page 18 24. A student connects four identical light emitting diodes (LEDs) to a 2 V DC supply as shown. P Q − + 2 V DC S R Which of the LEDs P, Q, R, and S will light? A P only B Q only C P and Q only D P and R only E Q and S only. 25. A student makes the following statements about uncertainties. I All measurements of physical quantities are liable to uncertainties. II Random uncertainties occur when a measurement is repeated and slight variations occur. III Systematic uncertainties in a quantity occur when measurements are either all smaller or all larger than the true value of the quantity. Which of these statements is/are correct? A I only B I and II only C I and III only D II and III only E I, II and III [END OF QUESTION PAPER] page 19 SPACE FOR ROUGH WORK page 20 SPACE FOR ROUGH WORK H FOR OFFICIAL USE Fill in these boxes and read what is printed below. Number of seat Town © Mark Full name of centre Forename(s) Surname Scottish candidate number Date of birth Year Day Month National Qualications 2019 Instructions for the completion of Paper 1 are given on page 02. Record your answers on the answer grid on page 03. Use blue or black ink. Before leaving the examination room you must give your answer booklet to the Invigilator; if you do not, you may lose all the marks for this paper. X857/76/02 WEDNESDAY, 15 MAY 9:00 AM – 9:45 AM Physics Paper 1 — Multiple choice Answer booklet A/PB page 02 The questions for Paper 1 are contained in the question paper X857/76/12. Read these and record your answers on the answer grid on page 03. Use blue or black ink. Do NOT use gel pens or pencil. 1. The answer to each question is either A, B, C, D or E. Decide what your answer is, then fill in the appropriate bubble (see sample question below). 2. There is only one correct answer to each question. 3. Any rough working should be done on the space for rough work at the end of the question paper X857/76/12. Sample question The energy unit measured by the electricity meter in your home is the A ampere B kilowatt-hour C watt D coulomb E volt. The correct answer is B — kilowatt-hour. The answer B bubble has been clearly filled in (see below). A B C D E Changing an answer If you decide to change your answer, cancel your first answer by putting a cross through it (see below) and fill in the answer you want. The answer below has been changed to D. A B C D E If you then decide to change back to an answer you have already scored out, put a tick (3) to the right of the answer you want, as shown below: A B C D E or A B C D E Paper 1 — 25 marks page 03 Paper 1 — Answer grid A B C D E 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Physics page 04 [BLANK PAGE] DO NOT WRITE ON THIS PAGE © National Qualications 2019 H X857/76/22 Physics Paper 1 — Relationships sheet WEDNESDAY, 15 MAY 9:00 AM – 9:45 AM A/PB page 02 d vt = s vt = v u at = + 2 1 2 s ut at = + 2 2 2 v u as = + ( ) 1 2 s u v t = + W mg = F ma = 2 1 t t v c ′ = ⎛ ⎞ −⎜ ⎟ ⎝ ⎠ 2 1 v l l c ⎛ ⎞ ′ = −⎜ ⎟ ⎝ ⎠ o s s v f f v v ⎛ ⎞ = ⎜ ⎟ ± ⎝ ⎠ observed rest rest λ λ z λ − = v z c = 0 v H d = 2 E mc = E hf = 0 k E hf hf = − 2 1 E E hf − = 1 T f = v fλ = sin d θ mλ = sin sin 1 2 θ n θ = sin sin 1 1 1 2 2 2 θ λ v θ λ v = = sin 1 cθ n = 2 k I d = P I A = , , ... mλ m λ m ⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠ = 1 2 or where 0 1 2 path difference − = max. value min. value random uncertainty number of values 2 peak rms V V = 2 peak rms I I = Q It = V IR = 2 2 V P IV I R R = = = ... T R R R = + + 1 2 ... T R R R = + + 1 2 1 1 1 E V Ir = + S R V V R R ⎛ ⎞ = ⎜ ⎟ ⎜ ⎟ + ⎝ ⎠ 1 1 1 2 1 1 2 2 V R V R = 2 2 1 1 1 2 2 2 Q E QV CV C = = = Q C V = W QV = , or w E Fd W Fd = = p E mgh = 2 1 2 k E mv = E P t = p mv = Ft mv mu = − 1 2 2 m m F G r = Relationships required for Physics Higher 2 2 1 1 2 2 I d I d = max min R R R n − Δ = or page 03 Additional relationships Circle Sphere Trigonometry circumference 2πr = 2 area πr = 2 area 4πr = 3 4 3 volume πr = sin opposite hypotenuse θ = cos adjacent hypotenuse θ = tan opposite adjacent θ = sin cos 2 2 1 θ θ + = page 04 Electron arrangements of