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1. Force per unit positive charge B1[1]

2. (i) Suitable recognisable pattern around (not just between) the charges B1Quality mark: symmetry spacing lines joined to charges B1!onsistent arrows toward B on some lines B1

(ii) "se o# $ % (1&'*)Q&r + !1Sum o# two e,ual terms$ % + - . - 1*. - 1/0 - 1* 1. & (+/* - 1* 1*)+ !1$ % 2/+ - 1*1* 3 ! 1 or 4 m 1 51

(iii) 6he separation between the ions because this has an e##ect on the

breaking #orce/ (5llow the si7e o# ionic 8charges9) B1[7]

3. (a) (i) ! p % + ' % 0 ;F 51

(ii) 1/! % 1&+ < !1

!s % '&= %1/== ;F 51 (b) (i) 0/* 4 51

(ii) Q % ! p4 !1

% 0 - 0 % =0 ;! 51

(c) $ % > !s4 + !1% +' - 1* 0 51

(d) (i) 6he capacitors discharge through the voltmeter/ B1

(ii) V %V *e t &CR

1&' %e t &(0-1+) !1ln ' %t & 2+ !1t % 2+ ln ' ? 1** s 51

[12]

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4. 5ny seven #rom:@ A particle scatteringsuitable diagram with source #oil moveable detector + or more trajectories shownvacuummost particles have little i# any de#lectionlarge de#lection o# very #ewre#erence to !oulomb9s law &elastic scatteringalphas repelled by nucleus (positive charges)monoenergetic

C electron scatteringDigh energy diagram with source sample moveable detector & #ilm4acuum$lectron accelerator or other detailEost have 7ero de#lection!haracteristic angular distribution with minimumEinimum not 7ero

e Broglie wavelengthGavelength comparable to nuclear si7e hence high energy B1 - 2

!learly shows how evidence #or the si7e o# the nucleus #ollows #romwhat is described/ (1)

[8]

5. (a) De nucleus a #ew cm & = to 1* cm5bout 1 m & */= to + m & several m 1 to 1* mm 5l & 1 mm Hb

(high energy) eAm radiation 1 to 1* cm o# Hb & several m o# concreteonly + correct 1 mark only ' correct + marks B= (b) Source absorbers placed in #ront o# detector on diagram B1

$Iplanation o# how results identi#y the source(+ marks possible) B+5llowance #or background (maI +)(allow #or distance eIpt to a maI +)

[6]

6. (a) (i) #luI % B - 5 (normal to B) with symbols eIplained B1

(ii) linkage % 3 - #luI B1

5 % x+ so linkage % 3B x+ B1

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(b) (i) Statement o# Faraday9s law or indicatione/g/ 4 % d(3B x+) & dt #rom (a)(ii)4 % 3B x+d x&dt or 4 % 3B xv & argue area swept out per second as xv B14 % 1+J* - */*=+ - */*+ - */1 B1

% */*K or K* m4 B15* (ii) e,ual positive and negative regions B1

e,ual positive and negative values o# 8maIima9 labelled on yAaIis B1value changes within correct time 7ones t % */+ to */' */0 to */K s B18s,uare pulse9 shape B1

sinusoidal graphs score zero marks[10]

7. "niverse is isotropic &same in all directions B1

Domogeneous & evenly distributed B1[2]

8. 5ny #our #rom:"ni#orm intensity in all directions & everywhereStructure in background intensity & ripplesHroduced when matter and radiation decoupled

riginally gamma radiation(gamma) redAshi#ted to microwave & originally higher energy$vidence that universe began with big bang6emperature corresponds to +/2 L & =L & that predicted by big bang model B1 - 'Mink between evidence and eIplanation/ (1)

[5]

9. 5ny two #rom: 3o eIperimental evidence & no physical evidenceState o# matter unknown & laws o# physics unknown$nergies unreproducible & re#/ to very high temperature B1 - +

[2]

10. pen: "niverse eIpands #or all timeFlat: eIpands to a limit (but never reaches it) B1!losed: "niverse contracts & collapses back B1Ce#erence to role o# gravity & critical density B1Earks #or (a) can be gained on a labelled diagram B1

[4]

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11. Do+ % (1 - 1* +0 - K - - 0/02 - 1* 11) & = !1Do % +/=0 - 1* 1K s 1 51

[2]

12. (a) ensity (o# medium) B1Speed o# ultrasound (in medium) or any #actors that a##ect the speed o# ultrasound in the medium e/g/ Noung modulus B1

(b) (i) blood:

# % (1/J. - 1* 0 1/0= - 1* 0)+ & (1/J. - 1* 0 1/0= - 1* 0)+

# % 1/J' - 1* ' B1muscle:# % 1/2* - 1* 0 1/0= - 1* 0)+ & (1/2* - 1* 0 1/0= - 1* 0)+ B1# % '/' - 1* ' B1so the medium is muscle 51(bald muscle scores zero)

(ii) (s % u - t)

s % 1/J' - 1*= - +0/J - 1* 0 % */*'*K m !1depth % */*'*K & + % */*+* m 51

(iii) O % 1/J' - 1*= & =/J - 1*0 !1% '/' - 1* ' m 51(do not penalise the same power o# ten error in (iii) as in (ii)

[10]

13. (a) Mow energy PArays are absorbed by the skin & undesirable as can causedamage &greater ionising B1

(b) % *e ;I ln % ln * ;I !1

* % ='2 & e +J* - */*+J ln

* % ln ='2 +J* - */*+J !1

* % 1/2. - 1*J Gm + 51

(c) H % - 5

H % ='2 - - (*/*1* - 1* +)+ !1H % 1/*. - 1* = G 51

[6]

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14. (i) H % 1K - 1** & */1J !1H% 1+*** G 51

(ii) $nergy o# one electron % 1+*** & 2/J - 1*12(1/0 - 1* 1') !1> m v+ % 1/0 - 1* 1'v % 1/. - 1*K m s 1 51

(iii) tube current % 2/J - 1*12 - 1/0 - 1* 1. % */1+ 5H % 4 - % 1+*** !14 % 1+*** & */1+ % 1***** 4 or 1** k4 !1

r: 4 % G&Q % 1/0 - 1* 1' & 1/0 - 1* 1. % 1/* - 1*J (4) 51[7]

15. 5ny six #rom:method does not use ionising radiationhence no radiation ha7ard to patient or sta## gives better so#t tissue contrast than !6 scansgenerates data #rom a = volume simultaneouslyin#ormation can be displayed on a screen as a section in any directionthere are no moving mechanisms involved in EC6here is no sensation a#ter e##ects at the #ield strengths used #or routine diagnosisStrong magnetic #ield could draw steel objects into the magnetEetallic objects may become heated!ardiac pacemakers may be a##ected by the magnetic #ields!6 scanners better #or viewing bony structures B1 - 0

[6]

16. (a) Cb .'!s JJ"1'= 1 #or each error B+

(b) 4alues #rom graph: " 2/' Ee4allow 7.3 to 7.

Cb K/0 Ee4allow !." to !.# !1!s K/' Ee46otal binding energies: " +=J - 2/' (12=.)Cb .' - K/0 (K*K) B+!s 1'+ - K/' (11.=)6otal energy released % K*K 11.= 12=. 51% +0+ Ee4allow K/0 K/' 2/' % ./' Ee4 #or 1 mark only

[6]

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17. 5ny siI #rom: (two advantages and two disadvantages needed) problems with the reaction getting out o# controlmaintaining the reaction so that it proceeds continuouslydoes not produce acid rain or waste gases that could cause pollutionrisks #rom radiation: emissions due to an accident (1)Remissions #rom radioactive wastes (1)long hal# li#e o# some o# the waste products (1)other eIamples are likely to be added but should be related to Scienti#icreasons rather than political/ B1 - 0

[6]

18. (a) (i) > mv+ % 2/0 - 1* 1= to give v % (+ - 2/0 - 1* 1= &0/0 - 1* +2 (1)evidence o# calculation v % +/= - 1*1' or % 1/J+ - 1*2 (m s 1) (1) +

(ii) (electrostatic) repulsion between charged particles (1)

slows alpha and accelerates nucleus&5G (1)momentum o# system is conserved(as no eIternal #orces) (1)sum o# momenta o# alpha and nucleus must always e,ual initialmomentum o# alpha&be a constant (1)so speed o# nucleus can be calculated as momentum % mv (1) =max 3

(iii) mv % E4 or 4 % 0/0 - 1* +2 - 1/J+ - 1*2 & =/* - 1* +JR % =/= - 1*J (m s 1) +

(iv) Ft % +mv or ./* - t % + - 0/0 - 1* +2

- 1/J+ - 1*2R t % +/+ - 1*

+* (s) + gi$e (%) mark &orchange in momentum % impulseor Tmv % F(T)t

(b) (i) !oulomb #orce @ distance + or F1&F+ % r ++&r 1+ or Fr + % constant (1)giving F % '/* 3 at 1* - 1* 1'R % 1/K 3 at 1J - 1* 1' m (+) =

(ii) plot and draw correct curveec& plausible $alues in b(i) (1) 1

[13]

19. (a) (i) v % + r# % + - */*1J - J*R % '/2 (m s 1) +

(ii) a % v+&r % '/2+&*/*1JR % 1/J - 1*= (m s +) ec&(a)(i) +

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(iii) the belt tension is insu##icient to provide the centripetal #orceR (1)so the belt does not 8grip9 the pulley&does not hold the belt againstthe pulley&there is insu##icient #riction to pull&push&move the belt/ (1) +alternati$e argument the belt does not 8grip9 the pulley&there isinsu##icient #riction to pull&push&move the beltR because o# itsinertia&insu##icient to provide #orce #or acceleration o# (belt)Adrum

