Markscheme Examiners Report

Examiners report[N/A]Alpha Centauri A and B is a binary star system in the main sequence.13a.[1 mark]State what is meant by a binary star system.Markschemetwo stars orbiting about a common centre «of mass/gravity»Do not accept two stars orbiting each other.Examiners report[N/A]13b. (i) CalculatebAbB apparent brightness of Alpha Centauri Aapparent brightness of Alpha Centauri B.(ii) The luminosity of the Sun is 3.8 10 26 W. Calculate the radius of Alpha Centauri A.[4 marks]

Markschemeistars are roughly at the same distance from EarthORd is constant for binariesLALB 1.50.5 3.0Award [2] for a bald correct answer.iir 1.5 3.8 10265.67 10 8 4π 58004 8.4 108 «m»Award [2] for a bald correct answer.Examiners report[N/A]13c.Show, without calculation, that the radius of Alpha Centauri B is smaller than the radius of Alpha Centauri A.Markscheme«A L»σT 4B and A have similar temperaturesso areas are in ratio of luminosities«so B radius is less than A»Examiners report[N/A][2 marks]

13d.Alpha Centauri A is in equilibrium at constant radius. Explain how this equilibrium is maintained.[3 marks]Markschemeradiation pressure/force outwardsgravitational pressure/force inwardsforces/pressures balanceExaminers report[N/A]13e.A standard Hertzsprung–Russell (HR) diagram is shown.Using the HR diagram, draw the present position of Alpha Centauri A and its expected evolutionary path.[2 marks]

MarkschemeAlpha Centauri A within allowable regionsome indication of star moving right and up then left and down ending in white dwarf region as indicatedExaminers report[N/A]

The first graph shows the variation of apparent brightness of a Cepheid star with time.The second graph shows the average luminosity with period for Cepheid stars.2614a. Determine the distance from Earth to the Cepheid star in parsecs. The luminosity of the Sun is 3.8 10 W. The averageapparent brightness of the Cepheid star is 1.1 10 –9 W m–2.Markschemefrom first graph period 5.7 «days» 0.3 «days»from second graphd « 2500 3.8 10264π 1.1 10 9LLSUN 2300 « 200» 8.3 1018m» 250 «pc»Accept answer from interval 240 to 270 pc If unit omitted, assume pc.Watch for ECF from mp1Examiners report[N/A][3 marks]

14b.Explain why Cephids are used as standard candles.[2 marks]MarkschemeCepheids have a definite/known «average» luminositywhich is determined from «measurement of» periodORdetermined from period-luminosity graphCepheids can be used to estimate the distance of galaxiesDo not accept brightness for luminosity.Examiners report[N/A]The peak wavelength of the cosmic microwave background (CMB) radiation spectrum corresponds to a temperature of 2.76 K.15a.Identify two other characteristics of the CMB radiation that are predicted from the Hot Big Bang theory.Markschemeisotropic/appears the same from every viewing anglehomogenous/same throughout the universeblack-body radiationExaminers report[N/A][2 marks]

15b.A spectral line in the hydrogen spectrum measured in the laboratory today has a wavelength of 21cm. Since the emission of the[1 mark]CMB radiation, the cosmic scale factor has changed by a factor of 1100. Determine the wavelength of the 21cm spectral line in the CMBradiation when it is observed today.Markscheme23 100 «cm»OR231 «m»Examiners report[N/A]16a.Describe how some white dwarf stars become type Ia supernovae.Markschemewhite dwarf must have companion «in binary system»white dwarf gains material «from companion»when dwarf reaches and exceeds the Chandrasekhar limit/1.4 MSUN supernova can occurExaminers report[N/A][3 marks]

16b.Hence, explain why a type Ia supernova is used as a standard candle.[2 marks]Markschemea standard candle represents a «stellar object» with a known luminositythis supernova occurs at an certain/known/exact mass so luminosity/energy released is also knownOWTTEMP1 for indication of known luminosity, MP2 for any relevant supportive argument.Examiners report[N/A]16c.Explain how the observation of type Ia supernovae led to the hypothesis that dark energy exists.Markschemedistant supernovae were dimmer/further away than expectedhence universe is acceleratingdark energy «is a hypothesis to» explain this[3 marks]

