Physics Data Booklet (Annotated).pdf

Physics data bookletFirst assessment 2016 Annotated by Boaz V. See http://www. No part of this publication may be reproduced. Diploma Programme Physics data booklet Published June 2014 Revised edition published January 2016 Published on behalf of the International Baccalaureate Organization. 1218 Le Grand-Saconnex. Email: [email protected]. This publication is one of a range of materials produced to support these programmes. 4082 . aiming to create a better. Cardiff Gate Cardiff. The IB is grateful for permissions received for material used in this publication and will be pleased to correct any errors or omissions at the earliest opportunity.org/copyright.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. or transmitted.org. 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Switzerland by the International Baccalaureate Organization (UK) Ltd Peterson House. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Physics data booklet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Equations—AHL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Unit conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Equations—Core . . . . . . . . . . . . . . . . 2 Electrical circuit symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Metric (SI) multipliers . . . . . . 8 Equations—Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Contents Fundamental constants . . . . . . . Physics data booklet . 00 × 108 m s−1 Planck’s constant h 6.008665 u = 940 MeV c −2 Unified atomic mass unit u 1.36 × 103 W m−2 Fermi radius R0 1.67 × 10−8 W m−2 K −4 Coulomb constant k 8.67 × 10−11 Nm2 kg−2 Avogadro’s constant NA 6.81m s 2 (Earth’s surface) Gravitational constant G 6.20 × 10−15 m Physics data booklet 1 .000549 u = 0.110 × 10−31 kg = 0.31JK 1 mol 1 Boltzmann’s constant kB 1.673 × 10−27 kg = 1.02 × 1023 mol−1 Gas constant R 8.Fundamental constants Quantity Symbol Approximate value Acceleration of free fall g 9.5 MeV c −2 Solar constant S 1.675 × 10−27 kg = 1.511MeV c −2 Proton rest mass mp 1.661× 10−27 kg = 931.63 × 10−34 Js Elementary charge e 1.85 × 10−12 C2 N−1 m−2 Permeability of free space 0 4π × 10−7 T m A −1 Speed of light in vacuum c 3.60 × 10−19 C Electron rest mass me 9.99 × 109 Nm2 C−2 Permittivity of free space 0 8.38 × 10−23 JK −1 Stefan–Boltzmann constant 5.007276 u = 938 MeV c −2 Neutron rest mass mn 1. 26 ly 1 astronomical unit (AU) = 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 10 –6 nano n 10 –9 pico p 10 –12 femto f 10 –15 Unit conversions 180° 1 radian (rad) ≡ π Temperature (K) = temperature (°C) + 273 1 light year (ly) = 9.50 × 1011 m 1 kilowatt-hour (kWh) = 3.46 × 1015 m 1 parsec (pc) 3.60 × 106 J hc = 1.24 × 10 −6 eV m 2 Physics data booklet .99 × 10−25 Jm = 1. Electrical circuit symbols cell battery ac supply switch voltmeter V ammeter A resistor variable resistor lamp potentiometer light-dependent thermistor resistor (LDR) transformer heating element diode capacitor Physics data booklet 3 . k = Spring constant useful work out EK = Kinetic energy. W = Work done. Sub-topic 2. then: = n A V = A sin θ y a F = Resultant force.2 – Forces u = Initial velocity.4 – Momentum force. p mv Momentum. impulse = F ∆t = ∆p t = Time. 2m v = Velocity. Δ = Uncertainty. EK mv 2 Kinetic energy. power Fv Power. energy Sub-topic 2.3 – Vectors and scalars If: y = a ± b Adding/subtracting quantities: uncertainty in result will be sum A AV then: ∆y = ∆a + ∆b of uncertainties of quantities. s = ut + at Equations applied to static friction. Vector notation has not been used. c component. AH = Horizontal component. a.2 – Uncertainties and errors Sub-topic 1. 