(b) resonance occursR when the natural #re,uency o# vibration o# the (1)

panel % rotational #re,uency o# the motor (1) + (c) (i) 1 J 1J +J (ms)

2 * 1* +* =* (ms) 1 (ii) Stating&using U % dV&dt (1)

gradient % */02 W */*J (Gb turns ms 1)R em# % gradient - 1*= (4) (+) =[12]

20. (a) Qo % !4 % 1/+ - 1* 11 - J/* - 1*=R % 0/* - 1* KR ! (=) =

(b) (i) C! % 1/+ - 1*1J - 1/+ - 1* 11 or % 1/'' - 1* ' (s) (1) 1

(ii) % 4&C % J***&1/+ - 1*1J or % '/10 - 1* 1+ (5) (1) 1

(iii) t % Qo& R % 0 - 1* K & '/10 - 1* 1+ % 1/'' - 1*' (s) +

(iv) Q % Qoe 1R Q % */=2Qo so Q lost % */0=Qo +

(c) (i) capacitors in parallel come to same voltage (1)

so Q stored @ ! o# capacitor (1)capacitors in ratio 1*= so only 1* = Q

o le#t on #ootball (1) =

(ii) 4 % Q&! % 0/* - 1* K &1/+ - 1* K or 0/* - 1* 11 &1/+ - 1* 11 or only 1* =

Q le#t so 1* = 4 le#tR % J/* (4) +[14]

21. (a) (i) e,ually spaced hori7ontal parallel lines #rom plate to plate (1)arrows towards cathode (1) +

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(ii) > mv+ % ,4R v % (+e4&m) % (+ - 1/0 - 1* 1. - 2***&./1 - 1* =1) so (1)v % '/.0 - 1*2 (m s 1) (1) +

(b) (i) arrow perpendicular to path towards centre o# arc (1) 1(ii) out o# paper&upwardsRusing Fleming9s MD rule (#or conventionalcurrent) (+) +

(iii) mv+&rR % B,vR r % mv&B, % 1.=2=1

1*0/11**/=

1*.0/'1*1/.

R% ./' - 1* +

(m) ' (c) change magnitude o# current in coils to change #ieldR (1)

change #ield to change de#lectionR (1)reverse #ield&current to change de#lection #rom up to down (1)max ' +[13]

22. (a) (i) +1+R X +(ii) +*KR @ +

(b) range&penetration&absorption eIperiment:

@ place detector very close& +cm #rom sourceR measure count rate (1)use paper screen or move back to 1* cm or moreR contrast to (1) background count level& other emissions #rom same source (1)X place detector eg 1* cm #rom sourceR measure count rate add (1)thin sheets o# 5l until count drops to very low or almost constant value (1)aliter de#lection eIperiment:needs vacuum #or @ eIperimentR (1)source #or radiation passes through region o# $A or BA #ieldR (1)de#lection o# particles detected by detector to distinguish emissionsR (1)detection method (1)max marks '

(c) (i) 5 % O3R% Om35&ER% */*11J - 0/*+ - 1*+= - 1 - 1* .&+1+ % =/+2 - 1*1*min 1 =

(ii) 61&+ % */0.=&O % 0*/= (min) (1) 1

(iii) !urve passing through (* =+) (0* 10) (1+* K)ec&s &rom (i) (ii) (1) 1

[13]

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23. o not score the same marking point twice* some marking pointsappear more than once in a di&&erent context

&ission is splitting o& nuclei:neutron is absorbed by the nucleusR (1)an (unstable) nucleus splits into two (major) #ragmentsR (1)and several&two&three neutrons (1)charges on&!oulomb repulsion pushes #ragments apartR (1)loss o# mass&increased binding energy accounts #or k/e o# #ragments&release o# energy (1)

&usion is &using o& nuclei+two light nuclei (are moving rapidly enough to overcome the!oulomb repulsion to 8touch9 and) #useR statement in brackets

gets second mark (1)has to be very hot #or nuclei to have enough kinetic energy& only (1)happens naturally inside Sun&staraccept DAbomb (1)loss o# mass&increased binding energy accounts #or release o# energy

similarity : release o# energy&total (rest) mass decrease&9increase9 in (1) binding energy &conservation o# charge&massAenergy etcdi&&erence: &cold hot&heavy light nuclei&large (+** Ee4) small (=* Ee4)energy release per reaction (1)conditions : #ission rate can be varied&controlled by absorbing and or slowing released neutrons in reactor where chain reaction isoccurring&5G (+)max ' marks#usion needs a very hot and su##iciently dense and plenti#ul plasma#or random #usion collisions to occur eg inside Sun&star&5G (+)max ' marks 2Quality o# Gritten !ommunication +

[9]

24. ,ppreciation that key is the di##erence in numbers o# atoms&nucleior e,ual number o# nucleons involvedi& nothing else is achie$ed (1)

-ull argument :+=J g o# uranium and ' g o# hydrogen&helium contain 1 mole o# (1)atoms (1)there are '/+0 moles o# uranium and +J* moles o# helium (1)so at least JK times as many energy releases in #usion (1)

ratio o# energies is only 2 #old in #avour o# uraniumthere#ore more energy release #rom 1 kg o# hydrogenany similar alternati$e argument along same lines scores marks (1)eg For " each nucleon 8provides9 */KJ Ee4 (1)For D each nucleon 8provides9 2 Ee4 (1)(5pproIimately) same number o# nucleons per kg o# " or D (1)so K/+ times as much energy #rom D 'Quality o# Gritten !ommunication +

[6]

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25. (a) Sketch to include: 4ariable #re,uency 5/! source to primary core coilsR (1)resistor connected to secondaryR (1)appropriate meters in primary and secondary circuitsR (1)Quantities kept constant: 4oltage o# sourceR (1)Hrimary current & powerR (1)Cesistance o# secondary circuit resistorR (1) 3umber o# turns in both coilsR (1)Hrocedure: "se several #re,uencies over a wide range & the range availableR (1)5t each #re,uency read metersR (1)6able headings to show: meter readingsR (1) primary power secondary power e##iciency/ (1)Yraph o# e##iciency against drawnR (1)

etails o# calculations o# power (may use meter readingsand value o# resistor)R (1)$Ipression #or e##iciency & Z e##iciency/ (1) maI 1*

(b) $nergy & heat is lost in core due to hysteresisR (1)

$nergy & heat loss in 1 cycle is proportional to area o# hysteresis loopR (1)Fre,uency increase reduces e##iciency because energy loss(per second) % #re,uency - area enclosed by hysteresis loop/ (1)$nergy loss takes place due to heat generated in core by induced &eddy currentsR (1)

nduced voltage in core increases with #re,uency & is proportionalto #re,uencyR (1)(so) induced current in core increases with #re,uency & is proportionalto #re,uency/ (1) maI '

[14]

26. acts only on nearest neighbour & when nuclei are 1 diameter apartR (1)eitherso #orce holding nucleons& neutrons together independent o# si7e o# nucleus (1)orre#erence to b so distance apart (o# nucleons) must be constantRso density o# nucleus is independent o# si7eR (1) =

[3]

27. (a) +=..+" [ +=..= 3p * 1X &* 1e $ (1)allow+=K.+" 1*n on MDS+=.

.= 3p [ +=..' Hu * 1X &* 1e $ (1) +

allow neutrino instead o# antineutrinoomits neutrino altogether A gets 1&+

(b) straight line starts #rom 7ero and reaches 1/*K - 1*1=att % 0/* - 1*J s or e,uivalent (1) 1

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(c) (i) rate o# decay increases with timeR (1) because rate o# decay increases with & is proportional tonumber o# nucleiR (1) +

(ii) (eventually) rate o# decay (o#+=..= 3p) % rate o# #ormation (1) 1

(iii) d &dt % ( ) / 0 e1uation (1) / % */0.= &2 >so % (d &dt ) & / % 1/K - 1*2 & (*/0.= & \+/*' - 1*J]) subs / (1)% J/= - 1*1+ ans / (1) =calculation o# / gets 1&=

(iv) correctly curved #rom 7ero to (J/= - 1*1+) or less (1) 1[10]

28. (a) (i) to come to rest simultaneously total mtm/ % *or 5G (1) 1

(but initial mtm/ not 7ero) (ii) initial mtm/ % =m u +m u %m u (1)

when closest mtm/ % (=m +m) $ (1) +so Jm $ %m u (and$ %u & J)

(b) (i) initial k/e/ % #inal k/e/ (gain o#) p/e/ (1) 1

(ii) k/e/ % >m $+ (1)

total k/e/ % > - =m u+ > - + m u+ (% +/Jm u+) (1)% +/J - 1/02 - 1* +2 u+ (% '/1K - 1* +2 u+) (1) =allowm % 1/00 - 1* +2 kg #or #ull credit

(iii) gain o# p/e/ % initial k/e/ #inal k/e/

)1*J/11*K/KJ'(

)1*0/1(1J1+

+1.