elements Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Group 0 (1) (18) 1 H 1 Hydrogen Key Atomic number Symbol Electron arrangement Name 2 He 2 Helium (13) (14) (15) (16) (17) (2) 3 Li 2,1 Lithium 4 Be 2,2 Beryllium 5 B 2,3 Boron 6 C 2,4 Carbon 7 N 2,5 Nitrogen 8 O 2,6 Oxygen 9 F 2,7 Fluorine 10 Ne 2,8 Neon 11 Na 2,8,1 Sodium 12 Mg 2,8,2 Magnesium Transition elements 13 Al 2,8,3 Aluminium 14 Si 2,8,4 Silicon 15 P 2,8,5 Phosphorus 16 S 2,8,6 Sulfur 17 Cl 2,8,7 Chlorine 18 Ar 2,8,8 Argon (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) 19 K 2,8,8,1 Potassium 20 Ca 2,8,8,2 Calcium 21 Sc 2,8,9,2 Scandium 22 Ti 2,8,10,2 Titanium 23 V 2,8,11,2 Vanadium 24 Cr 2,8,13,1 Chromium 25 Mn 2,8,13,2 Manganese 26 Fe 2,8,14,2 Iron 27 Co 2,8,15,2 Cobalt 28 Ni 2,8,16,2 Nickel 29 Cu 2,8,18,1 Copper 30 Zn 2,8,18,2 Zinc 31 Ga 2,8,18,3 Gallium 32 Ge 2,8,18,4 Germanium 33 As 2,8,18,5 Arsenic 34 Se 2,8,18,6 Selenium 35 Br 2,8,18,7 Bromine 36 Kr 2,8,18,8 Krypton 37 Rb 2,8,18,8,1 Rubidium 38 Sr 2,8,18,8,2 Strontium 39 Y 2,8,18,9,2 Yttrium 40 Zr 2,8,18, 10,2 Zirconium 41 Nb 2,8,18, 12,1 Niobium 42 Mo 2,8,18,13, 1 Molybdenum 43 Tc 2,8,18,13, 2 Technetium 44 Ru 2,8,18,15, 1 Ruthenium 45 Rh 2,8,18,16, 1 Rhodium 46 Pd 2,8,18, 18,0 Palladium 47 Ag 2,8,18, 18,1 Silver 48 Cd 2,8,18, 18,2 Cadmium 49 In 2,8,18, 18,3 Indium 50 Sn 2,8,18, 18,4 Tin 51 Sb 2,8,18, 18,5 Antimony 52 Te 2,8,18, 18,6 Tellurium 53 I 2,8,18, 18,7 Iodine 54 Xe 2,8,18, 18,8 Xenon 55 Cs 2,8,18,18, 8,1 Caesium 56 Ba 2,8,18,18, 8,2 Barium 57 La 2,8,18,18, 9,2 Lanthanum 72 Hf 2,8,18,32, 10,2 Hafnium 73 Ta 2,8,18, 32,11,2 Tantalum 74 W 2,8,18,32, 12,2 Tungsten 75 Re 2,8,18,32, 13,2 Rhenium 76 Os 2,8,18,32, 14,2 Osmium 77 Ir 2,8,18,32, 15,2 Iridium 78 Pt 2,8,18,32, 17,1 Platinum 79 Au 2,8,18, 32,18,1 Gold 80 Hg 2,8,18, 32,18,2 Mercury 81 Tl 2,8,18, 32,18,3 Thallium 82 Pb 2,8,18, 32,18,4 Lead 83 Bi 2,8,18, 32,18,5 Bismuth 84 Po 2,8,18, 32,18,6 Polonium 85 At 2,8,18, 32,18,7 Astatine 86 Rn 2,8,18, 32,18,8 Radon 87 Fr 2,8,18,32, 18,8,1 Francium 88 Ra 2,8,18,32, 18,8,2 Radium 89 Ac 2,8,18,32, 18,9,2 Actinium 104 Rf 2,8,18,32, 32,10,2 Rutherfordium 105 Db 2,8,18,32, 32,11,2 Dubnium 106 Sg 2,8,18,32, 32,12,2 Seaborgium 107 Bh 2,8,18,32, 32,13,2 Bohrium 108 Hs 2,8,18,32, 32,14,2 Hassium 109 Mt 2,8,18,32, 32,15,2 Meitnerium 110 Ds 2,8,18,32, 32,17,1 Darmstadtium 111 Rg 2,8,18,32, 32,18,1 Roentgenium 112 Cn 2,8,18,32, 32,18,2 Copernicium 57 La 2,8,18, 18,9,2 Lanthanum 58 Ce 2,8,18, 20,8,2 Cerium 59 Pr 2,8,18,21, 8,2 Praseodymium 60 Nd 2,8,18,22, 8,2 Neodymium 61 Pm 2,8,18,23, 8,2 Promethium 62 Sm 2,8,18,24, 8,2 Samarium 63 Eu 2,8,18,25, 8,2 Europium 64 Gd 2,8,18,25, 9,2 Gadolinium 65 Tb 2,8,18,27, 8,2 Terbium 66 Dy 2,8,18,28, 8,2 Dysprosium 67 Ho 2,8,18,29, 8,2 Holmium 68 Er 2,8,18,30, 8,2 Erbium 69 Tm 2,8,18,31, 8,2 Thulium 70 Yb 2,8,18,32, 8,2 Ytterbium 71 Lu 2,8,18,32, 9,2 Lutetium 89 Ac 2,8,18,32, 18,9,2 Actinium 90 Th 2,8,18,32, 18,10,2 Thorium 91 Pa 2,8,18,32, 20,9,2 Protactinium 92 U 2,8,18,32, 21,9,2 Uranium 93 Np 2,8,18,32, 22,9,2 Neptunium 94 Pu 2,8,18,32, 24,8,2 Plutonium 95 Am 2,8,18,32, 25,8,2 Americium 96 Cm 2,8,18,32, 25,9,2 Curium 97 Bk 2,8,18,32, 27,8,2 Berkelium 98 Cf 2,8,18,32, 28,8,2 Californium 99 Es 2,8,18,32, 29,8,2 Einsteinium 100 Fm 2,8,18,32, 30,8,2 Fermium 101 Md 2,8,18,32, 31,8,2 Mendelevium 102 No 2,8,18,32, 32,8,2 Nobelium 103 Lr 2,8,18,32, 32,9,2 Lawrencium Lanthanides Actinides H FOR OFFICIAL USE Fill in these boxes and read what is printed below. Number of seat Town © Mark Full name of centre Forename(s) Surname Scottish candidate number Date of birth Year Day Month National Qualications 2019 Total marks — 130 Attempt ALL questions. You may use a calculator. Reference may be made to the data sheet on page 02 of this booklet and to the relationships sheet X857/76/11. Care should be taken to give an appropriate number of significant figures in the final answers to calculations. Write your answers clearly in the spaces provided in this booklet. Additional space for answers and rough work is provided at the end of this booklet. If you use this space you must