Physics data booklet First assessment 2016 Diploma Programme Physics data booklet Published June 2014 Revised edition published January 2016 Published on behalf of the International Baccalaureate Organization, a not-for-profit educational foundation of 15 Route des Morillons, 1218 Le Grand-Saconnex, Geneva, Switzerland by the International Baccalaureate Organization (UK) Ltd Peterson House, Malthouse Avenue, Cardiff Gate Cardiff, Wales CF23 8GL United Kingdom Website: www.ibo.org © International Baccalaureate Organization 2014 The International Baccalaureate Organization (known as the IB) offers four high-quality and challenging educational programmes for a worldwide community of schools, aiming to create a better, more peaceful world. This publication is one of a range of materials produced to support these programmes. 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Email: sales@ibo.org International Baccalaureate, Baccalauréat International and Bachillerato Internacional are registered trademarks of the International Baccalaureate Organization. 4082 Contents Fundamental constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Metric (SI) multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Unit conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Electrical circuit symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Equations—Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Equations—AHL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Equations—Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Physics data booklet Physics data booklet Fundamental constants Quantity Symbol Approximate value Acceleration of free fall (Earth’s surface) g 9.81m s−2 Gravitational constant G 6.67 × 10−11 Nm2 kg−2 Avogadro’s constant NA 6.02 × 1023 mol−1 Gas constant R 8.31JK −1 mol−1 Boltzmann’s constant kB 1.38 × 10−23 JK −1 Stefan–Boltzmann constant σ 5.67 × 10−8 W m−2 K −4 Coulomb constant k 8.99 × 109 Nm2 C−2 Permittivity of free space ε0 8.85 × 10−12 C2 N−1 m−2 Permeability of free space µ0 4π × 10−7 T m A −1 Speed of light in vacuum c 3.00 × 108 m s−1 Planck’s constant h 6.63 × 10−34 Js Elementary charge e 1.60 × 10−19 C Electron rest mass me 9.110 × 10−31 kg = 0.000549 u = 0.511MeV c −2 Proton rest mass mp 1.673 × 10−27 kg = 1.007276 u = 938 MeV c −2 Neutron rest mass mn 1.675 × 10−27 kg = 1.008665 u = 940 MeV c −2 Unified atomic mass unit u 1.661× 10−27 kg = 931.5 MeV c −2 Solar constant S 1.36 × 103 W m−2 Fermi radius R0 1.20 × 10−15 m Physics data booklet 1 Metric (SI) multipliers Prefix Abbreviation Value peta P 1015 tera T 1012 giga G 109 mega M 106 kilo k 103 hecto h 102 deca da 101 deci d 10 –1 centi c 10 –2 milli m 10 –3 micro µ 10 –6 nano n 10 –9 pico p 10 –12 femto f 10 –15 Unit conversions 1 radian (rad) ≡ 180° π Temperature (K) = temperature (°C) + 273 1 light year (ly) = 9.46 × 1015 m 1 parsec (pc) = 3.26 ly 1 astronomical unit (AU) = 1.50 × 1011 m 1 kilowatt-hour (kWh) = 3.60 × 106 J hc = 1.99 × 10−25 Jm = 1.24 × 10 −6 eV m 2 Physics data booklet Electrical circuit symbols cell battery ac supply switch voltmeter V ammeter resistor variable resistor