Physics First examinations 2009 Diploma Programme Data booklet Diploma Programme Physics Data booklet First examinations 2009 International Baccalaureate Organization Buenos Aires Cardiff Geneva New York Singapore Diploma Programme Physics—data booklet Published September 2007 International Baccalaureate Organization Peterson House, Malthouse Avenue, Cardiff Gate Cardiff, Wales GB CF23 8GL United Kingdom Phone: +44 29 2054 7777 Fax: +44 29 2054 7778 Web site: http://www.ibo.org © International Baccalaureate Organization 2007 The International Baccalaureate Organization (IBO) was established in 1968 and is a non-profit, international educational foundation registered in Switzerland. The IBO is grateful for permission to reproduce and/or translate any copyright material used in this publication. Acknowledgments are included, where appropriate, and, if notified, the IBO will be pleased to rectify any errors or omissions at the earliest opportunity. 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Phone: +44 29 2054 7746 Fax: +44 29 2054 7779 E-mail: sales@ibo.org Printed in the United Kingdom by Antony Rowe Ltd, Chippenham, Wiltshire 4025a Contents Fundamental constants 1 Metric (SI) multipliers 2 Unit conversions 3 Electrical circuit symbols 4 Equations—Core and AHL 5 Equations—Options SL 11 Equations—Options SL and HL 13 Equations—Options HL 15 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 N m 2 kg −2 Avogadro’s constant NA 6.02 ×1023 mol−1 Gas constant R 8.31J K −1 mol −1 Boltzmann’s constant k 1.38 ×10−23 J K −1 Stefan–Boltzmann constant σ 5.67 × 10−8 W m −2 K −4 Coulomb constant k 8.99 × 109 N m 2 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 J s 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 © International Baccalaureate Organization 2007 1 Physics data booklet Metric (SI) multipliers 2 Prefix Abbreviation Value 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 © International Baccalaureate Organization 2007 Physics data booklet Unit conversions 1 light year (ly) = 9.46 ×1015 m 1 parsec (pc) = 3.26 ly 1 astronomical unit (AU) = 1.50 × 1011 m 1 radian (rad) = 180° π 1 kilowatt-hour (kW h) = 3.60 × 106 J 1 atm = 1.01×105 N m −2 = 101kPa = 760 mm Hg © International Baccalaureate Organization 2007 3 Physics data booklet Electrical circuit symbols cell battery lamp ac supply switch ammeter voltmeter V A variable resistor resistor potentiometer light-dependent resistor (LDR) thermistor transformer heating element operational amplifier (op-amp) 4 © International Baccalaureate Organization 2007 Physics data booklet Equations—Core and AHL Note: All equations relate to the magnitude of the quantities only. Vector notation has not been used. Core AHL Topic 1: Physics and physical measurement If y = a ± b then Δy = Δa + Δb If y = ab c then Δy Δa Δb Δc = + + y a b c A AV θ AH AH = A cos θ AV = A sin θ © International Baccalaureate Organization 2007 5 Equations—Core and AHL Core AHL Topic 2: Mechanics s= u+v t 2 s = ut + 12 at 2 v 2 = u 2 + 2as F = ma p = mv F= Δp Δt Impulse = F Δt = mΔv W = Fs cos θ EK = 12 mv 2 EK = p2 2m ΔEP = mg Δh power = Fv a= v 2 4π 2 r = 2 r T Topic 3: Thermal physics P= F A Q = mcΔT Topic 10: Thermal physics PV = nRT W = P ΔV Q = ΔU + W Q = mL 6 © International Baccalaureate Organization 2007 Equations—Core and AHL Core AHL Topic 4: Oscillations and waves 2π T Topic 11: Wave phenomena ⎛ v ⎞ f′ = f ⎜ ⎟ ⎝ v ± us ⎠ moving source v = v0 cos ωt ; v = −v0 sin ωt ⎛ v ± uo ⎞ f′= f ⎜ ⎟ ⎝ v ⎠ moving observer v = ±ω ( x0 2 − x 2 ) Δf = ω= x = x0 sin ω t ; x = x0 cos ω t EK = 12 mω 2 ( x0 2 − x 2 ) EK (max) = 12 mω 