% '/1K - 1* +2 u+ '/1K - 1* +2 (u&J)+ (+)

1/J= - 1* 1= % '/*1 - 1* +2 u+ (1)algebrau % 0/1K - 1*0 m s 1 (1) '

omits A '/1K - 1* +2 (u&J)+ getsu % 0/ *0 - 1*0 m s 1: 1&+ 1 1 % =&'[11]

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29. (much) greater energy per unit mass o# #uel (1^)detail: greater change o# binding energy & nucleon #or #usion than #ission (1)no & little radioactive waste (1^)detail: byAproduct is (stable) helium (1)materials in _$6 structure will not become radioactive over long period (1)tritium has short hal#Ali#e (and is used anyway) (1)#uel & reactants (virtually) limitless (1^)detail: deuterium available #rom water (1)deuterium easily separated #rom normal hydrogen (1)lithium is a common material (1) but not tritium is widely availableno chance o# runaway & meltdown (1^)

detail: only minute ,uantities o# reactants (in vessel) (1)reaction ceases immediately (temperature #alls) (1)any two reasons (^) ` 1mark corresponding detail ` 1 mark % + +accept other valid answers

[4]

30. (a) +=0.+" [ 1**'* r 1=1J+6e J1*n (1) 1

(b) (i) nucleon number: no change

proton number: increases by (1) 1(ii) nucleon number: 1**

proton number: '' (1) 1 (iii) J correct points (1)

' correct arrows (1) + (iv) straight line through & close to J0 & '' o# (1) gradient +

i# curved correct sense (1) 1 (c) (i) reactant mass % ../K.J K*K u

product mass % ../K.1 02. */*** J'. (% ../K.+ ++K u) (1)mass de#ect % */**= JK* u (1) +

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(ii) Tm % */**= JK* - 1/00 - 1* +2 (% J/.'= - 1* =* kg) (1) 4 % (T)m c+

% J/.'= - 1* =* - (=/* - 1*K)+ (% J/=J - 1* 1= _) (1) +or uses 1 u % .=1 Ee4 so */**=JK % .=1 - */**=JK (% =/== Ee4) (1)% =/== - 1/0 - 1* 1= (% J/== - 1* 1+ _) (1)

(iii) (antiA)neutrino is also emitted (1)

(antiA)neutrino has (some) energy (1)recoiling (niobium) nucleus has (kinetic) energy (1) +

any '[12]

31. (a) (i) Q % 4!R G % > 4!/4 ( % > !4+) (+)(ii) parabolic shape passing through origin (1)

plotted accurately as G % 1/1 4+ (1) '

(b) (i) 6 % C!R % 0/K - 1*= - +/+ % 1/J - 1*' s % '/10 h +

(ii) TG % > !(41+ 4++) % 1/1(+J 10) R % ./. (_) +

(iii) ' % J eIp( t&1/J - 1*'

) R giving t % 1/J - 1*'

- ln 1/+J % =/= - 1*=

(s) +(iv) H % TG&Tt % ./.&=/= - 1*= % =/* mG ec& b(ii) and (iii) 1

allow H % 4av+ &C % '/J+&0/K - 1*= % +/.K mG[11]

32. (a) (i) suitable patternR arrows #rom ion to ion +

(ii) F % kQ1Q+&r +R Q1 % Q+ % e (+)F % . - 1*. - 1/0+ - 1* =K&+J - 1* +* % ./+ - 1* 1* (3) (+) '

(b) (3+ gives) FD % mDaD and F % ma (1)

(3= gives) FD % F (1)can be implicit SDE gives a @ x (1)hence xD& x % aD&a % m&mD % 1+2 (1) '

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(c) (i) sine or cosine curveR amplitude K/* - 1* 1+ mR period % 1/J - 1* 1' s =(ii) resonance situationR driving #re,uency o# radiation % natural (1)

#re,uency o# oscillation o# molecule&5G (1) +[15]

33. 5: the number o# (undecayed) nuclei which decay per second&rate o# decay o# nuclei 1O: the probability o# a given nucleus decaying in the neIt second or in unittime&the (decay) constant relates the activity to the number o# undecayed nuclei 1 3: the number o# undecayed nuclei&nuclei o# the original nuclide (remaining) 1

[3]

34. (i) .* and +=' 1(ii) + - 1* 0 - 2/* - 1*0 % 1' (kg) 1

(iii) 3 % (m&E) 35 % 1' - 1*= - 0 - 1*+=&+=K (% =/J - 1*+J) 1

(iv) O % */0.&6 % */0.&'/J - 1*. - =/+ - 1*2 % '/K - 1* 1K (s 1) 15 % O3 % '/. - 1* 1K - =/J - 1*+J % 1/2 - 1*KR s 1 or B, +

[6]

35. #orce per unit (positive) charge 1#orce per unit mass 1#orce per unit length o# conductor carrying unit currentR 1 perpendicular to #ield and current 1

examples o& similarities :all eIplain action at a distance 1all #orces per unit something / 1#ield lines never crossR density o# lines indicates relative strength o# #ield +$ and g have the same laws&geometry e/g/ #or point and&or plane distributionsR 1#or $ and g #orce in direction o# #ieldR #ield lines perpendicular to sur#ace +

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examples o& di&&erences+#orces caused by di##erent entitiesR and act di##erently i/e/ $ and gdi##erent to BR 1#orce caused by stationary versus moving chargeR +direction o# #orce #or B given by F/M/D/rule etc/ +g is only attractive $ (and B) can cause attractive and repulsive #orces 1#ield lines #or B #ield closed loops others start and #inish on m Q 1magnitudes o# #orces very di##erent #or unit R detail/ +max 7 marks

,uality o# written communication +[9]

36. magnetic #luI % B5 1meanings o# B and 5 i/e/ #luI density or #ield strength and area to it 1magnetic #luI linkage re#ers to the #luI linking&passing through a coilR 1and e,uals 3 - #luI where 3 is the number o# turns (o# the coil) 1Faraday9s law: induced e/m/#/&voltage is proportional to rate o# change o# #luIlinkage through it &correct mathematical #ormulation&5G 1Men79s law: the direction o# the induced e/m/#/&voltage is such as tooppose the motion&change that produced it 1relationship o# Men79s law to conservation o# energy or other valideIplanation&discussion&description +max " marks

,uality o# written communication +[7]

37. (a) (to a maIimum o# 2 marks) e/g/PAray source detectors round patient

rotated around patient & the signal & PAray passes through thesame section o# the body #rom di##erent directions/

producing a (thin) slice & crossAsection/dea o# absorption & less gets through & more is absorbed

by dense material & bone & material o# high & Digh related tomaterials such as bone & Mow to materials such as so#t tissueattenuation is by the photoAelectric e##ectthe possibility o# using a contrast medium/better than a simple PAray at di##erentiating other organs/patient is moved a small distance and the process is repeated &

process continues in a spiral/a computer (analyses the data) & identi#ies the position o# organ&bone

and #orms a =A image/ 2 (b) Hatients are eIposed to ionising radiation/ (1)

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( onising radiation) could cause cancer & damage cells (1) 5lus a maximum o& 6 4 &rom+ e.g. (1)

t9s eIpensive/6ime consuming & uses valuable resources etc// =

[10]

38. 8to a max. o& 5 9

5 p/d/ & voltage must be applied causing the (pie7oelectric) crystal to change shape/

5 named crystal (eg ,uart7 lead 7irconate titanate \H 6] lithium sulphate barium titanate)

5n alternating p/d/ causes the crystal to oscillate & vibrate (accept resonate)/

# the #re,uency applied matches the natural #re,uency o# the crystalresonance occurs/6he crystal is damped & stops vibrating when the applied voltage stops

due to the backing material & epoIy resin which also absorbs backwardAtravelling sound waves (which

might give spurious re#lections)/ J[5]

39. (i) J/' cm & */1 cm read #rom the graph (1)% J/' - +* fs cm 1 - 1/J - 1*= m s 1 (1)% */10+ m (1)*/10+ & + % */*K1 m or K/1 cm (1) '

(ii) Digh re#lection at the airAskin boundary & Mittle ultrasound enters

the body & 5 very large peak right at the start (1) due to large di##erence in acoustic impedance &

allow 8 due to large di##erence in density9/ (1)4ery low peaks & no (subse,uent) peaks (not just 8nothing9) (1) =

[7]

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40. (i) (neutrons) having energies comparable with thermal energies &slow moving & low kinetic energy & energy in range 0 A 1** e4 &energy similar to (energy o# ) atoms o# surroundings R 1

(ii) either thermal neutrons will be captured & absorbed (by "A+=J nuclei)

or higher energy neutrons do not get absorbedR 1 [2]

41. (i) = points plottedR any point incorrect loses this mark 1(ii) curve through = points and heads down towards 7eroR (1)

line peaks between Br and originR (1) +

(iii) B$ pernucleus o#+=J.+" % 2/0* - +=J (% 12K0 Ee4)B$ o# products % K/+* - 1'0 K/0* - K2 both lines (1)(% 11.2 2'K Ee4)so energy released % (11.2 2'K) 12K0 (1)

% 1J. Ee4 (1)omits multiplication by nucleon number to get ./+ Ee4 gets * 1 * % 1 =

[6]

42. con#ines & pulls together plasma & nuclei & ions & nucleons & protonsR (1)so increases density& concentration & number per unit volumeR (1)

and increases #re,uency & number o# collisions among nucleiR (1)gravitational attraction heats plasma & gravitational p/e/ changed to heatR (1)any =

[3]

43. either area is potential & stored energy & work done & energy to overcomecoulomb barrier

or minimum k/e/ at in#inity or 5GR (1)it is (minimum) energy needed #or #usionR (1)

[2]

44. (i) reactant mass % + - 1/**2 +20 % +/*1' JJ+ u product mass % +/*1= JJ= */*** J'. % +/*1' 1*+ u

so Tm % '/J - 1* ' u (1) 4 % Tm c+ (1)% '/J - 1* ' - (1/00 - 1* +2) - (=/* - 1*K)+ %0/2 - 1* 1' _ (1) =allow conversion using 1 u % .=1 Ee4