clearly identify the question number you are attempting. Any rough work must be written in this booklet. Score through your rough work when you have written your final copy. Use blue or black ink. Before leaving the examination room you must give this booklet to the Invigilator; if you do not, you may lose all the marks for this paper. X857/76/01 WEDNESDAY, 15 MAY 10:15 AM – 12:30 PM A/PB Physics Paper 2 page 02 DATA SHEET COMMON PHYSICAL QUANTITIES Quantity Symbol Value Quantity Symbol Value Speed of light in vacuum c 3·00 × 108 m s−1 Planck’s constant h 6·63 × 10−34 J s Magnitude of the charge on an electron e 1·60 × 10−19 C Mass of electron me 9·11 × 10−31 kg Universal Constant of Gravitation G 6·67 × 10−11 m3 kg−1 s−2 Mass of neutron mn 1·675 × 10−27 kg Gravitational acceleration on Earth g 9·8 m s−2 Mass of proton mp 1·673 × 10−27 kg Hubble’s constant H0 2·3 × 10−18 s−1 REFRACTIVE INDICES The refractive indices refer to sodium light of wavelength 589 nm and to substances at a temperature of 273 K. Substance Refractive index Substance Refractive index Diamond 2·42 Water 1·33 Crown glass 1·50 Air 1·00 SPECTRAL LINES Element Wavelength/nm Colour Element Wavelength/nm Colour Hydrogen Sodium 656 486 434 410 397 389 589 Red Blue-green Blue-violet Violet Ultraviolet Ultraviolet Yellow Cadmium 644 509 480 Red Green Blue Lasers Element Wavelength/nm Colour Carbon dioxide Helium-neon 9550 10 590 633 Infrared Red PROPERTIES OF SELECTED MATERIALS Substance Density/kg m−3 Melting point/K Boiling point/K Aluminium Copper Ice Sea Water Water Air Hydrogen 2·70 × 103 8·96 × 103 9·20 × 102 1·02 × 103 1·00 × 103 1·29 9·0 × 10−2 933 1357 273 264 273 . . . . 14 2623 2853 . . . . 377 373 . . . . 20 The gas densities refer to a temperature of 273 K and a pressure of 1·01 × 105 Pa. } page 03 [Turn over for next question DO NOT WRITE ON THIS PAGE page 04 DO NOT WRITE IN THIS MARGIN Total marks — 130 Attempt ALL questions 1. A student carries out an experiment with a tennis ball and a motion sensor connected to a laptop. laptop not to scale ball motion sensor The ball is released from rest below the sensor. The graph shows how the vertical velocity v of the ball varies with time t, from the moment the ball is released until it rebounds to its new maximum height. 0·77 4·0 0·50 −4·9 0 t (s) 1·18 v (m s−1) page 05 MARKS DO NOT WRITE IN THIS MARGIN 1. (continued) (a) Using information from the graph (i) show that the initial acceleration of the ball is −9·8 m s−2 Space for working and answer (ii) determine the height from which the ball is released. Space for working and answer 2 3 [Turn over page 06 MARKS DO NOT WRITE IN THIS MARGIN 1. (continued) (b) The mass of the ball is 57·0 g. (i) Determine the magnitude of the change in momentum of the ball during the bounce. Space for working and answer (ii) Determine the magnitude of the average force exerted by the ball on the ground during the bounce. Space for working and answer 3 3 page 07 MARKS DO NOT WRITE IN THIS MARGIN 1. (continued) (c) Complete the sketch graph of acceleration a against time t for the ball, between 0 s and 1·18 s after it is released. Numerical values are not required on the acceleration axis. (An additional graph, if required, can be found on page 44) 0·77 0·50 1·18 0 t (s) a (m s−2) [Turn over 2 page 08 MARKS DO NOT WRITE IN THIS MARGIN 2. A student abseils down the outside of a building using a rope. W T not to scale X 15° The mass of the student is 55 kg. The rope, of negligible mass, is attached to a fixed point X at the top of the building. The rope makes an angle of 15° to the building. (a) Calculate the weight W of the student. Space for working and answer 3 page 09 MARKS DO NOT WRITE IN THIS MARGIN 2. (continued) (b) Determine the tension T in the rope. Space for working and answer (c) As the student abseils down the building the angle the rope makes with the building decreases. State whether the tension in the rope increases, decreases or stays the same. Justify your answer. [Turn over 3 2 page 10 MARKS DO NOT WRITE IN THIS MARGIN 3. A footballer tells teammates that a football can be kicked a much greater distance when the ball is initially travelling towards them, compared to kicking a stationary ball. Use your knowledge of physics to comment on this statement. 