Examiners report[N/A]The graph shows the observed orbital velocities of stars in a galaxy against their distance from the centre of the galaxy. The core of thegalaxy has a radius of 4.0 kpc.17a.Calculate the rotation velocity of stars 4.0 kpc from the centre of the galaxy. The average density of the galaxy is 5.0 10 –21 kg m –[2 marks]3.Markschemev « 4πGρr»3 43 π 6.67 10 11 5.0 10 21 (4000 3.1 1016)v is about 146000 «m s–1» or 146 «km s–1»Accept answer in the range of 140000 to 160000 «m s –1».Examiners report[N/A]

17b.[2 marks]Explain why the rotation curves are evidence for the existence of dark matter.Markschemerotation curves/velocity of stars were expected to decrease outside core of galaxyflat curve suggests existence of matter/mass that cannot be seen – now called dark matterExaminers report[N/A]The Sun has a radius of 7.0 10 8m and is a distance 1.5 10 11 m from Earth. The surface temperature of the Sun is 5800 K.18a.Show that the intensity of the solar radiation incident on the upper atmosphere of the Earth is approximately 1400Wm 2 .MarkschemeI σAT 44πd22 5.67 10 8 (7.0 108) 58004(1.5 1011)22OR5.67 10 8 4π (7.0 108) 5800424π (1.5 1011)I 1397 Wm 2In this question we must see 4SF to award MP3.Allow candidate to add radius of Sun to Earth–Sun distance. Yields 1386 Wm –2.Examiners report[N/A] 2[2 marks]

218b. The albedo of the atmosphere is 0.30. Deduce that the average intensity over the entire surface of the Earth is 245Wm .[2 marks]Markscheme«transmitted intensity » 0.70 1400 « 980Wm–2» πR24πR2 980Wm 2245Wm–2Examiners report[N/A]18c.Estimate the average surface temperature of the Earth.[2 marks]Markscheme5.67 10–8 T 4 245T 256KExaminers report[N/A]19a.Describe one key characteristic of a nebula.Markschememade of dust and/or gasformed from supernovacan form new starssome radiate light from enclosed starssome absorb light from distant stars[1 mark]

Examiners report[N/A] 319b. Beta Centauri is a star in the southern skies with a parallax angle of 8.32 10 arc-seconds. Calculate, in metres, the distance of [2 marks]this star from Earth.Markschemed 18.32 10 3OR 120pc120 3.26 9.46 1015 3.70 1018mAnswer must be in metres, watch for POT.Examiners report[N/A]19c.Outline why astrophysicists use non-SI units for the measurement of astronomical distance.[1 mark]Markschemedistances are so big/large OR to avoid using large powers of 10 OR they are based on convenient definitionsExaminers report[N/A]Aldebaran is a red giant star with a peak wavelength of 740 nm and a mass of 1.7 solar masses.20a.Show that the surface temperature of Aldebaran is about 4000 K.[2 marks]

MarkschemeT 2.9 10 3740 10 93900 KAnswer must be to at least 2SF.Examiners report[N/A]20b.The radius of Aldebaran is 3.1 10 10 m. Determine the luminosity of Aldebaran.[2 marks]MarkschemeL 5.67 10-8 4π (3.1 1010)2 40004 1.8 1029WAccept use of 3900 4 to give 1.6 10 29W.Examiners report[N/A]20c.Outline how the light from Aldebaran gives evidence of its composition.Markschemeabsorption lines in spectraare specific to particular elementsAccept “emission lines in spectra”.Examiners report[N/A][2 marks]

20d. Identify the element that is fusing in Aldebaran’s core at this stage in its evolution.[1 mark]MarkschemeheliumExaminers report[N/A]20e.Predict the likely future evolution of Aldebaran.[3 marks]Markschemehelium flashexpansion of outer shell OR surface temperature increaseplanetary nebula phaseonly the core remainsif below 1.4M S/Chandrasekhar limit then white dwarfExaminers report[N/A]21a.Light reaching Earth from quasar 3C273 has z 0.16.(i) Outline what is meant by z.(ii) Calculate the ratio of the size of the universe when the light was emitted by the quasar to the present size of the universe.(iii) Calculate the distance of 3C273 from Earth using Ho 68kms 1 Mpc 1 .[4 marks]

Markscheme(i)z Δλλowhere Δλ is the redshift of a wavelength and λ0 is the wavelength measured at rest on Earth OR it is a measure ofcosmological redshiftDo not allow just “redshift”.(ii) z RRo 1, RRo 1z 1 so RRo 11.16 0.86Do not accept answer 1.16.(iii) v zc 0.16 3 108 4.8 104kms-1d vHo 4.8 10468 706Mpc OR 2.2 1025mExaminers report[N/A]21b.Explain how cosmic microwave background (CMB) radiation provides support for the Hot Big Bang model.Markschemeas the universe expanded it cooled/wavelength increasedthe temperature dropped to the present approximate 3K OR wavelength stretched to the present approximate 1mmValue is required for MP2.Examiners report[N/A][2 marks]