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(ii) positron and electron annihilate 1[4]

45. (a) number o#decayed "A+=K nuclei % > - number o#undecayed "A+=K nucleiR (1)so 1&= o# "A+=K has decayed and +&= o# "A+=K has not decayedR (1) +(so ratio % +&=)

(b) either O % */0.= &2 > % */0.= & ('/'2 - 1*. ) (% 1/JJ - 1* 1* y 1) subs/ (1) % * e Ot so : * % e Ot and ln ( : *) % Ot ln (*/002) % 1/JJ - 1* 1* t alg/ & arith/ (1)so t % +/01 - 1*. y ans/ (1) =

or : * % (>) x

so */002 % (>) x

and ln (*/002) % x ln(*/J)and x % */JK' thent % x 2 > % */JK' - '/'2 - 1*. % +/01 - 1*. y

(c) either * % (J/** & +=K) - 0/*+ - 1*+= subs/ (1)% 1/+0 - 1*++ atoms ans/ (1) +

or * % (J/** - 1* =) & (1/02 - 1* +2 - +=K) (1)% 1/+0 - 1*++ atoms (1)

(d) eIponential decay graph #or ": starts #rom * and approachest aIisR (1)eIponential growth o# Hb #rom 7ero: approaches a constant value o# * R (1)lines sensibly 8mirror images9R (1) =

[10]

46. (i) leptonsR 1(ii) neutrino & muon & tau(on)R 1

[2]

47. (i) up down down & uddR 1 (ii) Q B S

u ( )+&= ( )1&= * u values (1)d 1&= ( )1&= * d values (1) +

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(iii) so #or neutron ; % * < % 1= % * 1

[4]

48. (a) one (or more) electrons removed (or added) to an atom 1(b) $ % h# % hc&O together with knowledge o# symbol meaning (1)

%.

K='

1*+=K

1***/=1*0=/0

(1)

% K/=0 - 1* 1. (_) (1) = (c) #re,uency o# "4 is greater than #re,uency o# light

C alternative statement in terms o# wavelength/so photon energy o# visible light is less than photon energy o# "4 (1)HM"S one o# the idea o# conservation o# energyit is not possible #or a low energy photon to give a high energy photonthis is a one to one process (1) +

(d) $ % 4&d and power o# 1* correct #or d (1)

% =*&*/***+* % 1J* *** (1)4 m 1 (1) =

[9]

49. (a) appropriate shapeR lines perpendicular to and touching plate and sphereR (+)arrows towards negative sphere (1) =

(b) (i) By moments e/g F cos +* % G sin +* & by triangle o# #orces &

by resolution o# #orces & other suitable methodRi.e. >usti&ication needed (1)F % 1/* - 1* J tan +*R % 1/* - 1* J - */=0'R (% =/0' - 1* 0 3) (+)triangle o# #orces gives G&F % tan 2* etc (1) =

(ii) $ % F&QR % =/0' - 1* 0 & 1/+ - 1* . % =/* - 1*=R3 ! 1 & 4 m 1 =

(c) $ % (1&'o)Q&r +R =/* - 1*= % . - 1*. - 1/+ - 1* .&r +R (+)or use F % (1&'o)Q+&r +R r + % =/0 - 1* = giving r % 0 - 1* + (m) (1) =

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(d) #ield line sketchminimum o& " lines symmetrical about line >oining centres with arrows R (1)Fig 1 sketch matches CDS o# Fig +&plate analogous to mirror&5Grelating to symmetry (1) +

[14]

50. (a) +.R =' +

(b) O % */0.=&6 % */0.=&(1+* - =/+ - 1*2) % (1/K - 1* 1* s 1) accept ln ' 1

(c) (i) Q % !4 % 1/+ - 1* 1+ - .*R evidence o# calculation (% 1/1 - 1* 1* !) +

(ii) n % Q&e % 1/1 - 1* 1*&1/0 - 1* 1.R % 0/. - 1*K allow sig. &ig. $ariations +

(iii) 5 % O3R 3 % 0/. - 1*K&1/K - 1* 1*R % =/K - 1*1K using 7.? gi$es 3.@ = (iv) 1 y is less than 1Z o# 1+* y so eIpect to be within 1Z&

using e Ot gives eIactly 1Z #all& problem o# random emissionor other relevant statement 1

[11]

51. (a) (i) F is towards 8open9 end o# tubeR using Fleming9s M/D/ rule +(ii) F % B w 1(iii) F % */1J - K** - */**+JR % =/* (3) +

(b) (i) 5 voltage is induced across moving metal as it cuts lines o# #luI&5GR (1)

voltage is proportional to #luI change per second&5GR (1)the #luI change per second is Bwv & is proportional to the area o# metal moving through the #ield per second & is proportional to v (1)or Faraday9s law #ully statedR with reasonable attempt toR (+)relate #luI linkage per second proportionally to speed (1) =

(ii) #luI (linkage) doublesR so using Faraday9s law 4 doubles&5G +

[10]

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52. nature and #eatures:@Aparticle is +p +n& mass ' u (1)charge o# +e (1)very short range&heavily ioni7ing&absorbed by paper (1)spontaneousR and random nature o# radioactive decay (+)energetically more #avourable to eject #our particles together than a singleone&other comment about energy minimisation&mainly occurs #rom higher 5 nuclei&5G (1)small mass decrease&loss provides kinetic energy o# @Aparticle (1) particle energy o# a #ew Ee4R particular decay is monoenergetic (+)@Aparticle scattering:suitable diagramand/or description to illustrate eIperimentup to ' marks (+)most particles have little i# any de#lection (1)large de#lection o# very #ew shows nucleus is smallR and very massive (+)(!oulomb9s law enables closest approach to) estimate nuclear si7e(in case o# @Aparticle back scattering with conservation o# energy argument) maI 2Quality o# Gritten !ommunication +

[9]

53. description:(') hydrogen or light nuclei&protons are #used together to #orm ahelium&heavier&larger nucleusR (1)two positrons must also be releasedR to conserve chargeR (+)the process is more complicated than the summary e,uation suggests&5GRmass reduction provides energy release& m % $&c+ (1)the process re,uires very high temperatures (to bring the protons together)R (1)normally achieved inside a starR only by man in a bomb so #arR (1)comparison: (+)$nergy release in #usion is much greater than in radioactive decayR because mass reduction&change in #usion is much greater than in radioactive (1)decay&5GR (1)as the helium nucleus is so strongly boundR (1)also energy release #rom annihilation o# positronsR (1) maI JQuality o# Gritten !ommunication +

[7]

54. (J/+ - 1/J - 1*11) % 2/K* - 1*11m 1[1]

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55. Dydrogen atoms&particles (1)!ollapse under gravity& decrease o# gpe (1)

ncrease in kinetic energy& temperature (1)Fusion o# protons (1)$nergy released& re#/ to $ % mc+ (1)

[5]

56. v @ r & v % Do - r (1)labels (including one re#erence to $arth&Sun&YalaIy) (1) +

[2]

57. in#inite "niverse (1)all lines o# sight end on star (1)so night sky should be bright& not dark (1)either eIpanding "niverse&light undergoes red shi#t (1)more distant galaIies have greater red shi#t (1)or age o# "niverse is #inite (1)light #rom distant stars not yet reached $arth (1)

[5]

58. (i) accept description of plan view or side view.

side: central bulge (1)galactic disc each side (1)

plan: accumulation o# stars in centre/ (1)spiral arms (minimum o# + arms) (1) +

(ii) correct position o# Sun (accept +K***ly #rom centre) (1) 1

[3]

59. (i) hydrogen & helium gas (1)#ormed a#ter big bang & remnants o# supernovas (1)

(ii) critical density is condition #or #lat "niverse/ (1)dark matter increases density o# "niverse/ (1)density greater than critical density/ (1)"niverse will contract & big crunch/ (1)

[6]

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60. For ation of i a!e to a ax 3 e/g/PArays are detected by a #ilm & scintillation counter etc/ (1)Digh 8 9 means high attenuation & low transmission\5llow atomic mass & nucleon number] (1)

shadow on the #ilm & re#erence to eIposure a#ter attenuation (1)Ce#erence to photoelectric e##ect & energy range around 1 1**ke4 &absorption = (1)"xplanation of the #se of a contrast edi# to a ax.4 e.!.