3 page 11 DO NOT WRITE IN THIS MARGIN 3. (continued) [Turn over page 12 MARKS DO NOT WRITE IN THIS MARGIN 4. A communications satellite orbits the Earth at a height of 36∙0 × 106 m above the surface of the Earth. not to scale satellite 36·0 × 106 m The mass of the Earth is 6·0 × 1024 kg and the radius of the Earth is 6·4 × 106 m. (a) Determine the distance between the centre of the Earth and the satellite. Space for working and answer (b) The gravitational force of attraction between the Earth and the satellite is 57 N. Calculate the mass of the satellite. Space for working and answer 1 3 page 13 MARKS DO NOT WRITE IN THIS MARGIN 4. (continued) (c) Determine the value of the Earth’s gravitational field strength g at the satellite. Space for working and answer (d) A second satellite has a quarter of the mass of the first satellite. The distance from the centre of the Earth to the second satellite is half the distance from the centre of the Earth to the first satellite. State how the gravitational force of attraction between the second satellite and the Earth compares to the gravitational force of attraction between the first satellite and the Earth. Justify your answer. 3 3 [Turn over page 14 MARKS DO NOT WRITE IN THIS MARGIN 5. (a) A person is standing at the side of a road. A car travels along the road towards the person, at a constant speed of 12 m s-1. The car emits a sound of frequency 510 Hz. The person observes that the frequency of the sound heard changes as the car passes. (i) State the name given to this effect. (ii) Calculate the frequency of the sound heard by the person as the car approaches. The speed of sound in air is 340 m s-1. Space for working and answer 1 3 page 15 MARKS DO NOT WRITE IN THIS MARGIN 5. (continued) (b) This same effect is used to determine the speed of red blood cells through blood vessels. θ direction of blood flow blood vessel red blood cell probe not to scale Ultrasound waves are transmitted by a probe. The frequency of the ultrasound waves changes as they reflect from the blood cells. The probe detects the reflected waves. The velocity of the red blood cells can be determined using the following relationship 2 cos rbc f v θ f v Δ = where Δf is the change in frequency f is the transmitted frequency vrbc is the velocity of the red blood cells v is the velocity of the ultrasound θ is the angle between the direction of the waves and the direction of the blood flow. The frequency of the ultrasound transmitted by the probe is 3∙70 MHz. The velocity of the ultrasound is 1540 m s-1. During one test, the angle between the direction of the waves and blood flow is 60∙0°. The change in frequency of the ultrasound is 286 Hz. Calculate the velocity of the red blood cells during this test. Space for working and answer 2 [Turn over page 16 MARKS DO NOT WRITE IN THIS MARGIN 6. Stars emit radiation with a range of wavelengths. The peak wavelength of the radiation depends on the surface temperature of the star. (a) The graph shows how the energy emitted per second per unit area varies with the wavelength λ of the radiation for a star with a surface temperature of 5000 K. 0 energy emitted per second per unit area λ A second star has a surface temperature of 6000 K. On the graph above, add a line to show how the energy emitted per second per unit area varies with the wavelength λ of the radiation for the second star. (An additional graph, if required, can be found on page 44) 2 page 17 MARKS DO NOT WRITE IN THIS MARGIN 6. (continued) (b) The table gives the surface temperature T, in kelvin, of four different stars and the peak wavelength λpeak of radiation emitted from each star. T (K) λpeak (m) 7700 3·76 × 10-7 8500 3·42 × 10-7 9600 3·01 × 10-7 12 000 2·42 × 10-7 Use all the data in the table to show that the relationship between the surface temperature T of a star and the peak wavelength λpeak radiated