This question is in two parts. Part 1 is about energy resources. Part 2 is about thermal physics.Part 1 Energy resourcesElectricity can be generated using nuclear fission, by burning fossil fuels or using pump storage hydroelectric schemes.22a.Outline which of the three generation methods above is renewable.[2 marks]Markschemepump storage;renewable as can be replaced in short time scale / storage water can be pumped back up to fall again / source will not run out; } (do notaccept “because water is used”)Examiners report[N/A]In a nuclear reactor, outline the purpose of the22b.heat exchanger.Markscheme(allows coolant to) transfer thermal/heat (energy) from the reactor/(nuclear) reaction to the water/steam;Must see reference to transfer – “cooling reactor/heating up water” is not enough.Examiners report[N/A][1 mark]

22c.moderator.[2 marks]Markschemereduces speed/kinetic energy of neutrons; (do not allow “particles”)improves likelihood of fission occurring/U-235 capturing neutrons;Examiners report[N/A]Fission of one uranium-235 nucleus releases 203 MeV.22d.Determine the maximum amount of energy, in joule, released by 1.0 g of uranium-235 as a result of fission.Markscheme(203 MeV is equivalent to) 3.25 10 11 (J);6.02 1023 nuclei have a mass of 235 (g) / evaluates number of nuclei;(2.56 1021 nuclei produce) 8.32 1010 (J) / multiplies two previous answers;Award [3] for bald correct answer.Award [1] for correct conversion from eV to J even if rest is incorrect.Examiners report[N/A][3 marks]

22e.Describe the main principles of the operation of a pump storage hydroelectric scheme.[3 marks]Markschemewater flows between water masses/reservoirs at different levels;flow of water drives turbine/generator to produce electricity;at off peak times the electricity produced is used to raise water from lower to higher reservoir;Examiners report[N/A]22f.A hydroelectric scheme has an efficiency of 92%. Water stored in the dam falls through an average height of 57 m. Determine the [3 marks]rate of flow of water, in kg s 1, required to generate an electrical output power of 4.5 MW.Markschemeuse ofmt mgh;t4.5 106;0.92 9.81 578.7 103(t is usually ignored, assume 1 s if not seen)(kg s 1);Award [3] for a bald correct answer.Examiners report[N/A]

This question is in two parts. Part 1 is about energy resources. Part 2 is about thermal physics.Part 2 Thermal physics22g.Distinguish between specific heat capacity and specific latent heat.[2 marks]Markschemespecific heat capacity is/refers to energy required to change the temperature (without changing state);specific latent heat is energy required to change the state/phase without changing the temperature;If definitions are given they must include salient points given above.Examiners reportThe essential difference between specific heat capacity and specific latent heat is that the former refers to a change of temperaturewithout changing state; whereas the latter refers to a change of state without changing temperature. Most candidates just wrotedefinitions which they had learnt by rote – and omitted the constant temperature for a substance changing state.

A mass of 0.22 kg of lead spheres is placed in a well-insulated tube. The tube is turned upside down several times so that the spheresfall through an average height of 0.45 m each time the tube is turned. The temperature of the spheres is found to increase by 8 C.22h.Discuss the changes to the energy of the lead spheres.[2 marks]Markschemegravitational potential energy kinetic energy;kinetic energy internal energy/thermal energy/heat energy;Do not allow heat.Two separate energy changes must be explicit.Examiners reportThis is a question specifically about energy changes so candidates are expected to use accurate language and spell out the changesone by one. Common mistakes were omitting the “gravitational” in gravitational potential energy; referring to “heat” rather than thermalenergy; and saying that gravitational potential energy changed to thermal and kinetic energy as if it were a single process.

22i.The specific heat capacity of lead is 1.3 102 J kg 1K 1. Deduce the number of times that the tube is turned upside down.[4 marks]Markschemeuse of mcΔT ;use of n mgΔh;equating (cΔT ngΔh);236 or 240;oruse of ΔU mcΔT ;(0.22 1.3 102 8 ) 229 (J);n mgΔh 229 (J);n 2290.22 9.81 0.45 236 or 240; } (allow if answer is rounded up to give complete number of inversions)Award [4] for a bald correct answer.Examiners reportThis was generally well done. There were four marks and the question asks the candidates to “deduce” so it is essential that theargument is transparent. The examiner cannot be expected to search through a mass of numbers in order to carry forward an error.