PArays do not di##erentiate & show up so#t tissues well (1) as similar absorption & 8 9 is similar & 8 9 is low #or these tissues/ (1)

!ontrast medium has high 8 9 & absorbs PArays strongly/(1)t is usually taken orally & as an enema & can be injected/(1)

"xa ple of t$pe of str#ct#re that can %e i a!ed to a ax.1 e.!.

digestive tract & throat & stomach/(1) to a maI/ K[8]

61. (a) 0 points plotted correctly (1)remaining point plotted correctly (1)sensible continuous smooth graph drawn (1) =

(b) (i) */.J & */1* mm (1) 1

(ii) & o % e I (1)*/J* % e */***. (1)f % 2=* (1)m 1 (1) '

[8]

62. (a) #orces - S and - Y acting inwards #orce - $ acting outwards A all throughcentre o# protonR= #orces +&+ + #orces 1&+ marked and labelled (+) +

(b) - $ % - S - YR

accept - $ - S - Y % *allow ec& &rom (a)(1) 1

(c) (i) - $ %; + & (' * r +) (1)% (1/0 - 1* 1.)+ & \' - K/KJ - 1* 1+ (+/K - 1* 1J)+] % +. 3 (1)use o#r % 1/' - 1* 1J m ( 1) once only +

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(ii) - Y %m+ A &r + (1)% (1/02 - 1* +2)+ - 0/02 - 1* 11 & (+/K - 1* 1J)+ % +/' - 1* =J 3 (1) +

(iii) - S % +. 3 & same as F$ allow ec& (1) 1

(d) - $ - Y so - Y negligible & insigni#icant & can be ignored or 5G (1) 1

(e) (i) - $ % * (1) 1

(ii) - Y % +/' - 1* =J 3 (approI/) allow ec# (1) 1

(iii) - S % +/' - 1* =J 3 (approI/) (1)

comment : - S now repulsive (not attractive) or 5Gor indicated by minus sign with - SR (1)any 3 1

[12]

63. (a) (i) "n" +=..+1*+=K.+ + 1

(ii) bar)(veP" ***1+=..=+=..+ ++ +

(iii) bar)(veHuP ***1+=..'+=..= ++ 1omits any neutrino ( 1) once onlyelectron incorrectly represented ( 1) once only

(b) (i) +' *** year & +' *** year 1

(ii) / % ln + &2 > % ln + & (+'*** - =0J - +' - =0**) subs / (1)

% ./10 - 1* 1= s 1 or ./10 - 1* 1= s 1 ans / (1) +#ailure to convert years to s giving +/K. - 1* J gets 1&+

(c) (i) +=. g o# Hu contain 0/*+ - 1*+= atomsor alternative correct use o# 5 (1) % (*/*J - '/' & */+=.) - 0/*+ - 1*+= ie applies Z and units correctly (1) +(% J/J' - 1*+= (atoms))

(ii) activity % / (1)

% ./10 - 1* 1= - J/J' - 1* += allow ec& % J/*K - 1*11 B, & s 1 ans. B unit (+) =

[12]

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(c) X mass de#ect & mass loss% 1.1/.+1 '2 1.1/.1K 2. (1)(% */**+ 0K u)

then either+ mass loss in kg % */**+ 0K - 1/00 - 1* +2 (1)(% '/'J - 1* =* kg)

so energy loss % m c+ (1)'/'J - 1* =* - (=/* - 1*K)+

% '/** - 1* 1= _ (1)or : */**+ 0Ku % */**+ 0K - .=+ Ee4 (+)

% (+/J* Ee4)% +/J* - 1*0 - 1/0 - 1* 1. (1)% '/** - 1* 1= _ (1)

accept .=* .=' Ee4 u 1 giving =/.. '/**(J) - 1* 1= _ '[11]

66. all #ree hadrons (thought to be) (somewhat) unstableR (1) protons and neutrons are (both) hadronsR (1) (1) protons and neutrons inside a nucleus are stableR (1)#ree neutrons have hal# li#e o# 1* A 1J minutesR (1)#ree protons are stable & have hal# li#e o# about 1*=+ yearR (1) any Jallow e,uivalent marks #or other hadrons and & or other relevant points

[5]

67. (i) weak (#orce & interaction)R (1) 1

(ii) =1D [ =+De * 1e $ R (1) 1

(iii) d [ u e $ R (+)

d [ u gets 1&+ud [ u e & X $ is not in simplest #orm so gets >d

baryon reaction1*n [ 1

1 p *

1e $ gets > +

[4]

68. #ission is when splitting (into two parts releasing energy) takes place and#usion is when joining together takes place (1)nuclei as the active particles (1) +

[2]

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69. (a) (i)capacitor capacitance & fF charge & f! p/d/ & 4 energy & f_

P J =*

%;:C % 0 (4) (1)

% >CV +(1)

% > - J - 0+

% .* (1)

N +J%CV

% +J - 0%1J* (f!) (1)

% 0 (4) (1) % 'J* (1)

1*=* 1J* %

1K* (f!) (1)%;:C 1K*&1*

% 1K (4) (1)% 10+* (1)

$ach boI correctly calculated scores (1) (1) #or >CV + . (ii) 1 1K 4 0 4 % +' (4) (1)

2 1K* (f!) (1)3 1K* & +' % 2/J (1)4 .* 'J* 10+* % +10* (f_) (1) '

(b) (i) Lirchho##9s second law C conservation o# energy (1) 1

(ii) Lirchho##9s #irst law C conservation o# charge (1) 1 (c) (i) time constant %CR (1)

% 2/J - 1* 0 - +** *** % 1/J (s) (1) +

(ii) !C !C '

o e

= ;; (1)

; &; o % e ' % */*1K= (1) +[19]

70. (a) 7ero (do not allow 8small9) (1) 1 (b) =** G #or 1 watt there#ore =** G - +* #or +* G 0*** G (1) 1

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(c) e/g/ i# run at .+ L there is a danger that superconductivity will cease as aresult o# a slight temperature rise (1)a 1J L di##erence provides a sa#ety region (1)22 L is the boiling point o# li,uid nitrogen (1)other sensible suggestion (1) +

D,EFDGD (')

(d) (i) area o# crossAsection o# wire % 1* 0 m+ (1)current % 1* 0 m+ - +/* - 1*K 5 m + (1)% +** 5 (*) +

(ii)=*/*+

=+**+**1*+0/1 0

=

< (1)

% 1/=' 6 (1) + (e) (i) - %

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(c) ray sourceR (1)the only radiation with su##icient penetrating power&ability todiscriminate between di##erent thicknesses&5G (1) +

[11]

72. (a) (i) J/* (4) (1) 1(ii) 1*/* (4) (1) 1

(b) (i) Q % !4R% 1/* - 1* = (!) (+) +(ii) 6he total capacitance o# each circuit is the same (namely 1** ;F)R (1)

because capacitors in series add as reciprocals& in parallel add&supply voltage is the same and Q % 4! etc/ (1)max ' marks +

(c) (i) 51 will give the same reading as 5+R because the two ammeters are (1)

connected in series &5G (1) +answer only in terms o& exponential decrease &or a maximum o& % mark

(ii) 5' will show the same reading as 5+ at all timesR (1)

5= will show hal# the reading o# 5+ initiallyRand at all subse,uent times (+) =

[11]

73. (a) Hositive as $A#ield is downwards&top plate is positive&like charges repel&5G (1) 1

(b) (i) k/e/ % Q4R % =** - 1/0 - 1* 1. % ('/K - 1* 12 _) (+) +

(ii) 1&+mv+ % '/K - 1* 12R % */J - +/= - 1* +0 - v+ so v+ % '/12 - 1*. R(giving v % 0/'0 - 1*' m s 1) (+) +

(c) $ % 4&dR so d % 4&$ % 0**&' - 1*' % */*1J m (+) + (d) (i) semicircle to right o# hole (1)ec&(a)* (a) and d(i) to be consistent 1

(ii) mv+&rR % BQvR (+)giving r % mv&BQ % +/= - 1* +0 - 0/J - 1* ' &(*/12 - 1/0 - 1* 1.)R (1)r % JJ mmRso distance % +r % */11 m (+) J

[13]

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74. (a) (i) 1=K (1) 1 (ii) K0 (1) 1

(b) (i) O % */0.=&10** - =/10 - 1*2 % 1/' - 1* 11 s 1 (1) 1

(ii) 5 % O3R 3 % 0/*+ - 1*+=&++0R evidence o# calculation to give =/0 or (+)=/2 - 1*1* B, (1) =

(c) Tm % */**J= u (% K/K - 1* =* kg)R (1)$ % c+TmR % . - K/K - 1* 1' % 2/. - 1* 1= (_) (+) =

(d) Q % mc R so */K - =/2 - 1*1* - 2/. - 1* 1= % */**1 - 11* : (+)giving % */+1= L s 1R and t % 1& % '/2 s (+)or Q % mc R Q&L % */**1 - 11* % */11 _ L 1R (+)Q&s % */*+=' _R so t % */11&*/*+=' % '/2 s (+) '

[13]

75. Faraday9s law: the em#&voltage induced across a coil&component&circuit is (1) proportional to the rate o# change o# #luI (linkage) through it &5G (1)magnetic #luI % B5R (1)meanings o# B and 5 i/e/ #luI density or #ield strength and area ( to it) (1)magnetic #luI linkage re#ers to the #luI linking&passing through a coilR (1)and e,uals 3 - #luI where 3 is the number o# turns o# the coil (1) maI JQuality o# Gritten !ommunication +

[7]

76. sine or cosine wave o# regular period and amplitude (1)4 doubles when the speed v o# rotation o# the coil doublesR (1)when v doubles the rate o# change o# #luI linking the coil doublesR (1)

the #re,uency o# the a/c/ signal doubles&period halves&5G (1)4 doubles when the number n o# turns on the coil doublesR (1)when n doubles there is twice as much #luI linking the coil&5GR (1)the #re,uency&period o# the signal is unchangedR (1)without iron core #luI linking coil is much lessluI would spread in alldirectionsluI not channelled through low reluctance path&5G (1)amplitude o# output voltage is smaller (1)actually is tiny:negligible:mV rather than V maI 2Quality o# Gritten !ommunication +

[9]

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77. an$ 4 fro &end o# D burning&red giant&supergiant (1)onset o# De #usionusion o# heavier nuclei (1)gravitational collapse o# core (1)supernova eIplosion& star eIplodes (1)suitable mass limit (chanderasekha limit 1/'E) (1)supported against gavity by neutron gas pressure& re# toFermi pressure (1)internal structure protons and electrons combined& verythin atmosphere& metallic crust (1) '

[4]