2 x0 2 θ= v f c λ b λ ET = 12 mω 2 x0 2 θ = 1.22 v= fλ I = I 0 cos 2 θ n1 sin θ 2 v2 = = n2 sin θ1 v1 b n = tanφ path difference = nλ path difference = ( n + 12 ) λ © International Baccalaureate Organization 2007 7 Equations—Core and AHL Core AHL Topic 5: Electric currents Topic 12: Electromagnetic induction Ve = 12 mv 2 Φ = BA cos θ I= Δq Δt R= V I R= ε = Bvl ε = − N ΔΦ Δt I s Vp N p = = I p Vs N s ρL A P = VI = I 2 R = V R 2 ε = I (R + r) I rms = I0 2 Vrms = V0 2 V0 Vrms = I 0 I rms R = R1 + R2 + ⋅⋅⋅ R= 1 1 1 = + + ⋅⋅⋅ R R1 R2 Pmax = I 0V0 Pav = 12 I 0V0 Topic 6: Fields and forces F =G m1m2 r2 g= F m F= q1q2 4πε0 r 2 F =k E= F q Topic 9: Motion in fields q1q2 r2 ΔV = ΔEp m ΔV = V =− Gm r V= g=− ΔV Δr E=− ΔEp q kq q = r 4πε 0 r ΔV Δx F = qvB sin θ F = BIL sin θ 8 © International Baccalaureate Organization 2007 Equations—Core and AHL Core Topic 7: Atomic and nuclear physics E = mc2 AHL Topic 13: Quantum physics and nuclear physics E = hf hf = φ + Emax hf = hf 0 + eV p= h λ EK = n2 h2 8me L2 Δx Δp ≥ h 4π ΔE Δ t ≥ h 4π N = N 0 e − λt A=− ΔN Δt A = λ N = λ N 0 e − λt T1 = 2 © International Baccalaureate Organization 2007 ln 2 λ 9 Equations—Core and AHL Core AHL Topic 8: Energy, power and climate change power = 12 Aρ v3 power per unit length = 12 A2 ρ gv I= power A albedo = Cs = total scattered power total incident power Q AΔT power = σ AT 4 power = e σ AT 4 ΔT = 10 ( Iin − I out ) Δt Cs © International Baccalaureate Organization 2007 Physics data booklet Equations—Options SL Option A: Sight and wave phenomena ⎛ v ⎞ f′= f ⎜ ⎟ ⎝ v ± us ⎠ ⎛ v ± uo ⎞ f′= f ⎜ ⎟ ⎝ v ⎠ moving source moving observer v Δf = f c θ= λ b θ = 1.22 λ b I = I 0 cos 2 θ n = tan φ Option B: Quantum physics and nuclear physics E = hf ΔE Δt ≥ hf = φ + Emax hf = hf 0 + eV p= N = N 0 e − λt A=− h λ n2 h2 EK = 8me L2 h Δx Δp ≥ 4π h 4π ΔN Δt A = λ N = λ N 0 e− λt T1 = 2 ln 2 λ Option C: Digital technology G=− RF R G = 1+ RF R © International Baccalaureate Organization 2007 11 Equations—Options SL Option D: Relativity and particle physics 1 γ= 1− v2 c2 Δt = γ Δ t0 L= 12 L0 ΔE Δt ≥ R≈ h 4π h 4πmc E = hf γ © International Baccalaureate Organization 2007 Physics data booklet Equations—Options SL and HL Core (SL and HL) Extension (HL only) Option E: Astrophysics L = σ AT 4 L ∝ mn λmax (metres) = d ( parsec ) = b= 2.90 × 10−3 T (kelvin) 1 p ( arc-second ) Δλ λ ≅ where 3 < n < 4 v c v = H 0d L 4πd 2 ⎛d ⎞ m − M = 5lg ⎜ ⎟ ⎝ 10 ⎠ Option F: Communications n= 1 sin C attenuation / dB = 10 lg G=− I1 I2 © International Baccalaureate Organization 2007 RF R G = 1+ RF R 13 Equations—Options SL and HL Core (SL and HL) Extension (HL only) Option G: Electromagnetic waves 1 1 1 = + f v u λmin = 2d sin θ = nλ P= 1 f m= hi v =− ho u 2nt = mλ M= f M= o fe m= s= hc eV θi θo 2nt = ( m + 12 ) λ 2nt cos φ = mλ 2nt cos φ = ( m + 12 ) λ D +1 f m= D f λD d sin θ = nλ d x nλ = D d λ x = (n+ 12 ) D d d sin θ = nλ 14 © International Baccalaureate Organization 2007 Physics data booklet Equations—Options HL Option H: Relativity EK = (γ − 1) m0 c 2 1 γ= 1− v2 c2 E 2 = p 2 c 2 + m02c 4 Δt = γ Δ t0 L= Δf g Δh = 2 f c L0 γ u x′ = ux − v uv 1 − x2 c Rs = E0 = m0c 2 Δt = E = γ m0c 2 2GM c2 Δt0 R 1− s r p = γ m0u Option I: Medical physics IL = 10 lg I = I 0e I I0 where I 0 = 1.0 × 10−12 W m −2 −μ x Z = ρc 1 1 1 = + TE TP TB μ x = ln 2 1 2 dose equivalent = absorbed dose × quality factor © International Baccalaureate Organization 2007 15 Equations—Options HL Option J: Particle physics ΔE Δt ≥ h 4π h R≈ 4πmc E = hf Ea2 = 2 Mc 2 E + ( Mc 2 ) 2 + (mc 2 ) 2 λ= h p EK = 32 kT E = mc 2 + EK 16 © International Baccalaureate Organization 2007