2 uniform motion (known as ‘suvat’ equations). Multiplying/dividing quantities: % ab uncertainties of quantities are added AV = Vertical If: y together to obtain % uncertainty in result. m = Mass.3 – Work. EP = Potential energy. ∆Ep = mg ∆h Gravitational potential energy. Acceleration due to resultant force a = Acceleration. Sub-topic 1. ∆y ∆a ∆b ∆c then: = + + y a b c AH Powers of quantities: % uncertainty of If: y an quantity is multiplied by power to obtain AH = A cos θ Trigonometric rules of triangles are applied when taking components of % uncertainty in result. 1 Ep = k ∆ x 2 Elastic potential energy (in a spring). efficiency total work in x = Extension. ∆y ∆a vector quantities. v 2 = u 2 + 2as μd = “ dynamic “. Equations—Core Note: All equations relate to the magnitude of the quantities only. m = Mass. s = Displacement. F = Force. 2 R = Normal reaction Sub-topic 2. v = u + at F ma (Newton’s 2nd law of motion). b. EK = Kinetic energy. 2 F= Resultant force due to momentum. y = Result. useful power out g = Earth’s gravity. t = Time elapsed. W = Fs cos θ Work done. c = Quantities. p2 v = Velocity. and power and impulse F = Force. v = Final velocity. ∆t m = Mass. 4 Physics data booklet . Ff = µdR Frictional force on a dynamic object. 1 ∆p p = Momentum. (v + u ) t s= Ff = Frictional force. a = Acceleration (‘g’ 1 2 Ff ≤ µsR Frictional force on a static object.1 – Motion Sub-topic 2. 2 EK Kinetic energy. s = Displacement. μs = Coefficient of for gravitational). total power in h = Height. pV nRT Ideal gas law. incidence/refraction. I A2 Intensity of a wave vs. kb = Boltzmann’s constant. v = Wave velocity. N = Number of Q = mc ∆T Energy/heat given/received in changing F Pressure. source.1 – Thermal concepts Sub-topic 3. atoms. L = Specific latent heat. I0 = Original n = Any integer (order intensity. p = Pressure. Sub-topic 3. p A NA = Avogadro’s capacity.2 – Travelling waves λD s= Fringe spacing in double slit diffraction. f = Frequency. ⎛ 1⎞ D = Distance to path difference = ⎜ n + ⎟ λ screen. R = Gas constant. EK = Kinetic energy. d = Slit spacing. Constructive interference: Sub-topic 4. N T = Temperature. Intensity of a wave’s radiation at a certain A = Amplitude. c = Specific heat an object’s temperature. amplitude. of minimum/ maximum).1 – Oscillations Sub-topic 4. 3 3 R Average kinetic energy per EK kBT T 2 2 NA molecule of a gas.2 – Modelling a gas m = Mass. 1 Period (time taken to complete 1 T oscillation). Transmitted intensity of light incident 2 ⎝ ⎠ x = Distance from I = I 0 cos2 on a polariser (Malus’s law). Maxima/minima on I = Intensity. T = Temperature.4 – Wave behaviour n1 sin θ 2 v 2 Refraction when a wave crosses a f = Frequency.3 – Wave characteristics path difference = nλ s = Fringe spacing. = = boundary between 2 media n1/n2 = Index of f n2 sin θ1 v1 (Snell’s law). constant. Destructive