physics higher level paper 3 - ib documents past papers - year/2009...8809-6503 36 pages...

8809-6503 36 pages

N09/4/PHYSI/HP3/ENG/TZ0/XX+

Tuesday 17 November 2009 (morning)

Physicshigher levelPaPer 3

INSTRUCTIONS TO CANDIDATES

• Write your session number in the boxes above.• Do not open this examination paper until instructed to do so.• Answer all of the questions from two of the Options in the spaces provided.• At the end of the examination, indicate the letters of the Options answered in the

candidate box on your cover sheet.

1 hour 15 minutes

Candidate session number

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Option E — Astrophysics

E1. ThisquestionisaboutthestarBecruxandCepheidvariables.

(a) Describewhat ismeantby

(i) theapparentmagnitudescale.

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(ii) absolutemagnitude.

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(b) BecruxisamainsequencestarandisoneofthestarsthatmakeuptheSouthernCross.ThefollowingdataareavailableforBecrux.

Apparentmagnitude =1.25Absolutemagnitude =–3.92Apparentbrightness =7.00×10–12bSun

bSunistheapparentbrightnessoftheSun.Usethedatatodeducethatthe

(i) distanceofBecruxfromEarthis108pc.

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(ii) luminosity of Becrux is 3.43×103LSun where LSun is the luminosity of the Sun.(1pc=2.05×105AU)

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(This question continues on the following page)

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(Question E1 continued)

(c) Giventhatthepowerinthemass–luminosityrelationshipis3.5,showthatthemassofBecruzisabout10MSunwhereMSunisthemassoftheSun.

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(d) StatethedifferencesbetweentheeventualfateoftheSunandBecruxaftertheyleavethemainsequence.

Sun: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Becrux: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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(e) BecruxisaspectralclassBstar.OntheaxesoftheHertzsprung–Russelldiagram

(i) label,withtheletterB,theapproximatepositionofBecrux. [1]

(ii) drawtheevolutionarypathofBecruxafteritleavesthemainsequence. [1]

absolutemagnitude

40 20 10 5 2.5temperature/K×103

(f) OntheaxesoftheHertzsprung–Russelldiagramabove,drawtheapproximateregioninwhichCepheidvariablestarsarelocated. [1]

(g) StatethereasonfortheperiodicvariationinluminosityofaCepheidvariable.

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(h) State the two quantities that need to bemeasured in order to use aCepheid variableas a “standard candle” to determine the distance to the galaxy inwhich theCepheidis located.

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E2. Thisquestionisaboutcosmology.

(a) ThediagrambelowrepresentsasphericalregionofspacebasedonNewton’smodeloftheuniverse.Earthisatthecentreoftheregion.ThedarklinerepresentsaverythinsphericalshellofspacedistanceRfromEarth.

WithreferencetothediagramandNewton’smodeloftheuniverseexplainquantitativelyOlbers’paradox.

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(b) TheBigBangtheoryprovidesaresolutiontoOlbers’paradox.Twopiecesofevidencetosupportthetheoryaretheexistenceofcosmicmicrowavebackgroundradiation(CMB)andthered-shiftedlightfromdistantgalaxies.

(i) OutlinehowCMBisconsistentwiththeBigBangtheory.

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(ii) Thefollowingdataareavailableforthered-shiftoflightfromadistantgalaxy.

Wavelengthoflightfromgalaxy =130nm Wavelengthmeasuredinlaboratory =120nm Hubbleconstant =74kms–1Mpc–1

UsethedatatodeterminethedistanceofthegalaxyfromEarth.

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Option F — Communications

F1. Thisquestionisaboutmodulation.

(a) Distinguishbetweenasignalwaveandcarrierwave.

Signalwave: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Carrierwave: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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(b) With reference to a carrier wave, distinguish between amplitude modulation andfrequencymodulation.

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(c) Thediagramisasketchofanaudiofrequencysignal.