from the star is 3 2 9 10 peak T λ − ⋅× = Space for working and answer [Turn over 3 page 18 MARKS DO NOT WRITE IN THIS MARGIN 7. Scientists have recently discovered a type of particle called a pentaquark. Pentaquarks are very short lived and contain five quarks. A lambda b (Λb) pentaquark contains the following quarks: 2 up, 1 down, 1 charm, and 1 anticharm quark. (a) Quarks and leptons are fundamental particles. (i) Explain what is meant by the term fundamental particle. (ii) State the name given to the group of matter particles that contains quarks and leptons. (b) The table contains information about the charge on the quarks that make up the Λb pentaquark. Type of quark Charge up 2 3 e + down 1 3 e − charm e + 2 3 anticharm e −2 3 Determine the total charge on the Λb pentaquark. Space for working and answer 1 1 2 page 19 MARKS DO NOT WRITE IN THIS MARGIN 7. (continued) (c) One theory to explain the structure of the Λb pentaquark suggests that three of the quarks group together and one quark and the antiquark group together within the pentaquark. Λb antiquark quarks (i) State the type of particle that is made of a quark-antiquark pair. (ii) The mean lifetime of another quark-antiquark pair is 8·0 × 10-21 s in its own frame of reference. During an experiment the quark-antiquark pair is travelling with a velocity of 0·91c relative to a stationary observer. Calculate the mean lifetime of this quark-antiquark pair relative to the stationary observer. Space for working and answer 1 3 [Turn over page 20 MARKS DO NOT WRITE IN THIS MARGIN 7. (continued) (d) The Λb pentaquark has a mass-energy equivalence of 4450 MeV. One eV is equal to 1∙60 × 10-19 J. (i) Determine the energy, in joules, of the Λb pentaquark. Space for working and answer (ii) Calculate the mass of the Λb pentaquark. Space for working and answer 1 3 page 21 [Turn over for next question DO NOT WRITE ON THIS PAGE page 22 MARKS DO NOT WRITE IN THIS MARGIN 8. The Sun emits energy at an average rate of 4·1 × 1026 J s-1. This energy is produced by nuclear reactions taking place inside the Sun. The following statement shows one reaction that takes place inside the Sun. 2 2 3 1 1 1 2 0 H H He n + → + (a) State the name given to this type of nuclear reaction. (b) The mass of the particles involved in this reaction are shown in the table. Particle Mass (kg) 2 1H 3·3436 × 10-27 3 2He 5·0082 × 10-27 1 0n 1·6749 × 10-27 Determine the energy released in this reaction. Space for working and answer 1 4 page 23 MARKS DO NOT WRITE IN THIS MARGIN 8. (continued) (c) Determine the number of these reactions that would be required per second to produce the Sun’s average energy output. Space for working and answer [Turn over 2 page 24 MARKS DO NOT WRITE IN THIS MARGIN 9. A laser emits light when electrons are stimulated to fall from a high energy level to a lower energy level. The diagram shows some of the energy levels involved. In one particular laser, a photon is produced by the electron transition from E5 to E3 as shown. E0 −2·976 × 10−18 J E1 E4 E2 E3 E5 −3·290 × 10−18 J (a) (i) Determine the wavelength of the photon emitted. Space for working and answer 4 page 25 MARKS DO NOT WRITE IN THIS MARGIN 9. (a) (continued) (ii) The laser beam is shone onto a screen. The beam produces a spot of diameter 8·00 × 10-4 m. 8·00 × 10−4 m spot of laser light The irradiance of the spot of light on the screen is 9950 W m-2. Determine the power of the laser beam. Space for working and answer (b) A student investigates how irradiance I varies with distance d from a point source of light, using the apparatus shown. bench covered with black cloth metre stick light meter light sensor small lamp Describe how this apparatus could be used to verify the inverse square law for a point source of light. 4 3 [Turn over page 26 MARKS DO NOT WRITE IN THIS MARGIN 10. A student carries out an experiment to investigate the effect of a grating on beams of light from three different lasers. first order maximum central maximum grating screen not to scale laser θ The three different lasers produce red, green and blue light respectively. Each laser beam is directed in turn towards the grating. The grating has a slit separation of 3·3 × 10-6 m. (a) State which of these three colours of laser light would produce the smallest angle θ between the central maximum and the first order maximum. Justify your answer. 