22 18 A negatively charged pion decays into a muon and an antineutrino. The diagram shows tracks in a particle detector formed in such an event. muon pion (a) Deduce whether the antineutrino is charged, giving two reasons for your decision. (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (b) Write a particle equation to represent this decay. (1) .................................................................................................................................................................................................................................................. 23 Turn over (c) According to the standard model, the pion and muon are classified within two different groups of particles. State which group each particle belongs to and describe the two groups. 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(d) The momentum of the pion just before it decays is 9.1 × 10 −20 N s. Determine the magnetic flux density of the magnetic field which acts in the detector and state its direction. Scale of diagram 1 cm represents 10 cm pion charge = −1.6 × 10 −19 C (4) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. Magnetic flux density = ...................................................... Direction of magnetic field = ............................................................................................................................... 24 (e) Use a vector diagram to determine the momentum of the antineutrino. The initial momentum of the muon is 1.59 × 10 −19 N s. (5) Momentum of antineutrino = ............................................................................................................. Direction of antineutrino = ............................................................................................................. (Total for Question 18 = 16 marks) TOTAL FOR PAPER = 90 MARKS 25 Turn over List of data, formulae and relationships Acceleration of free fall g = 9.81 m s−2 (close to Earth’s surface) Boltzmann constant k = 1.38 × 10−23 J K−1 Coulomb law constant k = 1 4πε0 = 8.99 × 109 N m2 C−2 Electron charge e = −1.60 × 10−19 C Electron mass me = 9.11 × 10−31 kg Electronvolt 1 eV = 1.60 × 10−19 J Gravitational constant G = 6.67 × 10−11 N m2 kg−2 Gravitational field strength g = 9.81 N kg−1 (close to Earth’s surface) Permittivity of free space ε0 = 8.85 × 10−12 F m−1 Planck constant h = 6.63 × 10−34 J s Proton mass mp = 1.67 × 10−27 kg Speed of light in a vacuum c = 3.00 × 108 m s−1 Stefan-Boltzmann constant σ = 5.67 × 10−8 W m−2 K−4 Unified atomic mass unit u = 1.66 × 10−27 kg Mechanics Kinematic equations of motion s =  (u + v)t 2 v = u + at s = ut + 1 2 at2 v2 = u2 + 2as Forces ∑F = ma g =  F m W = mg moment of force = Fx Momentum p = mv Work, energy and power ΔW = FΔs Ek = 1 2 mv2 ΔEgrav = mgΔh P = E t P =  W t efficiency = useful energy output total energy input efficiency =  useful power output total power input 26 Electric circuits Potential difference V =  W Q Resistance R = V I Electrical power and energy P = VI P = I 2R P = V 2 R W = VIt Resistivity R =  ρl A Current I = ΔQ Δt I = nqvA Materials Density ρ =  m V Stokes’ law F = 6πηrv Hooke’s law ΔF = kΔ x Young modulus Stress σ =  F A Strain ε = Δ x x E =  σ ε Elastic strain energy ΔEel = 1 2 FΔ x Waves and particle nature of light Wave speed v = f λ Speed of a transverse wave on a string v = T μ Intensity of radiation I =  P A Power of a lens P =  1 f P = P1 + P2 + P3 + … Thin lens equation 1 u  +  1 v  =  1 f Magnification for a lens m =  image height object height =  v u Diffraction grating nλ = d sin θ Refractive index n1 sin θ1 = n2 sin θ2 n = c v Critical angle sin C = 1 n Photon model E = h f Einstein’s photoelectric equation hf = ϕ + 1 2 mv2 max de Broglie wavelength λ = h p 27 Turn over Further mechanics Impulse FΔt = Δp Kinetic energy of a non-relativistic particle Ek =  p2 2m Motion in a circle v = ωr T = 2π ω F = ma =  mv2 r a = v2 r a = rω2 F = mrω2 Fields Coulomb’s law F =  Q1Q2 4πε0r2 Electric field strength E =  F Q E = Q 4πε0r2 E =  V d Electric potential V = Q 4πε0r Capacitance C = Q V Energy stored in a capacitor W = 1 2 QV W = 1 2 CV 2 W = 1 2 Q 2 C Capacitor discharge Q = Q0e−t/RC I = I0e−t/RC V = V0e−t/RC ln Q = ln Q0 −  t RC ln I = ln I0 −  t RC ln V = ln V0 −  t RC In a magnetic field F = BIl sin θ F = Bqv sin θ Faraday’s and Lenz’s laws E =  −d(Nϕ) dt Root-mean-square values Vr ms =  V0 √2 Ir ms =  I0 √2 28 Nuclear and particle physics In a magnetic field r =  p BQ Thermodynamics Heating ΔE = mcΔθ ΔE = LΔm Molecular kinetic theory 1 2 mác2ñ = 3 2 kT pV = 1 3 Nmác2ñ Ideal gas equation pV = NkT Stefan-Boltzmann law L = σAT 4 L = 4πr2σT 4 Wien’s law λmaxT = 2.898 × 10−3 m K Space Intensity I =  L 4πd 2 Redshift of electromagnetic radiation z = Δλ λ  ≈ Δf f  ≈ v c Cosmological expansion v = H0d Nuclear radiation Mass-energy ΔE = c2Δm Radioactive decay A = λN dN dt  = −λN λ =  ln 2 t½ N = N0 e−λt A = A0 e−λt Gravitational fields Gravitational force F = Gm1m2 r 2 Gravitational field strength g = Gm r 2 Gravitational potential Vgrav = −Gm r Oscillations Simple harmonic motion F = −k x a = −ω2x x = A cos ωt v = −Aω sin ωt a = ‒Aω2 cos ωt T = 1 f  =  2π ω ω = 2π f Simple harmonic oscillator T = 2π m k T = 2π l g