Aradiowaveisfrequencymodulatedbytheaudiofrequencysignal.Statethechanges,ifany, in thefrequencyof themodulatedsignal in thefollowing time intervals.

A→B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B→C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C→D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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(Question F1 continued)

(d) For a particular frequency modulated carrier wave, the maximum frequency occursevery 1.2ms. There are 2.2×105 oscillations between each maximum frequency.Determinethefrequencyofthe

(i) signalwave.

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(ii) carrierwave.

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F2. Thisquestionisaboutdigitalsignals.

(a) Thegraphshowsthevariationwithtimeofananaloguesignal.

outputsignal/V

00 1 2 3 4 5 6 7 8 9

time/×100µs

In order to convert the analogue signal into a 3-bit digital signal it is sampledevery 100µs. The possible output voltages of the analogue to digital converter thatis used are shown below.

Analogue signal / V Binary output

0–<0.5 000

0.5–<1.0 001

1.0–<1.5 010

1.5–<2.0 011

2.0–<2.5 100

2.5–<3.0 101

3.0–<3.5 110

3.5–<4.0 111

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Determine,explainingyouranswer,the

(i) bit-rate(datatransferrate).

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(ii) digitaloutputofthesignalforthesixthsamplestartingfromt=0s.

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(b) Explain the effects that increasing the sampling frequency and number of bits willhaveon thequalityof therepresentationof theanaloguesignal.

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(c) Thedigitalsignal in(a) is tobe transmittedalonganopticfibre thathasapower lossof2.0dBkm–1.

(i) State,inwatts,howpowerlossisdefinedonthedecibelscale.

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(ii) Calculate the distance travelled by the signal that will result in a power lossof75%.

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(d) As a result of noise in electric circuits, digital pulses can often lose their shape andhence distort the information that they carry. The pulses can be re-shaped using acircuitcalledaSchmitttrigger.ThediagramshowsaSchmitttriggerthatincorporatesanoperationalamplifier.

1.0V –

10kΩ 50kΩ

V0=–6.0V

(i) Statetwoessentialpropertiesofanoperationalamplifier.

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(ii) In the situation shown the output voltageV0 of the amplifier is at itsminimumvalueof–6.0V. Thevoltageat thenon-invertinginput to theamplifier isequalto1.0Vandattheinvertinginputit isVX. Theoutputvoltagewillswitchtoitsmaximum value +6.0V if the voltageVX just exceeds +1.0V. Determine theminimumvoltageVinthatwillresultinanoutputvoltageof+6.0V.

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F3. Outlineonemoralor ethical issue andone environmental issue that arise from the use ofmobilephones.

Moralorethicalissue: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Environmentalissue: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Option G — Electromagnetic waves

G1. Thisquestionisabouttheelectromagneticspectrum.

(a) Thetransmissionfromatelevisionstationhasafrequencyof100MHz.Itisknownthattheelectromagneticwavesassociatedwith this transmissionproduceamagneticfield.Stateonereasonwhyacompassdoesnotrespondtothisfield.

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(b) Itisproposedthatinsteadofusingradiowavesfortelevisiontransmissiongamma-raysareused.

(i) Stateatypicalgamma-rayfrequency.

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(ii) Suggestonedisadvantageofusinggamma-raysfortelevisiontransmission.

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G2. Thisquestionisaboutchromaticaberrationandalens.

(a) Twoparallelraysofwhitelightareincidentonaconvexlens.

whitelight

principalaxis

whitelight

convexlens

Onthediagram,afterrefractioninthelens,drawthepathsfortheraysofredlightandbluelightpresentinthewhitelight. [2]

(b) Useyourdiagramin(a)toexplainchromaticaberration.

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(c) Stateonewayinwhichchromaticaberrationmaybereduced.

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(Question G2 continued)

(d) Anobject isplaced5.0cmfrom the lensand is illuminatedwith red light. The focallengthofthelensforredlightis8.0cm.Calculatethe

(i) positionoftheimage.

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(ii) linearmagnification.