interference: diffraction. θ = Angle of polarizer. I ∝ x −2 distance from the source. Sub-topic 4. n Number of moles of a substance. T = Period. Physics data booklet 5 . n = Number of moles. Sub-topic 4. A = Area. d c = fλ Speed of a wave. λ = Wavelength. NA V = Volume. refraction. θ = Angle of c = Velocity. screen in double slit λ = Wavelength. Q mL Energy/heat given/received in changing an object’s phase. Q = Energy/heat. F = Force. v = Drift velocity. RA A = X-sectional area. Coulomb constant.. r ε0 = Permittivity of 1 k V ρ = Resistivity. θ = Angle with field. P VI I 2R Power supplied/dissipated. Total resistance of resistors Rtotal R1 R2 in parallel. T = Period of Field strength at a certain mv 2 M rotation. r = Separation qq Force experienced by 2 charges distance. v = ωr Velocity of body travelling in circle. V = Potential. q = Charge.2 – Newton’s law of Sub-topic 6. gravitation G = Gravitational ω = Angular velocity. Sub-topic 5.3 – Electric cells q = Charge. ρ= Resistivity of material of a wire.2 – Heating effect of F = Force. r T m m = Mass of body (in a field). F k 122 (Coulomb’s law). L = Length. r = Internal resistance. Rtotal = R1 + R2 + . free space. k = Coulomb ∆q Kirchhoff’s circuit laws: I = Current. constant. I = Current. Total resistance of resistors strength. I= Current... F = qvB sin θ magnetic field. Mm Force experienced by 2 masses F G (Newton’s law of gravitation). Sub-topic 6. q in series. F Field strength as experienced by a a = Acceleration. n = Number of 1 1 1 charges per unit I nAvq Current in a wire. t = Time. field strength 6 Physics data booklet . g G distance from body. R = Resistance. v = Velocity of charge. Sub-topic 5. F= = mω 2 r Centripetal force. F = Force. constant. electric currents ε = Emf.1 – Electric fields electric currents V = Potential. W V 2 V Potential difference. v = Velocity. W = Work done. volume. q R E = Electric field F E Electric field strength.4 – Magnetic effects of Sub-topic 5. L F = Force. Sub-topic 5. g = Gravitational m = Mass. v 2 4 π2 r Centripetal acceleration.. = + + . a= = 2 g mass in the field.I = Current. r2 r = Radius of circle. B = Magnitude of Force on a current-carrying wire in a magnetic field. ΣI = 0 (junction) P = Power. ∆t ΣV = 0 (loop) R = Resistance.1 – Circular motion F = Force. r = Separation r r2 distance of bodies. F = B IL sin θ magnetic field. Force on a charge moving through a ε = I (R + r ) Emf of a cell. M = Mass of body. 4 0 I A = X-sectional area. R Resistance. Wavelength at σ = Stefan-Boltzmann 1 Power available from a wind 2. Quarks. v = Wind speed. hc Wavelength of a photon. total scattered power albedo I = Intensity.1 – Energy sources transfer P = Power. a strangeness number of –1 b = Bottom. power I Intensity of radiation.2 – Thermal energy Sub-topic 8.90 × 10−3 power = Aρv 3 λmax (metres) = which intensity of constant. e d s b 3 3 number of –1 s = Strange. λ = Wavelength. Sub-topic 7. E Sub-topic 7. c = Charm.2 – Nuclear reactions E = Energy. T = Temperature. A λ = Wavelength.E = Energy. Z0 Gluons mediating Sub-topic 8. c = Speed of light. radioactivity h = Planck’s constant. power P = eσ AT 4 Power radiated by a body. –1 e 2 1 u = Muon. ∆E = ∆mc 2 assembled into nucleus.1 – Discrete energy and Sub-topic 7. A = Area swept out energy by turbine blades. number charge. All quarks have a strangeness number of 0 except the strange quark that has t = Top. W − . total incident power Physics data booklet 7 . All leptons have a lepton number 1 1 of 1 and antileptons have a lepton ν = Neutrino. m = Mass. e = Emissivity. time ρ = Air density. λ= c = Speed of light. 