lamp potentiometer light-dependent resistor (LDR) thermistor transformer heating element diode capacitor Physics data booklet A 3 Equations—Core Note: All equations relate to the magnitude of the quantities only. Vector notation has not been used. Sub-topic 1.2 – Uncertainties and errors If: y = a ± b then: ∆y = ∆a + ∆b If: y = then: A AV ab c ∆y y = ∆a ∆b ∆c + + a b c ∆y y θ = n ∆a a A V = A sin θ Sub-topic 2.1 – Motion 1 2 at 2 v 2 = u 2 + 2as s= Sub-topic 2.2 – Forces F = ma v = u + at s = ut + Ff ≤ µsR Ff = µdR (v + u ) t 2 Sub-topic 2.3 – Work, energy and power W = Fs cos θ Sub-topic 2.4 – Momentum and impulse p = mv EK = 1 mv 2 2 F= Ep = 1 k ∆ x2 2 EK = ∆Ep = mg ∆h power = Fv efficiency = = 4 AH AH = A cos θ If: y = a n then: Sub-topic 1.3 – Vectors and scalars ∆p ∆t p2 2m impulse = F ∆t = ∆p useful work out total work in useful power out total power in Physics data booklet Sub-topic 3.1 – Thermal concepts Q = mc ∆T Sub-topic 3.2 – Modelling a gas p= F A n= N NA Q = mL pV = nRT = EK Sub-topic 4.1 – Oscillations T= 1 f Sub-topic 4.2 – Travelling waves c = fλ Sub-topic 4.3 – Wave characteristics I ∝ A2 I ∝ x −2 I = I 0 cos2 θ Physics data booklet 3 3 R = kBT T 2 2 NA Sub-topic 4.4 – Wave behaviour n1 sin θ 2 v 2 = = n2 sin θ1 v1 s= λD d Constructive interference: path difference = nλ Destructive interference: 1 path difference = n + λ 2 5 Sub-topic 5.2 – Heating effect of electric currents Sub-topic 5.1 – Electric fields I= ∆q ∆t q1q2 r2 F =k k= 1 4ε 0 Kirchhoff’s circuit laws: ΣV = 0 (loop) ΣI = 0 (junction) R= V I V= W q = P V= I I 2R = E= F q Rtotal = R1 + R2 + ... I = nAvq 1 Rtotal ρ= Sub-topic 5.3 – Electric cells ε = I (R + r ) = V2 R 1 1 + + ... R1 R2 RA L Sub-topic 5.4 – Magnetic effects of electric currents F = qvB sin θ F = B IL sin θ Sub-topic 6.2 – Newton’s law of gravitation Sub-topic 6.1 – Circular motion v = ωr 6 F =G a= v 2 4 π2 r = 2 r T g= F= mv 2 = mω 2 r r g =G Mm r2 F m M r2 Physics data booklet Sub-topic 7.1 – Discrete energy and radioactivity E =hf λ= Sub-topic 7.2 – Nuclear reactions ∆E = ∆mc 2 hc E Sub-topic 7.3 – The structure of matter Charge 2 e 3 1 − e 3 Baryon number Quarks u d c s t 1 3 b 1 3 Charge Leptons –1 e µ τ 0 νe νµ ντ All leptons have a lepton number of 1 and antileptons have a lepton number of –1 All quarks have a strangeness number of 0 except the strange quark that has a strangeness number of –1 Particles experiencing Particles mediating Gravitational Weak Electromagnetic Strong All Quarks, leptons Charged Quarks, gluons Graviton W + , W − , Z0 γ Gluons Sub-topic 8.2 – Thermal energy transfer Sub-topic 8.1 – Energy sources power = energy time P = eσ AT 4 power = 1 Aρv 3 2 λmax (metres) = I= power A albedo = Physics data booklet 2.90 × 10−3 T (kelvin) total scattered power total incident power 7 Equations—AHL Sub-topic 9.1 – Simple harmonic motion ω= 2π T Sub-topic 9.2 – Single-slit diffraction θ= λ b a = −ω 2 x Sub-topic 9.3 – Interference x = x0 sin ω t ; x = x0 cos ω t nλ = d sin θ v = ω x0 cos ω t ; v = −ω x0 sin ω t 1 Constructive interference: 2dn = m + λ 2 v = ±ω ( x0 2 − x 2 ) Destructive interference: 2dn = mλ EK = 1 mω 2 ( x0 2 − x 2 ) 2 ET = 1 mω 2 x0 2 2 pendulum: T = 2π l g mass-spring:T = 2π m k Sub-topic 9.4 – Resolution θ = 1.22 R= λ b λ = mN ∆λ Sub-topic 9.5 – Doppler effect v Moving source: f ′ = f v ± us v ± uo Moving observer: f ′ = f v ∆f f 8 = ∆λ λ ≈ v c Physics data booklet Sub-topic 10.1 – Describing fields W = q ∆Ve W = m∆Vg Sub-topic 10.2 – Fields at work GM r Ve = ∆Vg ∆r E=− Vg = − g=− Ep = mVg = − Fg = Physics data booklet GMm r2 v esc = 2GM r v orbit = GM r kQ r ∆Ve ∆r GMm kQq = Ep qV = e r r Fe = kQq r2 9 Sub-topic 11.1 – Electromagnetic induction Φ = BA cos θ ∆Φ ∆t ε = −N ε = Bv l Sub-topic 11.3 – Capacitance C= q V Cparallel = C1 + C2 + ... 1 Cseries ε = Bv l N 1 1 + + ... C1 C2 = A Sub-topic 11.2 – Power generation and C =ε transmission d I0 Irms = E= 2 V0 Vrms = 1 CV 2 2 τ = RC 2 V0 V R = = rms I 0 Irms q = q0 e Pmax = I 0V0 I = I0e 1 I 0V0 2 V = V0 e P= − − t τ t τ − t τ ε p Np I s = = ε s Ns I p Sub-topic 12.1 – The interaction of matter with radiation Sub-topic 12.2 – Nuclear physics 1 E =hf R = R0 A 3 Emax = h f − Φ N = N0 e − λ t E=− 13.6 eV n2 mvr = nh 2π A = λ N0 e − λ t sin θ ≈ λ D 2 P (r ) = ψ ∆V ∆ x∆p ≥ h 4π ∆E ∆t ≥ h 4π 10 Physics data booklet Equations—Options Sub-topic A.1 – The beginnings of relativity x′ = x − v t Sub-topic A.2 – Lorentz transformations 1 γ= 1− u′ = u − v Sub-topic A.3 – Spacetime diagrams v θ = tan−1 c v2 c2 x′ = γ ( x − vt ); ∆ x′ = γ ( ∆ x − v ∆t ) vx ; ∆t ′ = γ c 2 t′ = γ t − v∆x ∆t − c 2 u −v uv 1− 2 c u′ = ∆t = γ ∆t0 L= L0 γ (ct ′)2 − ( x′)2 = (ct )2 − ( x )2 Sub-topic A.4 – Relativistic mechanics (HL only) E = γ m0 c 2 E0 = m0 c 2 EK = (γ − 1) m0 c 2 p = γ m0v E 2 = p 2c 2 + m0 2c 4 Sub-topic A.5 – General relativity (HL only) ∆f = g ∆h c2 Rs = 2GM c2 f ∆t = ∆t0 1− Rs r qV = ∆EK Physics data booklet 11 Sub-topic B.1 – Rigid bodies and rotational dynamics Γ = Fr sin θ I = ∑ mr 2 Γ = Iα ω = 2πf ωf = ωi + α t ω f2 = ω 2i + 2αθ 1 θ = ωi t + α t 2 2 L = Iω EKrot = 1 2 Iω 2 Sub-topic B.3 – Fluids and fluid dynamics (HL only) Sub-topic B.2 – Thermodynamics Q = ∆U + W 3 nRT 2 U= ∆S = ∆Q T 5 pV 3 = constant (for monatomic gases) W = p∆V η= useful work done energy input ηCarnot = 1 − Tcold Thot Sub-topic B.4 – Forced vibrations and resonance (HL only) energy stored energy dissipated per cycle B = ρ fVf g Q = 2π P = P0 + ρ f gd Q = 2π × resonant frequency × energy stored power loss Av = constant 1 2 ρv + ρ gz + p = constant 2 FD = 6πη rv R= 12 vr ρ η Physics data booklet Sub-topic C.1 – Introduction to imaging 1 f = 1 1 + v u Sub-topic C.2 – Imaging instrumentation fo fe M= 1 P= Sub-topic C.3 – Fibre optics f n= h v m= i =− ho u M= attenuation = 10 log θi θo Mnear point = 1 sin c D f + 1; Minfinity = Sub-topic C.4 – Medical imaging (HL only) D f I I0 LI = 10 log I1 I0 I = I0e − µ x µ x 1 = In2 2 Z = ρc Sub-topic D.1 – Stellar quantities d (parsec) = 1 p (arc-second) L = σ AT 4 b= Sub-topic D.2 – Stellar characteristics and stellar evolution λmaxT = 2.9 × 10−3 mK L ∝ M 3 .5 L 4πd 2 Sub-topic D.3 – Cosmology Sub-topic D.5 – Further cosmology (HL only) z= ∆λ v ≈ λ0 c v= 4πG ρ r 3 z= R −1 R0 ρc = 3H 2 8πG v = H0 d T ≈ 1 H0 Physics data booklet 13