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G3. Thisquestionisabouttwo-sourceinterference.

(a) Light from a laser is incident on two identical parallel slits whose width is smallcompared to theirseparation.

doubleslit screen

0.50mm

(diagram not to scale)

Afterpassingthroughtheslits the light is incidentonascreen. Theseparationof theslitsis0.50mmandthedistancebetweenslitsandscreenis2.0m.Thewavelengthofthe light is700nm.

(i) Statewhyalaserisusedasthelightsource.

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(ii) Determinetheseparationofpointsofmaximumintensityonthescreen.

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(iii) Describetheeffectthatincreasingthenumberofslitswouldhaveontheintensitypatternonthescreen.

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(Question G3 continued)

(b) Theslitsin(a)arereplacedwithadiffractiongratingthathas3.5×105linespermetre.Determine the number of positions of maximum intensity that will be observed onthe screen.

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G4. Thisquestionisaboutthinfilminterference.

A transparent thinfilm is sometimesused tocoat spectacle lensesas shown in thediagrambelow.

air,refractive coating,refractiveindex=1.00 index=1.30

glasslens,refractive index=1.53

incominglight

boundaryA boundaryB

(a) Statethephasechangewhichoccurstolightthat

(i) istransmittedatboundaryAintothefilm.

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(ii) isreflectedatboundaryB.

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(iii) istransmittedatboundaryAfromthefilmintotheair.

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(b) Light ofwavelength 570nm in air is incident on the coating. Determine the smallestthicknessofthecoatingrequiredsothatthereflectionisminimizedfornormalincidence.

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G5. ThisquestionisaboutX-rays.

(a) Thediagrambelowisasketch thatshows theX-rayspectraproducedbyelectronsofenergy25keVandofenergy20keVstrikingamolybdenumtarget.

X-rayintensity

wavelength

Suggestwhynocharacteristicspectraareproducedbythe20keVelectrons.

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(b) Show that theminimumX-raywavelengthproducedby the25keVelectrons in (a) is0.050nm.

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(c) ThewavelengthsoftheX-raysin(a)aremeasuredbyscatteringthemfromthesurfaceofacrystalthathasacubiclatticestructure.Thespacingofthelatticeionsis0.28nm.CalculatethewavelengthoftheX-raysthatproduceafirstorderBraggangleof21.

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Option H — Relativity

H1. Thisquestionisaboutspecialrelativity.

(a) Statewhatismeantbyaninertialframeofreference.

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(b) AibheisatrestinaninertialframeofreferenceAandEuanisatrestinaninertialframeofreferenceB.Bismovinginthex-direction,withspeedv,relativetoA.ThetableTisatrestwithrespecttoAibhe.

Aibhe Euan

AibhemeasuresthelengthofTtobe1.5mandEuanmeasuresittobe1.2m.

(i) ExplainwhichobservermeasurestheproperlengthofT.

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(ii) Determinethespeedv.

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(Question H1 continued)

(c) TwoinsectslandatthesamepointonT.AccordingtoaclockatrestwithrespecttoAibhe,oneoftheinsectslands2.4secondsaftertheother.Calculate,accordingtoEuan,thetimeintervalbetweenthelandingsofeachinsect.

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(d) Twoother insects landateitherendof the table. These twoeventsmayoccur at thesame timeasmeasuredbyoneof theobservers (AibheorEuan)butnot to theother.Outline,withreference to thepostulatesof relativity,why thesetimesdiffer.

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(e) Muons are produced in the upper atmosphere by the bombardment of cosmic rays.Themuonstravelclosetothespeedoflightandareunstable.Theyhaveaveryshorthalf-life as measured in a muon’s frameof reference. Explainhow thedetectionofmuonsatthesurfaceoftheEarthprovidesevidenceforthespecialtheoryofrelativity.

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H2. Thisquestionisaboutrelativisticenergyandmomentum.

