Cambridge A Level Physics 9702 — 2012 Oct/Nov Paper 4 · Variant 3

1 An ideal gas has volume V and pressure p. For this gas, the product pV is given by the expression pV = 13Nm <c 2> where m is the mass of a molecule of the gas. (a) State the meaning of the symbol (i) N, ..............................................................................................................................[1] (ii) <c 2>. ..............................................................................................................................[1] (b) A gas cylinder of volume 2.1 × 104 cm3 contains helium-4 gas at pressure 6.1 × 105 Pa and temperature 12 °C. Helium-4 may be assumed to be an ideal gas. (i) Determine, for the helium gas, 1. the amount, in mol, amount = ......................................... mol [3] 2. the number of atoms. number = ..................................................[2] (ii) Calculate the root-mean-square (r.m.s.) speed of the helium atoms. For Examiner’s Use r.m.s. speed = ....................................... m s–1 [3]

Mark scheme: 1 (a) (i) number of molecules B1 [1] (ii) mean square speed B1 [1] (b) (i) 1. pV = nRT C1 n = (6.1 × 105 × 2.1 × 104 × 10–6) / (8.31 × 285) C1 n = 5.4 mol A1 [3] 2. either N = nNA = 5.4 × 6.02 × 1023 C1 = 3.26 × 1024 A1 or pV = NkT N = (6.1 × 105 × 2.1 × 104 × 10–6) / (1.38 × 10–23 × 285) (C1) N = 3.26 × 1024 (A1) [2] (ii) either 6.1 × 105 × 2.1 × 10–2 = 1/3 × 3.25 × 1024 × 4 × 1.66 × 10–27× <c2> C1 <c2> = 1.78 × 106 C1 cRMS = 1.33 × 103 m s–1 A1 or 1/2 × 4 × 1.66 × 10–27 × <c2> = 3/2 × 1.38 × 10–23 × 285 (C1) <c2> = 1.78 × 106 (C1) cRMS = 1.33 × 103 m s–1 (A1) [3]

More questions on Kinetic theory of gases

2 A small frictionless trolley is attached to a fixed point A by means of a spring. A second For spring is used to attach the trolley to a variable frequency oscillator, as shown in Fig. 2.1. Examiner’s Use trolley variable frequency oscillator A Fig. 2.1 Both springs remain extended within the limit of proportionality. Initially, the oscillator is switched off. The trolley is displaced horizontally along the line joining the two springs and is then released. The variation with time t of the velocity v of the trolley is shown in Fig. 2.2. 0.3 v / m s–1 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1.0 1.2 t / s −0.1 −0.2 −0.3 Fig. 2.2 (a) (i) Using Fig. 2.2, state two different times at which 1. the displacement of the trolley is zero, time = ........................... s and time = ........................... s [1] 2. the acceleration in one direction is maximum. time = ........................... s and time = ........................... s [1] (ii) Determine the frequency of oscillation of the trolley. For Examiner’s Use frequency = ........................................... Hz [2] (iii) The variation with time of the displacement of the trolley is sinusoidal. The variation with time of the velocity of the trolley is also sinusoidal. State the phase difference between the displacement and the velocity. phase difference = ................................................. [1] (b) The oscillator is now switched on. The amplitude of vibration of the oscillator is constant. The frequency f of vibration of the oscillator is varied. The trolley is forced to oscillate by means of vibrations of the oscillator. The variation with f of the amplitude a0 of the oscillations of the trolley is shown in Fig. 2.3. a0 f Fig. 2.3 By reference to your answer in (a), state the approximate frequency at which the amplitude is maximum. frequency = ........................................... Hz [1] (c) The amplitude of the oscillations in (b) may be reduced without changing significantly the frequency at which the amplitude is a maximum. State how this may be done and give a reason for your answer. You may draw on Fig. 2.1 if you wish. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2]

