity Sub-topic C.4 – Medical imaging(HL only)DfII0LI 10 logI1I0I I0e µ xµ x 1 In22Z ρcSub-topic D.1 – Stellar quantitiesd (parsec) 1p (arc-second)L σ AT 4b Sub-topic D.2 – Stellar characteristicsand stellar evolutionλmaxT 2.9 10 3 mKL M 3 .5L4πd 2Sub-topic D.3 – CosmologySub-topic D.5 – Further cosmology(HL only)z λ v λ0 cv 4πG ρr3z R 1R0ρc 3H 28πGv H0 dT 141H0Physics data booklet

Fundamental constants Quantity Symbol Approximate value Acceleration of free fall (Earth's surface) g 98.m1 s 2 Gravitational constant G 66. 71 0 11Nm22kg Avogadro's constant N A 60. 21 023 mol 1 Gas constant R 83.J1 Km 11 ol Boltzmann's constant k B 13. 81 0 23 JK 1 Stefan-Boltzmann constant σ 56. 71 0 82Wm K 4 Coulomb constant k 89. 91 092Nm C 2