(a) ParticleAisatrestwithrespecttoanobserver.AnotheridenticalparticleBismovingwithrespecttotheobserver.DistinguishbetweenthetotalenergyofparticleAandthetotalenergyofparticleBasmeasuredbytheobserver.

ParticleA: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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ParticleB: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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(b) Twoprotonsaretravellingtowardseachotheralongthesamestraightlineinavacuum.

0.960c 0.960c

Thespeedofeachproton,asmeasuredinthelaboratoryframeofreference,is0.960c.

(i) Calculatetherelativespeedofoneprotonwithrespecttotheotherproton.

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(ii) Showthatthetotalenergyofoneoftheprotons,accordingtoanobserveratrestinthelaboratory,is3.35GeV.

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(Question H2 continued)

(c) Thecollisionofthetwoprotonsresultsinthefollowingreaction

p p p n+ + + 0 +π+ = + +

whereπ+isaparticlecalledapionandhasarestmassof140MeVc–2.Thetotalenergyofthepionis502MeV.Determine,accordingtoanobserveratrestinthelaboratory,the

(i) totalenergyoftheprotonformedplusthetotalenergyoftheneutronformedbythecollision.

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(ii) momentumofthepion.

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(d) Thediagramshowsthepathsfollowedbytheneutronandpionin(c).

Thedotted line shows thepathof theoriginalcollisionof theprotons in (b). On thediagram,drawthedirectionoftheprotonformedinthecollision. [1]

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H3. Thisquestionisaboutspacetimeandblackholes.

(a) Statewhatismeantbytheconceptofspacetime.

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(b) Outline,with reference to themotion of photons in spacetime,what ismeant by theSchwarzschildradius.

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(c) The mass of the Sun is about 2×1030kg. Show that, if the Sun were to become ablackhole, its radiuswouldbeabout3km.

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Option I — Medical physics

I1. Thisquestionisabouthearing.

(a) Outlinehowvariationsinsoundpressureintheairareamplifiedinthemiddleear.

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(b) AsoundofintensityI=2.0×10–6Wm–2isincidentontheear.TheloudnessdetectedbytheearduetothissoundisL.

(i) Suggestwhytheloudnessofasoundofintensity4.0×10–6Wm–2detectedbytheearisnot2L.

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(ii) UsethedecibelscaletodeterminetowhatvaluetheintensityImustbeincreasedinorder that the loudnessdetectedby theear is2L.

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(iii) Inlightofyouranswerto(b)(ii),outlinepossibleeffectsoflong-termexposureofsoundatthisloudness.

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I2. ThisquestionisabouttheuseofX-raysandtheuseoflaserlightinclinicaldiagnosis.

(a) A parallel beam of X-rays of intensity I0 is incident on a block of material ofthickness x.

The intensityof theX-raysemerging from theblock is I and thehalf-value thicknessof thematerial is x1

Using theaxesbelow, sketchagraphshowing fourdatapoints, to showhow Ivarieswithxforblocksofthesamematerialbutdifferingthicknesses.ThepositionofI0andof x1

2areshownmarkedon therespectiveaxes. [2]

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(Question I2 continued)

(b) Theattenuationcoefficientforboneisµbandfortissueµt.Thetableshowstheratioµµb

forX-raysofthreedifferentphotonenergies.

Photon energy / MeVµµb

0.08 3.00.01 8.01.00 1.0

(i) ExplainwhyX-raysofphotonenergy0.01MeVarethemostsuitableforuseindetectingabonefracture.

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(ii) The attenuation coefficient of bone for X-rays with photon energy 0.01MeVis0.60cm–1. X-raysof this energyused to imagea suspected legbone fracturepassthroughbonethicknessof6.0cmandtissuethickness9.6cm.Determinethefollowingratio.

finalintensityofx-raysafterpassingthroughbonefinalintensityofx-raysafterpassingthroughtissue

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(Question I2 continued)

(c) RegionsoftheelectromagneticspectrumotherthantheX-rayregion,canalsobeusedinclinicaldiagnosis.Inthisrespect,lightfromtwolasersisusedinpulseoximetry.