78. (i) volume % ' (1* ***)= &= % '/+ - 1*1+ (1)density % =/J - 1*=* & '/+ - 1*1+ ec# (1)density % K/' - 1*12 kg&m= (1) =

(ii) anytwo #rom

density (very) much greater than material on $arth (1),uotes typical density on $arth 1 1*' kg m = (1)atomic structure collapsed & density same as atomic nucleus (1) +

[5]

79. (i) energies&temperatures irreproducible on $arth & laws o# Hhysics break down (1) 1 (ii) temperature decreases (1)

universe eIpanding&work done against attractive #orces& energyconverted to mass (1) +

(iii) an$ 3 #rom

protons and electrons separate initially (1)matterAradiation e,uilibrium&charge prevents passage o# em waves (1) protonAelectron recombination ormation o# atoms (1)gamma& em waves no longer absorbed (1) =

[6]

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80. an$ 5 #rom:starAlight shows red shi#t (1)galaIies (stars) receding #rom $arth (1)recessional velocity proportional to distance (1)cosmological microwave background radiation (!EBC) (1)uni#orm intensity in all directions (1)small ripple (1)(black body temperature) +/2 L (=L) (1)Digh ratio o# helium to hydrogen (1)

ndicates very high temperatures eIisted (1)ratio too high to originate #rom stellar #usion (1) J

[5]

81. isotropic (1)

homogenous (1) + [2]

82. (i) D* % 2J & =/1 - 1*1. (1)t* % 1 & D* % '/1= - 1*12 s (1)t* % '/1= - 1*12 s & =0J - +' - =0** % 1/= - 1*1*y (1) =

(ii) any two #rom

universe eIpands to a limit& #lat universe (1) but never reaches that limit (1)density o# universe % critical density (1) +

(iii) curve: passes through H (1)

curves over and back to time aIis (1) + (iv) "niverse not so old (no ec# #rom (iii)& "niverse will end

in big crunch (no ec# #rom iii) & universe has #inite li#etime (1) 1[8]

83. (a) 6he intensity o# sunlight is too small (inverse s,uare law) or 6he area o# panel re,uired would be too large&massive to launch 1

(b) (i) $nergy re,uired % 4 t

% 1+ - J - 1+* - 0* (1)% '/=+ - 1*J _ (1) +

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(ii) Steady power re,uired % ('/=+ - 1*J - 1**&+J) +' - =0** (+)% +* G (1K/JG i# */'* E_ used) +(or H % 4 % 1+ - J % 0*G #or +h so only JG #or +'h i# 1**Ze##icient but % J & */+J % +*G)

(iii) $nergy carried by alpha % J - 1*0 - 1/0 - 1* 1. % K/* - 1* 1= _ (1)

5ctivity re,uired % +* (K - 1* 1=)% +/J - 1*1= B, (1) +(or */'=+E_ & K - 1* 1= _ alphas per day % */'=+ E_ & K - 1* 1= &+' - =0** alphas per sec)

(c) ecay constant o# Hu +=K % */0. & 6>

% */0. & KK - =0J - +' - =0**

% +/J - 1* 1*

sec 1

(+)(allow mark #or conversion o# KK years to +/2K - 1*. seconds)

3umber o# nuclei re,uired % 5 & O % +/J - 1*1= & +/J - 1* 1* (1)% 1/* - 1*+= (1)(allow mark #or #ormula 5 % O3)Eass re,uired % 1/* - 1*+= - +=K & 0/*+ - 1*+= (1)% '* gms % */*'* kg (1) 0

(d) n launch the rocket gives the spacecra#t a huge kinetic energy (in

order to escape)Failure at this point could cause spacecra#t and contents to burn upin atmosphereBut plutonium would still be radioactive and being vaporised it could be ingested/Sensible comment on danger periods o# launch (or reAentry)Sensible comment on mechanism o# ingesting Hlutonium5llow one sensible comment on no risks in the isolation o# deep space +

[15]

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84. PAray (photons penetrate patient (1)attenuation by di##erent media & bones attenuate more than so#t tissue (1)less PAray reach #ilm under bone & shadow e##ect (1)intensity o# PArays is proportional to darkening o# #ilm & re#/ 6o #ogging or blackening (1)PAray photons hit crystals & atoms in intensi#ying layer (1)atoms become eIcited & #luorescence occurs (1)emitting light (photons) (1)detail : as they return to ground state (1)so eItra #ogging o# #ilm (1)detail : metal backing stops PArays passing through & #ilm more sensitive to lightthan PArays & most PArays pass through the #ilm & double sided & photographic#ilm & more contrast but not clearer (1)Cesponse is ,uicker & less PArays needed (1)so less eIposure (1)to axi # of 8 K

[8]

85. alternating voltage or alternating $A#ield across crystal (1)at resonant #re,uency (1) allow re#erence to resonance o# crystal +

[2]

86. (i) position o# = lower oIygen ions closer to positive plate (1) 1

(ii) re#/ to change in dimension & shape & distort& it gets longer (1) 1[2]

87. (a) (i) #or air is '+. (kg m + s 1) and #or skin is 1/21 - 1*0 (kg m +s 1) (1)

Substitution into e,uation leading to F % */... (1) + (ii) with gel more ultrasound enters body & without gel

most ultrasound is re#lected (1)most ultrasound is re#lected (without gel) when the di##erence in is largeor most ultrasound enters body when the di##erent in is small (1) +

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(b) 1.5 cm - 1 - 1* J % 1/J - 1* J s (1)

s % vt or4080 - 1/J - 1* J (1)s % 0/1+ cm (1)ec& i& speed is wrong

&+ % =/*0 cm (1) '[8]

88. 5t least = #ield lines inside solenoid parallel to aIisR (1)Mines e,ually spaced over some o# length o# solenoid/ (1)5rrows on lines pointing le#t to right/ (1) =

[3]

89. (a) similar mass means large momentum trans#er (in collision)R (1)

hence #ewer collisions are neededR (1) +neutron colliding with heavy nucleus bounces o## with similar speed & k/e/scores 1&+ maI/neutron colliding with similar mass nucleus trans#ers large k/e/ & speedscores 1&+ maI/

(b) +=0.+" [ 11*'J Ch 1+1'2 5g J1*n (+)

allow+=J

.+" 1*n [

11*'J Ch

1+1'2 5g J

1*n

no neutrons *&+ incorrect number o# neutrons >J1* 3 gets 1&+ maI/J*n gets *&+i#1* missing #rom neutron symbol 1&+ maI/+=0

.+" 1*n [ 11*'J Ch 1+1'2 5g 01*n gets > +[4]

90. neutron is udd & proton is uudR (1),uarks are: up down strange top bottom charmR (1)either up & u has; % ( )+&= < % ( )1&=Ror down & d has; % 1&= < % ( )1&=R (1),uarks are #undamental particlesR (1)#or every ,uark there is an anti,uarkR (1)anti,uarks have opposite values o#; < and= (compared to ,uark) (1),uarks are held together by strong #orce & gluons (1); < and= are conserved in (,uark) reactions (1)any ' J

[5]

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91. (a) (i) calculates b/e/ per nucleus: 1/11 - + (% +/++)+/J2 - = (% 2/21) both expressions (1)

so energy released % 2/21 + - +/++ (% =/+2 Ee4) (1)% =/+2 - 1*0 - 1/0 - 1* 1.

% J/+(=) - 1* 1=

_ (1) =omits multiplication by + and = 1&= maI/

(ii) reaction + generates more energy (than reaction 1)R (1) 1

(b) initial mtm/ % #inal mtm/

so * %mD $D mn $n (1)* % ('mn)$D mn $n so$n % '$D (1)

k/e/ o#' +De % >mD $D+ k/e/ e,uation applied (to n or De) (1)

% > ('mn) $D+ % +mn $D+k/e/ o#1*n % >mn $n+ % >mn (' $D)+ % Kmn $D+ alg / (1)either k/e/ o#1*n % ' - (k/e/ o# De)or 1*n has K*Z o# total energy (1) J

K*Z unsupported scores 1&Jk/e/ stated to be proportional to 1&(mass) scores +&J i# correct answer obtained

[9]

92. (i) n _: 4 %m c+ (1) % (+ - 1/02 - 1* +2) - (=/* - 1*K)+ (% =/* - 1* 1* _) subs / (1)

n Ye4: =/* - 1* 1* % =/* - 1* 1* & (1/0 - 1* 1. - 1*. )% 1/KK Ye4ans / (1) =

allow 1/. Ye4uses only one mass can get +&= maI/

(ii) particle mass increases with energy & speedR (1)

accelerating voltage gets out o# step with passage o# particle between

electrodes & i# voltage out o# synch/ proton energy cannot increase or 5GR (1)1/KK Ye4 is high enough to cause (signi#icant) mass increaseR (1) =[6]

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93. (a) 3p graph: graph has eIponential shape & there is eIponential decay o# 3pnuclei & number (o# 3p nuclei) is halved in +/= days & constanttime & in its hal# li#eR (1)

Hu graph: sum o# Hu 3p nuclei % =/* - 1*+* at all timesR (1)either because one 3p nucleus decays to one Hu nucleusor rate o# decay o# 3p and #ormation o# Hu are e,ualR (1)and hal# li#e o# Hu & much bigger than hal# li#e o# 3pR (1) =

any ' (')