Mark scheme: 2 (a) (i) 1. 0.1 s, 0.3 s, 0.5 s, etc (any two) A1 [1] 2. either 0, 0.4 s, 0.8 s, 1.2 s or 0.2 s, 0.6 s, 1.0 s (any two) A1 [1] (ii) period = 0.4 s C1 frequency = (1/0.4 =) 2.5 Hz A1 [2] (iii) phase difference = 90 ° or ½ π rad B1 [1] (b) frequency = 2.4 – 2.5 Hz B1 [1] (c) e.g. attach sheet of card to trolley M1 increases damping / frictional force A1 e.g. reduce oscillator amplitude (M1) reduces power/energy input to system (A1) [2] GCE AS/A LEVEL – October/November 2012 9702 43

More questions on Simple harmonic oscillations

3 (a) State what is meant by a line of force in For Examiner’s (i) a gravitational field, Use .................................................................................................................................. ..............................................................................................................................[1] (ii) an electric field. .................................................................................................................................. ..............................................................................................................................[2] (b) A charged metal sphere is isolated in space. State one similarity and one difference between the gravitational force field and the electric force field around the sphere. similarity: .......................................................................................................................... .......................................................................................................................................... difference: ........................................................................................................................ .......................................................................................................................................... .......................................................................................................................................... [3] (c) Two horizontal metal plates are separated by a distance of 1.8 cm in a vacuum. A potential difference of 270 V is maintained between the plates, as shown in Fig. 3.1. 0 V proton 1.8 cm +270 V Fig. 3.1 A proton is in the space between the plates. Explain quantitatively why, when predicting the motion of the proton between the plates, the gravitational field is not taken into consideration. [4]

Mark scheme: 3 (a) (i) (tangent to line gives) direction of force on a (small test) mass B1 [1] (ii) (tangent to line gives) direction of force on a (small test) charge M1 charge is positive A1 [2] (b) similarity: e.g. radial fields lines normal to surface greater separation of lines with increased distance from sphere field strength ∝ 1 / (distance to centre of sphere)2 (allow any sensible answer) B1 difference: e.g. gravitational force (always) towards sphere B1 electric force direction depends on sign of charge on sphere / towards or away from sphere B1 e.g. gravitational field/force is attractive (B1) electric field/force is attractive or repulsive (B1) (allow any sensible comparison) [3] (c) gravitational force = 1.67 × 10–27 × 9.81 = 1.6 × 10–26 N A1 electric force = 1.6 × 10–19 × 270 / (1.8 × 10–2) C1 = 2.4 × 10–15 N A1 electric force very much greater than gravitational force B1 [4]

More questions on Gravitational field

4 A proton of mass m and charge +q is travelling through a vacuum in a straight line with For speed v. Examiner’s It enters a region of uniform magnetic field of magnetic flux density B, as shown in Fig. 4.1. Use region of uniform magnetic field proton mass m charge +q v Fig. 4.1 The magnetic field is normal to the direction of motion of the proton. (a) Explain why the path of the proton in the magnetic field is an arc of a circle. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2] (b) The angular speed of the proton in the magnetic field is ω. Derive an expression for ω in terms of B, q and m. [4]

Mark scheme: 4 (a) force on proton is normal to velocity and field M1 provides centripetal force (for circular motion) A1 [2] (b) magnetic force = Bqv B1 centripetal force = mrω2 or mv2/r B1 v = rω B1 Bqv = Bqrω = mrω2 ω = Bq/m A1 [4]