2 turbine. e u c t 0 νµ ντ 3 3 e τ = Tau. E hf Energy of a photon. T (kelvin) radiation is at a maximum. A = Area. All Charged experiencing leptons gluons Particles Graviton W + . Energy released when nucleons are f = Frequency. d = Down.3 – The structure of matter Baryon Charge Leptons e = Elementary Charge Quarks e = Electron. Gravitational Weak Electromagnetic Strong Particles Quarks. u = Up. 4 – Resolution Sub-topic 9.2 – Single-slit diffraction θ = Angle. f λ c λ = Wavelength. v = −ω x0 sin ω t object in ⎛ 1⎞ displacement. a = −ω 2 x Acceleration of object in SHM. Destructive interference: 2dn = mλ EK = Kinetic energy.5 – Doppler effect frequency. x = x0 cos ω t nλ = d sin θ Path difference between slits for a n = Any integer (for object in SHM. illuminated. wavelength = ≈ Doppler effect for light. observer and source. diameter. EK = mω 2 ( x0 2 − x 2 ) SHM. ∆λ ⎝ v ⎠ Δλ = Smallest uo = Velocity of possible resolvable ∆f v∆λ observer. from equilibrium. Sub-topic 9. Moving source: f ′ = f ⎜ ⎟ b = Slit width/ b ⎝ v ± us ⎠ v = Wave speed. Sub-topic 9. ⎝ 2⎠ d = Slit spacing (for t = Time elapsed. θ = Angle. pendulum: T = 2π a pendulum in SHM. g = Gravitational field 2 strength. m = Any integer (for l Period of oscillation of TFI). Equations—AHL Sub-topic 9. f = Actual frequency. θ= in single-slit diffraction. x0 = Maximum v = ω x0 cos ω t . N = Number of slits c = Speed of light. λ = Wavelength. interference. T b b = Slit width.22 aperture. diffraction grating (constructive/ diffraction grating).3 – Interference Displacement of x = Displacement x = x0 sin ω t . Constructive interference: 2dn = ⎜ m + ⎟ λ SHM. 1 ET = mω 2 x0 2 Total energy of object in SHM. of medium (for TFI). m = Diffraction v = Relative speed of order. λ First minimum for diffraction in a circular ⎛ v ⎞ θ = 1.1 – Simple harmonic Sub-topic 9. g Period of oscillation of m a mass on a spring in mass-spring:T = 2π k SHM. Moving observer: f ′ = f ⎜ ⎟ source. diffraction grating). Velocity of λ = Wavelength. destructive interference). 2π λ Angle at which first minimum occurs λ = Wavelength. ω= Angular frequency of oscillation. a = Acceleration. 2 medium (for TFI). 8 Physics data booklet . k = Spring constant. f’ = Perceived θ = Angle. difference. l = Length of n = Refractive index pendulum. T = Period. Interference patterns for thin-film 1 Kinetic energy of object in d = Thickness of ET = Total energy. v = ±ω ( x0 2 − x 2 ) Velocity of object in SHM. us = Velocity of λ ⎛ v ± uo ⎞ R = Resolvance R= = mN Resolvance of a diffraction grating. motion ω = Angular frequency. W = q ∆Ve GM kQ G = Gravitational q = Charge. Vg = Gravitational potential. GM Velocity of a body in circular orbit Ep = Potential v orbit around another body. Work done moving a mass ∆r ∆r m = Mass. V(esc) = Escape velocity. r r r = Separation GMm kQq Force. Physics data booklet 9 . potential. Fg Fe distance. Work done moving a charge Potential. r r between 2 points in a field. W = m∆Vg Field strength. v esc E = Electric field r strength. between 2 points in a field. W = Work done. Fe = Electric force. M = Mass.1 – Describing fields Sub-topic 10. 