(b) time re,uired % time #or 3p nucleus to #all to */=* - 1*+*R (1)

theneither % * (>)t &2 > (1)so & * % (>)t &2 > lg( & *) %t &2 > (lg */J) lg (*/1) %t &+/=0 lg (*/J) (1)

t % 2/K days (1)or uses % * e /t where / % ln + & +/=0 (% */+.' day 1) (1)

so */1 % e */+.' t (1)ln (*/1) % */+.'t t % 2/K days (1)

or / % ln + & (+/=0 - +' - =0**) % =/'1 - 1* 0 s 1 (1)*/1 % e =/'1 - 1*eIp( 0) t ln (*/1) % =/'1 - 1* 0 t (1)t % 0/20 - 1*J s % 0/20 - 1*J & (+' - =0**) % 2/K days (1) '

calculates time #or 3p to #all to +/2 - 1*+* & Hu to rise to */= - 1*+* % */=0 daygets * 1 1 1 % =&'uses2 > #or plutonium can get +&' maI/attempts to use repeated halving o# can get +&' maI/ i# using */= (not +/2)

[7]

94. (a) e,ually spaced hori7ontal parallel lines #rom plate to plateR arrowstowards BR ,uality mark =

(b) $ % 4&dR % 0**&*/*'R(% 1/J - 1*'

4 m 1

) +

(c) F % Q$ & 1/0 - 1* 1. - 1/J - 1* ' R% +/' - 1* 1J (3) +

(d) 1&+mv+ % Fdor Q4R % 1/0 - 1* 1. - 0** or % +/' - 1* 1J - */*' ec& (c) +or alternative method by constant acceleration #ormulaeR(either method giving v+ % +/1 - 1*1' and v % 1/'J - 1*2 m s 1)

(e) +v % +/*J - 1*2 (m s

1) 1

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(#) #ewer electrons will reach grid Bor ! (as higher initial speed re,uired)Rso current will #all (to 7ero i# beam is taken to be monoenergetic) +

[12]

95. (i) ! % Q&4 or gradient o# graph & % +' ;!&=4R % K/* (;F) +

(ii) $ % > !4+ & % > - K - =+R % =0 (;_)ec& a(i) +or > Q4 & % > - +' - =R % =0 (;_)

(iii) 6 % C! % (*/*')R C % */*'&K/*; % J/* - 1*= ( ) ec& a(i) +(iv) idea o# eIponential&constant ratio in e,ual timesR which is independent o#

initial value&5G or argued mathematically in terms o# Q&Qo % e t&C!

gi$e % mark &or statement that time depends only on time constant:RC +[8]

96. (i) ! p % ! ! % 0 ;FR 1&!s % 1&+! 1&!R % =&+! giving !s % +!&= % (+ ;F) =

(ii) + sets o# (= in series) in parallel& = sets o# (+ in parallel) in series +[5]

97. (i) number o# decays&atoms&nuclei decaying per second&unit time in the 1source&5Gcount (rate) without source present&5G 1

(ii) distance o# detector #rom source&dimensions o# source or detector

window&e##iciency o# detector&rate o# emission v detection e/g dead timecorrection&other sensible suggestionR 1reason&e##ect on count rate 1

[4]

98. (i) (take lns o# both sides) appreciate ln e Ot % OtR and ln !&!o % ln ! ln !oor when multiplying logs add +

(ii) gradient % */*J0 h 1 allow H ?.??' h R 6 % ln+&O % ln+&gradient % ln+&*/*J0 hR6 % 1+/' hallow H ?. h =

[5]

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(b) Dydrogen and helium in early stars and sun 1Sun has greater proportion o# helium than early stars&D changed to De by #usion in sun/ 14irtually no higher elements in #irst stars& sun containstraces o# higher elements (accept speci#ic eIamples up to iron) 1

[4]

103. 5ny J #romred shi#t data #or galaIies (accept stars) 1calculate velocity #rom red shi#t 1galaIies& stars receding #rom $arth 1distance data #or galaIies& stars 1velocity @ distance & v&r % constant & vAr graph straight line 1universe began at a single point 1

[5]

104. (a) 5ny twostars rotate around galactic centre 1star with velocity component towards $arth 1re#erence to motion&shape o# galaIy 1or other valid points eg blue shi#t

(b) Do % 2J& = - 1*1.

s 1

1t ? 1& +/J - 1* 1K 1t ? ' - 1* 12 s 1

[5]

105. critical density is that #or #lat universe 1density p* universe closed&contracts&big crunch 1density p* universe open& eIpands #orever 1any + #rom#ate unknown because si7e&mass&density universe uncertain 1#ate unknown because p* & D* not known 1

[5]

106. (i) H % 4 (1)% =/* - 1+ % =0 G (1) +

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(ii) either / % */0.=&+'*** or % * (>).***&+'*** e1uation(s) (1)% +/K. - 1* J y 1 % J - 1*+* (>)*/=2J subs / (1)

% * e /t (% =/KJ - 1*+*)% J - 1*+* eIp( +/K. - 1* J - .***)(% =/KJ - 1*+*) +

(d) (i) ratio % '/* (1) 1

(ii) original ratio +'* & +=. % '* - 1*+* &(J - 1*+*) % K (1)(ratio a#ter .*** years % ')e,ual numbers a#ter another .*** .*** % 1K*** years (1)so total time % .*** 1K*** % +2*** years (1) =

[12]

109. either number o# atoms o#' +De in 1/* kg % (1 & */**') - 0/*+ - 1*+= (% 1/J1 - 1*+0) (1)so total energy % 1/J1 - 1*+0 - +K/' - 1/0 - 1* 1. - 1*0 (1)

% 0/. - 1*1' _ (accept 0/K - 1*1' _) (1) =or mass o#' +De % ' - 1/02 - 1* +2 (% 0/0K - 1* +2 kg)so number o#' +De in 1/* kg % 1 & (0/0K - 1* +2) (% 1/J* - 1*+0) (1)and energy generated % 1/J* - 1*+0 - +K/' Ee4 (% '/+J - 1*== e4) (1)

% '/+J - 1*== - 1/0 - 1* 1. _ % 0/K - 1*1' _ (1) =

[3]

110. (a) e,uation11D +1D [ =+De ( energy) (1) 1

(b) (i) ke o# nuclei converted to (electric) potential energy (1)

all ke is converted (1) +

(ii) pe % (1/0 - 1* 1.) - (1/0 - 1* 1.) & (' - K/KJ - 1* 1+ - =/*2 - 1* 1=)correct charge subs/ (1) correct remaining subs/ (1)(% 2/J - 1* 10 _) +

(iii) initial momentum % #inal momentum or e,uivalent (1)

m u (+m) $ % * (sou % +$) (1) +

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112. (a) the splitting o# a nucleus into two (or more) smaller nuclei&particlesragments (spontaneously&a#ter absorption o# a neutron) 1

(b) +=J.+" 1*n [ 1'1 J0Ba .+=0Lr =1*n + % mark per error

(c) $ % c+ mR m % */1K0 u (% =/*. - 1* +K kg)R (+)$ % . - 1*10 - */1K0 - 1/00 - 1* +2 % +/2K - 1* 11 (_) (1) =

(d) F % kQ1Q+&r +R Q1 % J0e Q+ % =0eR (+)F % . - 1*. - J0 - =0 - (1/0 - 1* 1.)+&(1/= - 1* 1')+R % +/2(') - 1*= (3) (+) '

[10]

113. (a) B % F& l with symbols eIplained or appropriate statement in wordsR (1)eIplicit re#erence to and B at right angles&de#ine #rom F % BQv etc (1) +

(b) (i) arrow towards centre o# circle 1

(ii) #ield out o# paperR Fleming9s M/D/ rule&moving protons act asconventional current +

(iii) F % Bevallow

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114. @ helium nucleus X electron photon&eAm radiation&energy (1)@ charge (+e) mass 'm p&'u X charge (e) mass me charge * mass * (+)@ emission energy = 2 Ee4 X emission energy 1 + Ee4 emission energy about 1 + Ee4or all o# the same order o# magnitude&5G (1)@ monoenergetic #rom given nuclide X range o# emission energies #romgiven nuclide #rom 7ero to a maIimum monoenergetic #rom givennuclideor comparison in terms o# velocities (1)@ range = 2 cm o# air X range 1 + m o# air range inverse s,uarelaw in air& order o# kms (1)@ absorbed by paper X absorbed by thin& 1 mm 5l sheet up to cm o# Hb sheet (1)@ strongly ionising X weakly ionising hardly ionising at all (1)any other sensible comparison (1) 0

max # marks

Quality o# written communication +[8]

115. range&penetration&absorption&de#lection eIperiment suggested (1)but no &urther progress made to answer 1uestion otherwise+suitable arrangement and choice o# apparatusall can be shown on a diagram (+)

range&penetration&absorption eIperiment:@ place detector very close& +cm #rom sourceR measure count rate

use paper screen or move back to 1* cm or more measure count rateinterpret resultR contrast to background count level& other emissions#rom same source (=)

X place detector e/g/ 1* cm #rom source measure count rateadd thin sheets o# 5l until count drops to very low or almostconstant valueR interpret result (+)place detector e/g/ 1* cm #rom source measure count rateadd thin sheets o# Hb until count drops to very low&backgroundlevelR interpret result (+)max # marks

aliter de#lection eIperiment:needs vacuum #or @ eIperimentR (1)source #or radiation passes through region o# $A or BA #ieldR (1)de#lection or not o# particles detected by detector to distinguish emissionsR (1)

detail o# directionsRall 3 correct ' marks can only score maxo& % mark unless $acuum mentioned (+)amount o# curvature determines energy o# emissionRand nature o# particle (1)max # marks 0

Quality o# written communication +[8]