More questions on Centripetal acceleration

5 (a) State the relation between magnetic flux density B and magnetic flux Φ, explaining any For other symbols you use. Examiner’s Use .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2] (b) A large horseshoe magnet has a uniform magnetic field between its poles. The magnetic field is zero outside the space between the poles. A small Hall probe is moved at constant speed along a line XY that is midway between, and parallel to, the faces of the poles of the magnet, as shown in Fig. 5.1. Hall probe pole of X magnet pole of magnet Y Fig. 5.1 An e.m.f. is produced by the Hall probe when it is in the magnetic field. For The angle between the plane of the probe and the direction of the magnetic field is not Examiner’s varied. Use On the axes of Fig. 5.2, sketch a graph to show the variation with time t of the e.m.f. VH produced by the Hall probe. VH 0 t probe enters probe leaves magnetic magnetic field field Fig. 5.2 [2] (c) (i) State Faraday’s law of electromagnetic induction. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[2] (ii) The Hall probe in (b) is replaced by a small flat coil of wire. The coil is moved at constant speed along the line XY. The plane of the coil is parallel to the faces of the poles of the magnet. On the axes of Fig. 5.3, sketch a graph to show the variation with time t of the e.m.f. E induced in the coil. E 0 t coil enters coil leaves magnetic magnetic field field Fig. 5.3 [3]

Mark scheme: 5 (a) either φ = BA sinθ M1 where A is the area (through which flux passes) θ is the angle between B and (plane of) A A1 or φ = BA (M1) where A is area normal to B (A1) [2] (b) graph: VH constant and non zero between the poles and zero outside M1 sharp increase/decrease at ends of magnet A1 [2] GCE AS/A LEVEL – October/November 2012 9702 43 (c) (i) (induced) e.m.f. proportional to M1 rate of change of (magnetic) flux (linkage) A1 [2] (ii) short pulse on entering and on leaving region between poles M1 pulses approximately the same shape but opposite polarities A1 e.m.f. zero between poles and outside A1 [3]

More questions on Electromagnetic induction

6 A bridge rectifier consists of four ideal diodes A, B, C and D, connected as shown in Fig. 6.1. For Examiner’s Use A B R X D C Y Fig. 6.1 An alternating supply is applied between the terminals X and Y. (a) (i) On Fig. 6.1, label the positive (+) connection to the load resistor R. [1] (ii) State which diodes are conducting when terminal Y of the supply is positive. diode .................... and diode ....................[1] (b) The variation with time t of the potential difference V across the load resistor R is shown in Fig. 6.2. +8 +6 V / V +4 +2 0 t −2 −4 −6 −8 Fig. 6.2 The load resistor R has resistance 2700 Ω. For Examiner’s (i) Use Fig. 6.2 to determine the mean power dissipated in the resistor R. Use power = ............................................ W [3] (ii) On Fig. 6.1, draw the symbol for a capacitor, connected so as to increase the mean power dissipated in the resistor R. [1] (c) The capacitor in (b)(ii) is now removed from the circuit. The diode A in Fig. 6.1 stops functioning, so that it now has infinite resistance. On Fig. 6.2, draw the variation with time t of the new potential difference across the resistor R. [2]

Mark scheme: 6 (a) (i) connection to ‘top’ of resistor labelled as positive B1 [1] (ii) diode B and diode D B1 [1] (b) (i) VP = 4.0 V C1 mean power = VP2/2R C1 = 42 / (2 × 2700) = 2.96 × 10–3 W A1 [3] (ii) capacitor, correct symbol, connected in parallel with R B1 [1] (c) graph: half-wave rectification M1 same period and same peak value A1 [2]

More questions on Practical circuits

7 (a) State what is meant by the de Broglie wavelength. For Examiner’s .......................................................................................................................................... Use .......................................................................................................................................... ......................................................................................................................................[2] (b) An electron is accelerated from rest in a vacuum through a potential difference of 4.7 kV. (i) Calculate the de Broglie wavelength of the accelerated electron. wavelength = ............................................ m [5] (ii) By reference to your answer in (i), suggest why such electrons may assist with an understanding of crystal structure. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[2]

Mark scheme: 7 (a) wavelength associated with a particle M1 that is moving A1 [2] (b) (i) kinetic energy = 1.6 × 10–19 × 4700 C1 = 7.52 × 10–16 J either energy = p2/2m or EK = ½mv2 and p = mv C1 p = √(7.52 × 10–16 × 2 × 9.1 × 10–31) C1 = 3.7 × 10–23 N s λ = h/p C1 = (6.63 × 10–34) / (3.7 × 10–23) = 1.8 × 10–11 m A1 [5] (ii) wavelength is about separation of atoms B1 can be used in (electron) diffraction B1 [2]