2GM Escape velocity of a planet. r energy. r2 r2 g = Gravitational field strength. GMm kQq Vg = Gravitational Potential energy. Ep = mVg = − Ep qVe Q = Charge. m = Mass. ∆Vg ∆Ve g=− E=− constant. q = Charge. Ve = Electric Sub-topic 10.2 – Fields at work potential. Fg = Gravitational force. Vg = − Ve constant. V(orbit) = velocity of orbit. Ve = Electric k = Coulomb potential. 2 V = V0 e τ difference for a discharging capacitor. transmission d I(rms) = Effective current.1 – Electromagnetic C = Capacitance. 1 (constant). R R0 A 3 Nuclear radius of an element. D pattern around a circular object. Sub-topic 11. parallel.2 – Power generation and A Capacitance of a capacitor. P (r ) = ψ ∆V found within a small volume ΔV. nh Angular momentum of the orbiting λ number of nuclei. P I 0V0 − t Exponential decrease of potential ε = Emf. E CV 2 Energy stored in a capacitor. t V0 Vrms q = q0 e − τ Exponential decrease of charge R = Resistance R Resistance. λ = Decay constant. A = Atomic mass Kinetic energy of freed electron number. Irms Effective (root mean square) current in 1 2 an AC generator. Φ = BA cos θ Magnetic flux. E hf Energy of a photon. stopping voltage). − Exponential decrease of current for a Pmax I 0V0 Maximum power dissipated. I = I0e τ discharging capacitor. I0 Irms P(max) = Maximum t I = Current. N0 = Original v = Velocity. 4π position of a particle (Heisenberg). h Uncertainty in momentum and ∆ x∆p ≥ minimum. d = Separation of C =ε plates. 10 Physics data booklet . x = Position. ∆E ∆t ≥ the state of a particle (Heisenberg). p = Momentum. N = Number of turns. ε = −N Induced emf in a coil.2 – Nuclear physics matter with radiation R0 = Fermi radius h = Planck’s constant. 2 q0 = Original charge. n hydrogen atom. mvr = sin θ ≈ First minimum of an electron diffraction 2π electron in the hydrogen atom. current. circular object. ε = Permittivity of Induced emf in a conductor moving t = Time elapsed. 1 1 1 Capacitance of capacitors in dielectric material. Φ = Work function. 4π D = Diameter of t = Time. E = − 2 eV Quantised energy of electron in the A = λ N0 e − λt Activity of a radioactive sample.. B = B = Magnitude of Sub-topic 11. I0 E = Energy stored. power dissipated. f = Frequency.. Vrms difference in an AC generator. N = Number of n = State of atom. Emax = h f − Φ (photoelectric effect) (= e × N = N0 e − λt Number of nuclei left in a radioactive sample. Sub-topic 12. R = Nuclear radius. through a field. τ = RC Time constant for a circuit. 13. turns and current in a = = p/s = Primary/ ε s Ns I p transformer. A = Area of coil.. q = Charge.1 – The interaction of Sub-topic 12. I0 = Maximum current. r = Radius. 1 Average power dissipated. C V V = Potential ∆Φ N = Number of turns. I0 = Initial maximum P = Power dissipated. t = Time elapsed. ε p Np I s Ratios of emf. Capacitance of capacitors in (difference). Induced emf in a coiled wire moving = + + . V0 = Initial maximum potential difference.6 nuclei. m = Mass. V0 Effective (root mean square) potential R = Resistance. A = Activity. θ = Angle of first V = Volume. 