(i) Identifythetworegionsoftheelectromagneticspectruminwhichthewavelengthofthelightemittedbyeachlaserisfound.

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(ii) Outline how the laser light is used to measure hemoglobin saturation in theblood.

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I3. Thisquestionisaboutradioactiveisotopesusedastracers.

(a) Definebiological half-lifeandphysical half-life.

Biologicalhalf-life: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Physicalhalf-life: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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(b) Radioactive isotopes can be used as “tracers” in order to study certain physiologicalprocessesinthebody.State,fortheseisotopes,one reasonwhy

(i) itisimportantthatsuchisotopeshaveashortbiologicalhalf-life.

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(ii) thephysicalhalf-lifeisgreaterthanthebiologicalhalf-life.

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(c) The physical half-life of a particular isotope used as a tracer is 4.0 days and itsbiologicalhalf-lifeis2.0days.Calculatethepercentagedecreaseintheactivityoftheisotope4.0daysafter it is introduced into thebody.

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Option J — Particle physics

J1. Thisquestionisaboutfermionsandbosons.

(a) Distinguish, with reference to the Pauli exclusion principle, the difference betweenfermionsandbosons.

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(b) Identifythebosonthatmediatesthe

(i) electromagneticinteractionbetweenelectrons.

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(ii) stronginteractionbetweennucleons.

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(c) Thestronginteractionbetweennucleonshasarangeoftheorderof10–15m.Showthatthemassofthebosonin(b)(ii)isabout100MeVc–2.

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(Question J1 continued)

(d) TheFeynmandiagramshowsthedecayofamesonintoananti-muonandaneutrino.

(i) Statethechargeonthemesonandontheanti-muonandexplainyouranswer.

Meson: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Anti-muon: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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(ii) IdentifytheparticlelabelledX.

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J2. Thisquestionisaboutparticleaccelerators.

(a) Differenttypesofparticlesmaybeproducedbythecollisionofacceleratedprotonswithstationaryprotons.Explainwhytheacceleratedprotonsmusthavehighenergy.

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(b) Thediagramshowssomeofthefeaturesofalinearparticleacceleratorusedtoaccelerateprotons.

anodes anodes

protonbeam

1 2 3 4

protonsource vacuumchamber

The vacuum chamber contains a succession of cylindrical anodes ofwhich only fourareshown,anodes1,2,3and4.

(i) Statewhytheprotonsarenotacceleratedwhilsttravellinginsidetheanodes.

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(ii) Describe themechanismbywhichtheprotonsareacceleratedbytheanodes.

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(Question J2 continued)

(c) The minimum energy required to produce a K– meson in the collision between ahigh energy proton and a stationary proton is 1890MeV. Determine the minimumkinetic energy EK that the high energy proton must have in order to produce aK– meson.

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(d) In particle accelerators such as synchrotrons, it can be arranged to have collisionsbetweenprotonsandantiprotonstravellinginoppositedirections.Stateoneadvantageandonedisadvantageofthisarrangementintermsofparticleproductionascomparedwith thatdescribed in (c).

Advantage: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Disadvantage:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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J3. Thisquestionisaboutquarks.

(a) ThestrangenessoftheΩ–hadronis–3anditsspinis+ 32.

(i) ExplainhowitisknownthatthequarkstructureoftheΩ–hadronissss.

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(ii) Explain,withreferencetothequarkstructureoftheΩ–hadron,whytheconceptofthecolourofquarkswasintroduced.

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(iii) StatewhytheΩ–hadronhasnocolour.

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(b) Aswell as providing evidence for the existence of quarks, deep inelastic scatteringexperimentsalsoprovideevidencefor theexistenceofgluons.

(i) Statewhatismeantbydeepinelasticscattering.

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(ii) Outlinehowtheexperimentsprovideevidencefortheexistenceofgluons.

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3 6 3 6

physics higher level paper 3 - ib documents past papers - year/2009...8809-6503 36 pages...

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