3 page 27 MARKS DO NOT WRITE IN THIS MARGIN 10. (continued) (b) The angle θ between the central maximum and the first order maximum for light from one of the lasers is 8·9°. (i) Calculate the wavelength of this light. Space for working and answer (ii) Determine the colour of the light from this laser. (iii) Another student suggests that a more accurate value for the wavelength of this laser light can be found if a grating with a slit separation of 5·0 × 10-6 m is used. Explain why this suggestion is incorrect. [Turn over 3 1 2 page 28 MARKS DO NOT WRITE IN THIS MARGIN 11. Diamonds sparkle because light that enters the diamond is reflected back to an observer. θ 49·0° diamond air (a) A ray of monochromatic light is incident on a diamond at an angle of 49∙0°. The refractive index of diamond for this light is 2·42. Calculate the angle of refraction θ. Space for working and answer (b) Calculate the critical angle of the diamond for this light. Space for working and answer 3 3 page 29 MARKS DO NOT WRITE IN THIS MARGIN 11. (continued) (c) Moissanite is a transparent material with a greater refractive index than diamond. A sample of moissanite is made into the same shape as the diamond. State whether the sample of moissanite sparkles more or less than the diamond. You must justify your answer. [Turn over 3 page 30 MARKS DO NOT WRITE IN THIS MARGIN 12. (a) A student sets up the circuit shown. S A V E r R When switch S is open the reading on the voltmeter is 1∙5 V. Switch S is now closed. The reading on the voltmeter is now 1∙3 V and the reading on the ammeter is 0∙88 A. (i) State the EMF E of the cell. (ii) Calculate the internal resistance r of the cell. Space for working and answer (iii) Explain why the reading on the voltmeter decreases when the switch is closed. 1 3 2 page 31 MARKS DO NOT WRITE IN THIS MARGIN 12. (continued) (b) A battery of EMF 9∙0 V and internal resistance 1∙2 Ω is connected in series with a lamp. The lamp has a resistance of 2∙4 Ω. A V 2·4 Ω 9·0 V 1·2 Ω (i) Determine the current in the lamp. Space for working and answer (ii) Calculate the power dissipated in the lamp. Space for working and answer 3 3 [Turn over page 32 MARKS DO NOT WRITE IN THIS MARGIN 13. A student investigates the charging of a capacitor. The student sets up the circuit as shown using a 47 µF capacitor. − + laptop interface 0 – 12 V 47 µF S R The capacitor is initially uncharged. The switch S is now closed. A laptop connected to an interface displays a graph of current against time as the capacitor charges. (a) The variable voltage supply is set at 6∙0 V. Calculate the maximum charge stored by the capacitor. Space for working and answer 3 page 33 MARKS DO NOT WRITE IN THIS MARGIN 13. (continued) (b) The graph shows how the current I varies with time t as the capacitor charges. 0 I t Switch S is opened, and the capacitor is discharged. The resistor is now replaced with one that has a greater resistance. Switch S is again closed and the capacitor charges. Add a line to the graph above to show how the current now varies with time as the capacitor charges. (An additional graph, if required, can be found on page 45.) (c) Suggest an alteration the student could make to this circuit to increase the maximum energy stored by the 47 µF capacitor. [Turn over 2 1 page 34 MARKS DO NOT WRITE IN THIS MARGIN 13. (continued) (d) The use of analogies from everyday life can help improve the understanding of physics concepts. Vehicles using a car park may be taken as an analogy for the charging of a capacitor. speed bump Use your knowledge of physics to comment on this analogy. 