More questions on Wave-particle duality

8 When a neutron is captured by a uranium-235 nucleus, the outcome may be represented by For the nuclear equation shown below. Examiner’s Use 235 1 95 139 1 0 U + n Mo + La + x n + 7 e 92 0 42 57 0 –1 (a) (i) Use the equation to determine the value of x. x = ...................................................[1] 0 (ii) State the name of the particle represented by the symbol e. –1 ..............................................................................................................................[1] (b) Some data for the nuclei in the reaction are given in Fig. 8.1. mass / u binding energy per nucleon / MeV 235 uranium-235 ( U) 235.123 92 95 molybdenum-95 ( Mo) 94.945 8.09 42 139 lanthanum-139 ( La) 138.955 7.92 57 1 proton ( p) 1.007 1 1 neutron ( n) 1.009 0 Fig. 8.1 Use data from Fig. 8.1 to (i) determine the binding energy, in u, of a nucleus of uranium-235, binding energy = ............................................. u [3] (ii) show that the binding energy per nucleon of a nucleus of uranium-235 is 7.18 MeV. For Examiner’s Use [3] (c) The kinetic energy of the neutron before the reaction is negligible. Use data from (b) to calculate the total energy, in MeV, released in this reaction. energy = ........................................ MeV [2]

Mark scheme: 8 (a) (i) x = 2 A1 [1] (ii) either beta particle or electron B1 [1] (b) (i) mass of separate nucleons = {(92 × 1.007) + (143 × 1.009)} u C1 = 236.931 u C1 binding energy = 236.931 u – 235.123 u = 1.808 u A1 [3] GCE AS/A LEVEL – October/November 2012 9702 43 (ii) E = mc2 C1 energy = 1.808 × 1.66 × 10–27 × (3.0 × 108)2 = 2.7 × 10–10 J C1 binding energy per nucleon = (2.7 × 10–10) / (235 × 1.6 × 10–13) M1 = 7.18 MeV A0 [3] (c) energy released = (95 × 8.09) + (139 × 7.92) – (235 × 7.18) C1 = 1869.43 – 1687.3 = 182 MeV A1 [2] (allow calculation using mass difference between products and reactants) Section B

More questions on Atoms, nuclei and radiation

9 A student designs an electronic sensor to monitor whether the temperature in a refrigerator is above or below a particular value. The circuit is shown in Fig. 9.1. A D +5 V – + –5 V B C sensing processing output device unit device Fig. 9.1 (a) Name the components used in the output device. ......................................................................................................................................[1] (b) An operational amplifier (op-amp) is used as the processing unit. Describe the function of this processing unit. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2] (c) State the function of (i) the resistors C and D, .................................................................................................................................. ..............................................................................................................................[1] (ii) the resistor B. .................................................................................................................................. ..............................................................................................................................[1] (d) The output device of the circuit in Fig. 9.1 is changed so that the new output device may For be used to switch on a high-voltage circuit. Examiner’s Use (i) State the component that is used in the new output device. .................................................................................................................................. ..............................................................................................................................[1] (ii) Draw on Fig. 9.2 to show how the component in (i), together with a diode, are connected so that the high voltage may be switched on when the output of the op-amp is negative. +5 V – + –5 V connections to high-voltage circuit output device Fig. 9.2 [2]

Mark scheme: 9 (a) light-emitting diode (allow LED) B1 [1] (b) gives a high or a low output / +5 V or –5 V output M1 dependent on which of the inputs is at a higher potential A1 [2] (c) (i) provides a reference/constant potential B1 [1] (ii) determines temperature of ‘switch-over’ B1 [1] (d) (i) relay A1 [1] (ii) relay connected correctly for op-amp output and high-voltage circuit B1 diode with correct polarity in output from op-amp B1 [2]