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116. Hlanets move in ellipses (Sun at one #ocus) (1)Hlanet sweeps out e,ual areas in e,ual times/ (1)Heriod+ @ radius= & 6+& r = % constant (1) =

[3]

117. (i) v&c % O & O (1)O % 0J0/= - 1* . - 0/1 & = - 1*K (ignore minus sign) (1)O % 1/== - 1* 1' m (1) =

(ii) Yraph: any ' points plotted correctly (1)

all correct (1) + (iii) graph: draw curve reasonable attempt (1) 1(iv) $ither point where star moves perpendicular to line o# sight (1) 1 (v) time % 2+ h W (1)h (ec# read value #rom their graph W 1 h) (1) 1

(vi) r %= (0/2 - 1* 11 - ' - 1* =* - \2+ - =0**]+& ' +) ec# (1)r % 2/2* - 1*. m ec# / (1) +(use o# t % 2+h 1&+)

[10]

118. correct re#erence to (1) 5" (1) parallaI o# (1) arcsecond(marks can be gained on labelled diagram) (1) +

[2]

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123. 'n$ 2 fro 3o eIperimental evidence& no physical evidence (1)State o# matter unknown& laws o# physics unknown (1)$nergies unreproducible& re#/ to very high temperature (1) +

[2]

124. pen: "niverse eIpands #or all time (1)Flat: eIpands to a limit (but never reaches it) (1)!losed: "niverse contracts& collapses back (1)re#erence to role o# gravity& critical density (1)Earks #or a/ can be gained on labelled diagram/ '

[4]

125. Do+ % 1 - 1* +0 - K - - 0/02 - 1* 11 & = (1)

Do % +/=0 - 1* 1K s 1 (1) +[2]

126. 1 each to a axi # of 7&

$lectrons are emitted #rom ! & (hot) cathode/6here is a high voltage between ! and 5 / or stated p/d/ 1*** 4

(so) electrons are accelerated towards 5 & anode/$lectrical energy becomes L$ (o# electron)/$lectrons undergo a sudden deceleration at 5 & collide with 5(Some o#) the L$ is converted to PArays & (electromagnetic) radiation6he PArays are produced by the deceleration & re#erence to bremsstrahlungPArays characteristic o# target produced)/

Eost o# the (kinetic) energy becomes heat & thermal energy/6he reason #or the vacuum/

ther good point (eg anode rotated & inner shell electron o# target atomknocked out & higher pd gives more penetrating PArays&higher energy photons)/ 2

[7]

127. (a) Mow energy PArays are absorbed by the skin & undesirable as can causedamage & greater ionising (1) 1

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(b) % *e fI (1) ln % ln o f I

o % *+J/*+J*e='2

(1) ln o % ln ='2 +J* - */*+J

o % 1/2. - 1*J Gm + (1) =

(c) H % - 5 (*)

H % ='2 - - (*/1* - 1* +)+ (1)H % 1/*. - 1* = G (1) +

(d) (i) H % 1K - 1** & */1J (1)

H % 1+*** G (1) +

(ii) 1+*** & 2/J - 1*12 (% 1/0 - 1* 1' _ % energy o# each electron) (1)*/J m v+ % 1/0 - 1* 1' (*)v % 1/. - 1*K ms 1 (1) +

(iii) tube current % 2/J - 1*12 - 1/0 - 1* 1. % */1+ 5 (1)4 - % 1+*** (1)4 %1+*** & */1+ % 1** *** 4 or 1** k4 (1) =

[13]

128. (a) density (o# medium) (1)

speed o# ultrasound (in the medium) (1) or any #actors that a##ect thespeed o# ultrasound in the medium e/g/ the Noung modulus +

(b) (i) blood:

# % (1/J. - 1*0 1/0= - 1*0)+ & (1/J. - 1*0 1/0= - 1*0)+ (*)# % 1/J' - 1* ' (1)muscle:# % (1/2* - 1*0 1/0= - 1*0)+ & (1/2* - 1*0 1/0= - 1*0)+ (1)# % '/' - 1* ' (1)so the medium is muscle (1) bald muscle gets *&' '

(ii) (s % u - t)

s % 1/J' - 1*= - +0/J - 1* 0 % */*'*K m (1)*/*'*K & + % */*+* m (1) +

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(iii) 1/J' - 1*= & =/J - 1*0 % O (1)'/' - 1* ' m (1) . J %? 7 m gets &ull credit i& %?3 penalised in (ii) +

[10]

129. (i) % 4&C % 1+&J* (1)% */+' 5 (1) +

(ii) Hower in primary % power in secondary & p4 p % s4 s (1)

p % */+' - 1+ & +=* % */*1+J 5 (1) +[4]

130. (a) (i) either (mass & massAenergy & energy o# separate nucleons) A (mass &massAenergy & energy o# whole nucleus) or 5GR

or energy needed to separate & split & break apart neutronsand protons (completely)R

or energy released when separate nucleons & protons andneutrons combine to #orm nucleusR

but 3 6 energy that binds & holds nucleus together 3 6 energy to break bonds between nucleons

8atoms9 gets * 1 (ii) either high binding energy (& nucleon) means greater

stability & less likely to #use or #issionor nuclides (tend to) move to & react towards the lowest

potential energy& highest binding energy (&nucleon)can be won in any o# ! " or Fe eIplanations or as separate statementR (1)1+

0! can undergo #usionR (1)+=J

.+" can undergo #issionR (1)1+

0! and +=J.+" are both unstable gets 1&+J0

+0Fe is stable & does not eIperience #ission or #usionR (1) '

(b) (i) either neutron that is at (thermal) e,uilibrium with medium &

substance & material through which it is passingor neutron whose (kinetic) energy is e,ual & comparable &

similar & to energy o# atoms & molecules through whichit is passing

or slow moving neutronor neutron having low (kinetic) energy & energy o# 1 1* e4R 1

(ii) +=J.+

" 1*n [ +=0

.+" LB neutrinoM gets ? (1) 1

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132. %ar$on : two eIamples protonR (1)neutronR (1)

= particles ,uoted including one wrong gets 1&+ only,uark composition: proton uudR (1)

neutron uddR (1)(aware consists o# = ,uarks unspeci#ied gets 1&+)stability: proton stable inside (stable) nucleusR (1)

proton possible decay & hal# li#e % 1*=+ years when #reeR (1)allow any hal& li&e N %?3? years

neutron stable inside (stable) nucleusR (1)neutron hal# li#e % 1*&1J minutes when #reeR (1) any 0

[6]

133. lepton : two eIamples: electronR (1) positronR (1)neutrinoR (1)any ' (+)(allow muon tauon)

= particles including one wrong gets 1 onlycomposition: #undamental (A no ,uark components)R (1)#orces: weak #orce & interactionR (1)

electron & positron A (also) electromagnetic & electrostatic #orceR (1)

where #ound: electron A in atom outside nucleus or in X

decayR (1) positron (rarely) emerging #rom (high mass) radioisotopes &in X decay & acceleratingAcolliding machinesR (1)neutrino A travelling in space eg #rom Sunor emitted (with electron & positron) in beta decayR (1)

allow 3!$ 8resulting #rom high energy particle collisions9 any 0[6]

134. (a) $ %u at no but i#u is 7ero then$ is proportional tot (1) provideda is constant (1) pV %nR2 not unless2 is in kelvin (1)

and bothn andV are constant ( R is a constant) (1) 5 % -$ yes i#$ is constant (1)

but all three terms can vary so proportion unlikely (1)then $ 6D$C i#$ is constant then 5 and - will also be constant

C 5 is proportional to - when going up hills o# di##erentgradient (at constant$) (1) D,EFDGD '

, % r +

yes ( is a constant and , is directly proportional tor +) (1) 2

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(b) graph must be a straight line (1)graph must go through the origin (1) +

[9]

135. (a) (i) radioactive implies the emission o# ionising radiation (1)

C emits alpha beta and gamma radiation (1) 1 (ii) n#clide re#ers to a particular nuclear structure (with a stated number

o# protons and neutrons) (1) 1 (iii) half(life is the (average) time taken #or the activity to #all to hal# its

original value (1) 1 (b)

time & hour activity o#material & B, activity o#nuclide) &B, activity o#nuclide* &B,* '0** '+** '**0 =21= ===' 3791+ =**+ +0'0 3561K +'=0 2100 336+' 1.K' 1667 317=* 101. 1=+= +.0

=0 1=== 1050 283(i) and (ii) +1** as #irst #igure to be #illed in #or nuclide) (1)

1002 (1)1*J* (1)idea o# subtraction #or nuclide* (1)correct values #or the ones given in nuclide* column (1) J

(c) sensible graph plotted (1)

eItrapolation done (1)value 2* W J hours (1) =

C , % , * e Ot (1)ln , % ln , * /t e/g/ when , % +.0 t % =* hJ/0.*' % J/..1J / - =* (1)*/=*11&=* % */*1**' % /O % ln +& / % 0./* h answers will vary slightly dependent on starting and#inishing times (1)

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(d) separate the two nuclides (be#ore starting the count) (1) by chemical means (i# possible) (1) +

C using a centri#uge or di##usion (i# isotopes)C sensible idea about shielding against one o# the emitted particles

(e) decay constants or hal# lives are di##erent (1)

hal#Ali#e at the start is approIimately that #or) (1)) decays more rapidly than* so a#ter a long time the hal#Ali#e is that #or* (1)in between it has a value intermediate between the two (which varies) (1) =

D,EFDGD 3

C dealt with mathematically along the lines o# two separate eIponential decays (1)when added together do not give an eIponential graph (1)with back up maths (1)

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