3 page 35 DO NOT WRITE IN THIS MARGIN 13. (d) (continued) [Turn over page 36 MARKS DO NOT WRITE IN THIS MARGIN 14. Solids can be categorised as conductors, insulators or semiconductors depending on their ability to conduct electricity. Their electrical conductivity can be explained using band theory. The diagrams show the valence and conduction bands of three solids X, Y and Z. One represents a conductor, one represents an insulator and one represents a semiconductor. valence band solid Z conduction band valence band solid Y conduction band conduction band energy of electrons valence band solid X (a) Complete the table to show which solid represents a conductor, an insulator and a semiconductor. Solid Category X Y Z 1 page 37 MARKS DO NOT WRITE IN THIS MARGIN 14. (continued) (b) Using band theory, explain why conduction can take place in a semiconductor at room temperature. (c) Silicon can be doped with arsenic to produce an n-type semiconductor. State the effect that doping has on the conductivity of silicon. (d) Resistivity is a measure of a material’s property to oppose the flow of charge. The resistivity of silicon is 2∙3 × 103 Ω m. The resistivity of copper is 1∙7 × 10-8 Ω m. Compare the resistivity of silicon to the resistivity of copper in terms of orders of magnitude. Space for working and answer 2 1 2 [Turn over page 38 [BLANK PAGE] DO NOT WRITE ON THIS PAGE page 39 MARKS DO NOT WRITE IN THIS MARGIN 15. A 1·00 m long wooden rod has a series of small holes drilled at 10 mm intervals along its length. The rod is hung on a horizontal pin passing through a hole 50 mm from one end. not to scale pin A B The rod is then raised through a small angle and released. The period T is the time for the rod to travel from A to B and back to A. (a) Describe a method to obtain an accurate value for the period T using only a stopwatch. 2 [Turn over page 40 MARKS DO NOT WRITE IN THIS MARGIN 15. (continued) (b) The rod is hung from different holes in turn, and the distance h from the pin to the midpoint of the rod is recorded. T is determined for each value of h. The results are shown in the table. h (m) T (s) 0·45 1·60 0·40 1·56 0·35 1·54 0·30 1·53 0·25 1·53 0·22 1·55 0·20 1·58 (i) Using the square-ruled paper on page 41, draw a graph of T against h. (ii) Using your graph, state the two values of h that produce a period of 1·57 s. (iii) (A) Using your graph, estimate the minimum period T. (B) Suggest an improvement to the experimental procedure that would allow a more precise value for the minimum period T to be determined. 3 1 1 1 page 41 [Turn over for next question page 42 MARKS DO NOT WRITE IN THIS MARGIN 15. (continued) (c) The quantities T and h are related by the relationship 2 2 2 4π h T h C g = + where g is the gravitational field strength and C is a constant. Use data from the table on page 40 to calculate a value for C when h is 0∙30 m. A unit is not required. Space for working and answer [END OF QUESTION PAPER] 2 page 43 page 44 MARKS DO NOT WRITE IN THIS MARGIN ADDITIONAL SPACE FOR ANSWERS AND ROUGH WORK Additional graph for use with Question 1 (c) 0·77 0·50 1·18 0 t (s) a (m s−2) Additional graph for use with Question 6 (a) 0 energy emitted per second per unit area λ page 45 MARKS DO NOT WRITE IN THIS MARGIN ADDITIONAL SPACE FOR ANSWERS AND ROUGH WORK Additional graph for use with Question 13 (b) 0 I t page 46 MARKS DO NOT WRITE IN THIS MARGIN ADDITIONAL SPACE FOR ANSWERS AND ROUGH WORK page 47 MARKS DO NOT WRITE IN THIS MARGIN ADDITIONAL SPACE FOR ANSWERS AND ROUGH WORK page 48 [BLANK PAGE] DO NOT WRITE ON THIS PAGE © National Qualications 2019 H X857/76/11 Physics Paper 2 — Relationships sheet WEDNESDAY, 15 MAY 10:15 AM – 12:30 PM A/PB page 02 d vt = s vt = v u at = + 2 1 2 s ut at = + 2 2 2 v u as = + ( ) 1 2 s u v t = + W mg = F ma = 2 1 t t v c ′ = ⎛ ⎞ −⎜ ⎟ ⎝ ⎠ 2 1 v l l c ⎛ ⎞ ′ = −⎜ ⎟ ⎝ ⎠ o s s v f f v v ⎛ ⎞ = ⎜ ⎟ ± ⎝ ⎠ observed rest rest λ λ z λ − = v z c = 0 v H d = 2 E mc = E hf = 0 k E hf hf = − 2 1 E E hf − = 1 T f = v fλ = sin d θ mλ = sin sin 1 2 θ n θ = sin sin 1 1 1 2 2 2 θ λ v θ λ v = = sin 1 cθ n = 2 k I d = P I A = , , ... mλ m λ m ⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠ = 1 2 or where 0 1 2 path difference − = max. value min. value random uncertainty number