More questions on Potential dividers

10 A simple model of one section of a CT scan is shown in Fig. 10.1. For Examiner’s Use A B D C Fig. 10.1 The model consists of four voxels with pixel numbers A, B, C and D. In this model, the voxels are viewed in turn along four different directions D1, D2, D3 and D4 as shown in Fig. 10.2. D3 D2 D4 A B D1 D C Fig. 10.2 The pixel readings in each of the four directions are noted. The total pixel reading for any one direction is 19. The pixel readings for all of the directions are summed to give the pattern of readings shown in Fig. 10.3. 25 34 28 46 Fig. 10.3 (a) State the background reading in this model. background reading = ..................................................[1] (b) Determine each of the pixel readings. For Examiner’s Use A = B = ............ ............ D = C = ............ ............ [4] (c) Use your answers in (b) to determine the pixel readings along (i) the direction D3, ..............................................................................................................................[1] (ii) the direction D4. ..............................................................................................................................[2]

Mark scheme: 10 (a) background reading = 19 B1 [1] (b) A = 2 A1 B = 5 A1 C = 9 A1 D = 3 A1 [4] (Allow 1 mark if only subtracts background reading) (c) (i) either 5, 14 or 14, 5 (A+D, B+C or v.v.) B1 [1] (ii) Three numbers and ‘inside’ number is 8 (B+D) B1 Three numbers and ‘outside’ numbers are either 2,9 or 9,2 (A,C or v.v.) B1 [2]

More questions on Production and use of ultrasound

11 In commercial radio, transmissions are made by means of carrier waves that are modulated For by the audio signals. Examiner’s Use (a) State what is meant by a modulated carrier wave. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[3] (b) State three reasons why modulated carrier waves are used, rather than the direct transmission of electromagnetic waves having audio frequencies. 1. ...................................................................................................................................... .......................................................................................................................................... 2. ...................................................................................................................................... .......................................................................................................................................... 3. ...................................................................................................................................... .......................................................................................................................................... [3]

Mark scheme: 11 (a) high frequency wave B1 the amplitude or the frequency is varied M1 the variation represents the information signal / in synchrony with (the displacement of) the information signal. A1 [3] GCE AS/A LEVEL – October/November 2012 9702 43 (b) e.g. shorter aerial required longer transmission range / lower transmitter power / less attenuation allows more than one station in a region less distortion (allow any three sensible suggestions, 1 mark each) B3 [3]

More questions on Electromagnetic spectrum

12 (a) Suggest applications, one in each case, for the transmission of signals using For Examiner’s (i) a wire pair, Use ..............................................................................................................................[1] (ii) a coaxial cable, ..............................................................................................................................[1] (iii) a microwave link. ..............................................................................................................................[1] (b) A cable used for the transmission of a signal has an attenuation per unit length of 2.1 dB km–1. There are no amplifiers along the cable. The input power of the signal is 450 mW. (i) Calculate the output power of the signal for the cable of length 40 km. output power = ............................................ W [3] (ii) The minimum acceptable signal power in the cable is 7.2 × 10–11 W. Calculate the maximum uninterrupted length of the cable. length = .......................................... km [2]

Mark scheme: 12 (a) (i) e.g. linking a (land) telephone to the (local) exchange B1 [1] (ii) e.g. connecting an aerial to a television B1 [1] (iii) e.g. linking a ground station to a satellite B1 [1] (b) (i) attenuation = 10 lg (P2 / P1) C1 total attenuation = 2.1 × 40 (= 84 dB) C1 84 = 10 lg ({450 × 10–3} / P) P = 1.8 × 10–9 W A1 [3] (answer 1.1 ×108 W scores 1 mark only) (ii) maximum attenuation = 10 lg ({450 × 10–3} / {7.2 × 10–11}) = 98 dB C1 maximum length = 98/2.1 = 47 km A1 [2]

More questions on Practical circuits