This question is about the Hertzsprung–Russell (HR) diagram and the Sun.A Hertzsprung–Russell (HR) diagram is shown.23a.The following data are given for the Sun and a star Vega.[3 marks] 3.85 1026 WLuminosity of the Sun 1.54 1028 WLuminosity of VegaSurface temperature of the SunSurface temperature of Vega 5800 K 9600 KDetermine, using the data, the radius of Vega in terms of solar radii.MarkschemeLVLS (1.54 10283.85 1026σAV[TV]4σAS[TS]4 [rV]2[rS]2 ) 28σ[rS]2[TS]49600458004rV ( 1.54 1026 3.85 10σ[rV]2[TV]4;;5800496004rS ) 2.3 rS;Do not award third marking point if radius of the Sun is lost.Examiners reportcandidates notably addressed absolute magnitude without referring to apparent magnitude as the question asked. Well-preparedcandidates (both HL and SL) only had a problem with the part related to the use of a non-linear temperature scale. Average preparedcandidates displayed difficulty in the experimental measurement of the temperature of the distant star and also with details of nuclearprocesses occurring in the Sun during transformation to a red giant.

23b.Outline how observers on Earth can determine experimentally the temperature of a distant star.[3 marks]Markschemeobtain the spectrum of the star;measure the position of the wavelength corresponding to maximum intensity;use Wien’s law (to determine temperature); } (allow quotation of Wien’s equation if symbols defined)Award [3 max] for referring to identification of temperature via different ionizations of different elements.Examiners reportcandidates notably addressed absolute magnitude without referring to apparent magnitude as the question asked. Well-preparedcandidates (both HL and SL) only had a problem with the part related to the use of a non-linear temperature scale. Average preparedcandidates displayed difficulty in the experimental measurement of the temperature of the distant star and also with details of nuclearprocesses occurring in the Sun during transformation to a red giant.This question is about the Hertzsprung–Russell (HR) diagram and the Sun.A Hertzsprung–Russell (HR) diagram is shown.The Sun will remain on the main sequence of the HR diagram for about another five billion years. After this time it will become a redgiant, following the evolutionary path shown in the diagram.

24a.Outline why the Sun will leave the main sequence, and describe the nuclear processes that occur as it becomes a red giant.[4 marks]Markschemeinsufficient hydrogen (to continue fusion);star collapses (under gravity);temperature increases;initiated fusion of helium, (energy released causes) rapid expansion of star;Examiners reportWell-prepared candidates (both HL and SL) only had a problem with the part related to the use of a non-linear temperature scale.Average prepared candidates displayed difficulty in the experimental measurement of the temperature of the distant star and also withdetails of nuclear processes occurring in the Sun during transformation to a red giant.

24b.Describe two physical changes that the Sun will undergo as it enters the red giant stage.[2 marks]Markschemerapid expansion / increase of size;decrease in temperature / cooler stars appear red in colour / increase of luminosity;Examiners reportWell-prepared candidates (both HL and SL) only had a problem with the part related to the use of a non-linear temperature scale.Average prepared candidates displayed difficulty in the experimental measurement of the temperature of the distant star and also withdetails of nuclear processes occurring in the Sun during transformation to a red giant.This question is about cosmic microwave background (CMB) radiation.A line in the hydrogen spectrum is measured in the laboratory to have a wavelength of 656 nm. The same line from a distant galaxy ismeasured to have a wavelength of 730 nm. Assuming that the Hubble constant H0 is 69.3 km s 1Mpc 1,25a.calculate the distance of this galaxy from Earth.Markscheme( Δλλ d vH0vc 10 74 ) v ( 3.00 656 ) 3.38 107 (ms 1);83.38 10469.3 488 Mpc;[2 marks]

Examiners reportWell done by candidates, weaker candidates did not write their ideas clearly enough in (a)(ii). Part (b) was also quite well done, but onlybetter candidates mentioned uncertainty in measurement of distances to galaxies.25b. di

2b.The hydroelectric system has four 250 MW generators. The specific energy available from the water is 2.7 kJ kg . Determine the[2 marks] maximum time for which the hydroelectric system can maintain full outp