of values 2 peak rms V V = 2 peak rms I I = Q It = V IR = 2 2 V P IV I R R = = = ... T R R R = + + 1 2 ... T R R R = + + 1 2 1 1 1 E V Ir = + S R V V R R ⎛ ⎞ = ⎜ ⎟ ⎜ ⎟ + ⎝ ⎠ 1 1 1 2 1 1 2 2 V R V R = 2 2 1 1 1 2 2 2 Q E QV CV C = = = Q C V = W QV = , or w E Fd W Fd = = p E mgh = 2 1 2 k E mv = E P t = p mv = Ft mv mu = − 1 2 2 m m F G r = Relationships required for Physics Higher 2 2 1 1 2 2 I d I d = max min R R R n − Δ = or page 03 Additional relationships Circle Sphere Trigonometry circumference 2πr = 2 area πr = 2 area 4πr = 3 4 3 volume πr = sin opposite hypotenuse θ = cos adjacent hypotenuse θ = tan opposite adjacent θ = sin cos 2 2 1 θ θ + = page 04 Electron arrangements of elements Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Group 0 (1) (18) 1 H 1 Hydrogen Key Atomic number Symbol Electron arrangement Name 2 He 2 Helium (13) (14) (15) (16) (17) (2) 3 Li 2,1 Lithium 4 Be 2,2 Beryllium 5 B 2,3 Boron 6 C 2,4 Carbon 7 N 2,5 Nitrogen 8 O 2,6 Oxygen 9 F 2,7 Fluorine 10 Ne 2,8 Neon 11 Na 2,8,1 Sodium 12 Mg 2,8,2 Magnesium Transition elements 13 Al 2,8,3 Aluminium 14 Si 2,8,4 Silicon 15 P 2,8,5 Phosphorus 16 S 2,8,6 Sulfur 17 Cl 2,8,7 Chlorine 18 Ar 2,8,8 Argon (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) 19 K 2,8,8,1 Potassium 20 Ca 2,8,8,2 Calcium 21 Sc 2,8,9,2 Scandium 22 Ti 2,8,10,2 Titanium 23 V 2,8,11,2 Vanadium 24 Cr 2,8,13,1 Chromium 25 Mn 2,8,13,2 Manganese 26 Fe 2,8,14,2 Iron 27 Co 2,8,15,2 Cobalt 28 Ni 2,8,16,2 Nickel 29 Cu 2,8,18,1 Copper 30 Zn 2,8,18,2 Zinc 31 Ga 2,8,18,3 Gallium 32 Ge 2,8,18,4 Germanium 33 As 2,8,18,5 Arsenic 34 Se 2,8,18,6 Selenium 35 Br 2,8,18,7 Bromine 36 Kr 2,8,18,8 Krypton 37 Rb 2,8,18,8,1 Rubidium 38 Sr 2,8,18,8,2 Strontium 39 Y 2,8,18,9,2 Yttrium 40 Zr 2,8,18, 10,2 Zirconium 41 Nb 2,8,18, 12,1 Niobium 42 Mo 2,8,18,13, 1 Molybdenum 43 Tc 2,8,18,13, 2 Technetium 44 Ru 2,8,18,15, 1 Ruthenium 45 Rh 2,8,18,16, 1 Rhodium 46 Pd 2,8,18, 18,0 Palladium 47 Ag 2,8,18, 18,1 Silver 48 Cd 2,8,18, 18,2 Cadmium 49 In 2,8,18, 18,3 Indium 50 Sn 2,8,18, 18,4 Tin 51 Sb 2,8,18, 18,5 Antimony 52 Te 2,8,18, 18,6 Tellurium 53 I 2,8,18, 18,7 Iodine 54 Xe 2,8,18, 18,8 Xenon 55 Cs 2,8,18,18, 8,1 Caesium 56 Ba 2,8,18,18, 8,2 Barium 57 La 2,8,18,18, 9,2 Lanthanum 72 Hf 2,8,18,32, 10,2 Hafnium 73 Ta 2,8,18, 32,11,2 Tantalum 74 W 2,8,18,32, 12,2 Tungsten 75 Re 2,8,18,32, 13,2 Rhenium 76 Os 2,8,18,32, 14,2 Osmium 77 Ir 2,8,18,32, 15,2 Iridium 78 Pt 2,8,18,32, 17,1 Platinum 79 Au 2,8,18, 32,18,1 Gold 80 Hg 2,8,18, 32,18,2 Mercury 81 Tl 2,8,18, 32,18,3 Thallium 82 Pb 2,8,18, 32,18,4 Lead 83 Bi 2,8,18, 32,18,5 Bismuth 84 Po 2,8,18, 32,18,6 Polonium 85 At 2,8,18, 32,18,7 Astatine 86 Rn 2,8,18, 32,18,8 Radon 87 Fr 2,8,18,32, 18,8,1 Francium 88 Ra 2,8,18,32, 18,8,2 Radium 89 Ac 2,8,18,32, 18,9,2 Actinium 104 Rf 2,8,18,32, 32,10,2 Rutherfordium 105 Db 2,8,18,32, 32,11,2 Dubnium 106 Sg 2,8,18,32, 32,12,2 Seaborgium 107 Bh 2,8,18,32, 32,13,2 Bohrium 108 Hs 2,8,18,32, 32,14,2 Hassium 109 Mt 2,8,18,32, 32,15,2 Meitnerium 110 Ds 2,8,18,32, 32,17,1 Darmstadtium 111 Rg 2,8,18,32, 32,18,1 Roentgenium 112 Cn 2,8,18,32, 32,18,2 Copernicium 57 La 2,8,18, 18,9,2 Lanthanum 58 Ce 2,8,18, 20,8,2 Cerium 59 Pr 2,8,18,21, 8,2 Praseodymium 60 Nd 2,8,18,22, 8,2 Neodymium 61 Pm 2,8,18,23, 8,2 Promethium 62 Sm 2,8,18,24, 8,2 Samarium 63 Eu 2,8,18,25, 8,2 Europium 64 Gd 2,8,18,25, 9,2 Gadolinium 65 Tb 2,8,18,27, 8,2 Terbium 66 Dy 2,8,18,28, 8,2 Dysprosium 67 Ho 2,8,18,29, 8,2 Holmium 68 Er 2,8,18,30, 8,2 Erbium 69 Tm 2,8,18,31, 8,2 Thulium 70 Yb 2,8,18,32, 8,2 Ytterbium 71 Lu 2,8,18,32, 9,2 Lutetium 89 Ac 2,8,18,32, 18,9,2 Actinium 90 Th 2,8,18,32, 18,10,2 Thorium 91 Pa 2,8,18,32, 20,9,2 Protactinium 92 U 2,8,18,32, 21,9,2 Uranium 93 Np 2,8,18,32, 22,9,2 Neptunium 94 Pu 2,8,18,32, 24,8,2 Plutonium 95 Am 2,8,18,32, 25,8,2 Americium 96 Cm 2,8,18,32, 25,9,2 Curium 97 Bk 2,8,18,32, 27,8,2 Berkelium 98 Cf 2,8,18,32, 28,8,2 Californium 99 Es 2,8,18,32, 29,8,2 Einsteinium 100 Fm 2,8,18,32, 30,8,2 Fermium 101 Md 2,8,18,32, 31,8,2 Mendelevium 102 No 2,8,18,32, 32,8,2 Nobelium 103 Lr 2,8,18,32, 32,9,2 Lawrencium Lanthanides Actinides