2 τ = Time constant.3 – Capacitance induction magnetic field. secondary. ε = Bv l N Cseries C1 C2 A = Area of plates. l = Length of wire. V(rms) = Effective pd.. v = Speed of wire. series. q Capacitance of a capacitor. V0 = Maximum pd. ∆t Cparallel = C1 + C2 + . stored for a discharging capacitor. λ = De Broglie h Uncertainty in energy and lifetime of wavelength. Sub-topic 11. E = Energy. 2 Probability that an electron will be Ψ = Wave function. ε = Bv l through a field.Φ = Magnetic flux. 3 – Spacetime diagrams x′ = γ ( x − vt ).1 – The beginnings of Sub-topic A.4 – Relativistic mechanics Sub-topic A. ∆t ′ = γ ⎜ ∆t − c 2 ⎟ ⎝c⎠ ⎝ c 2 ⎟⎠ ⎝ ⎠ u −v u′ = uv 1− 2 c ∆t = γ ∆t0 L0 L= γ (ct ′)2 − ( x′)2 = (ct )2 − ( x )2 Sub-topic A.5 – General relativity (HL only) (HL only) E = γ m0 c 2 ∆f g ∆h = f c2 E0 m0 c 2 2GM EK = (γ − 1) m0 c 2 Rs c2 p = γ m0v ∆t0 ∆t = Rs E 2 = p 2c 2 + m0 2c 4 1− r qV = ∆EK Physics data booklet 11 . ∆ x′ = γ ( ∆ x − v ∆t ) ⎛v ⎞ ⎛ vx ⎞ ⎛ v∆x ⎞ θ = tan−1 ⎜ ⎟ t′ = γ ⎜t − .2 – Lorentz relativity transformations x′ = x − v t 1 γ= v2 u′ = u − v 1− c2 Sub-topic A.Equations—Options Sub-topic A. Sub-topic B.3 – Fluids and fluid Sub-topic B.1 – Rigid bodies Sub-topic B.2 – Thermodynamics and rotational dynamics Γ = Fr sin θ Q = ∆U + W I = ∑ mr 2 3 U nRT 2 Γ = Iα ∆Q ω = 2πf ∆S = T ωf = ωi + α t 5 pV 3 constant (for monatomic gases) ω f2 = ω 2i + 2αθ W = p∆V 1 θ = ωi t + α t 2 2 useful work done η= L = Iω energy input 1 2 Tcold EKrot = Iω ηCarnot = 1 − 2 Thot Sub-topic B.4 – Forced vibrations and dynamics (HL only) resonance (HL only) energy stored B = ρ fVf g Q = 2π energy dissipated per cycle energy stored P = P0 + ρ f gd Q = 2π × resonant frequency × power loss Av constant 1 2 ρv + ρ gz + p = constant 2 FD = 6πη rv vr ρ R= η 12 Physics data booklet . Sub-topic D. . v= r wavelength. L = σ AT 4 Luminosity of a star. v H0 d R = Cosmic scale factor. L = Luminosity. 4πd 2 d = Distance to star. A = Area. T = Temperature.3 – Cosmology (HL only) z = Red shift. λmaxT = 2.4 – Medical imaging D D (HL only) Mnear point = + 1. ρc = R0 8πG c = Speed of light.1 – Introduction to Sub-topic C. z= −1 scale factor. L M 3 . Z = ρc p = Parallax angle. L = Luminosity. Minfinity = f f I1 LI 10 log I0 I = I0e − µ x µ x 1 = In2 d = Distance from 2 Earth to a star. Sub-topic C.2 – Imaging imaging instrumentation 1 1 1 fo = + M f v u fe 1 Sub-topic C. ∆λ v Red shift of a star/galaxy moving 4πG ρ λ(0) =Emitted z= ≈ away from us. Relation between Boltzmann constant. 1 T H0 R(0) = H(0) = Hubble constant.1 – Stellar quantities and stellar evolution σ = Stefan.9 × 10−3 mK wavelength of maximum T = Temperature. b= Apparent brightness of a star.5 – Further cosmology Sub-topic D. p (arc-second) intensity radiation of a star and its temperature.2 – Stellar characteristics Sub-topic D. Sub-topic D. 1 Distance to a d (parsec) star in parsec. brightness. b = Apparent L sequence stars. λ = Wavelength. λ0 c 3 v = Relative velocity R Red shift depending on cosmic 3H 2 of light source.5 Mass-luminosity relation for main M = Mass. d = Distance from Physics data booklet 13 Earth.3 – Fibre optics P f 1 h n v sin c m= i =− ho u I θi attenuation 10 log M= I0 θo Sub-topic C.