is constant of proportionality [or probability of decay] (1) [or is probability of decay (1) in unit time (1)] max 6

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1 PhysicsAndMathsTutor.com 1 1. (a) (i) which atom decays at what time is chance (ii) isotopes are (different forms) of same element same proton number, Z, different nucleon number, A [or with same number of protons but different number of neutrons] half-life is time for number of nuclei to halve [or to halve activity] for a particular isotope dn = N dt is constant of proportionality [or probability of decay] [or is probability of decay in unit time ] max 6 ln (b) (i) = = s (ii) N = = N (iii) ln 0 = t N ln t = = s = = 1(.4) (hour) max [1]. (a) (i) 38 9U Th (ii) m = = (u) Q = (MeV) = 4.3MeV 5 (b) (i) overall change in proton number (= 9 8) = 10 change in proton number due to particles (= 8 ) = 16 therefore Z = 6 for the particles corresponding to the six particles

2 PhysicsAndMathsTutor.com (ii) proton changes to a neutron plus a positron [or p n + + (+ v e + Q)] Pb-06 has a lower neutron to proton ratio than U-38 alpha emission raises the neutron to proton ratio slightly emission lowers the ratio (more) + emission increases neutron to proton ratio positron emission competes with emission but is energetically less favourable max 6 [11] 3. (a) m = (kg) (= kg electron masses are not significant) kinetic energy (= 1 m ) = ( ) (= J) (b) loss in k.e. = gain in p.e. loss of ke. [or ] = Qq 4 0 R Ze 4 0R 19 R = 79 ( ) = m 4 (c) any valid point including: strong force complicates the process (*) scattering caused by distribution of protons not whole nucleon distribution (*) particles are massive causing recoil of nucleus which complicates results (*) (*) any one 1 [7] 4. (a) (i) proton number = 36 neutron number = 56 (ii) krypton 3

3 PhysicsAndMathsTutor.com (b) one-fifth efficiency so total output (= 10 = 50(MW) 0 energy in one day = (J) ( J) 1 fission atoms per day = = [6] 5. (a) intensity of scattered electrons diffraction angle graph shows a minimum which does not touch the axis (b) the (de Broglie) wavelength of high energy electrons is comparable to nuclear radii [or not subject to the strong nuclear force] 1 (c) nuclear density is constant separation of neighbouring nucleons is constant [or nucleons are close-packed] R (d) A correct curve 1

4 PhysicsAndMathsTutor.com 4 (e) R = r 0 A 3 1 R A0 R c = Ac R 0 = m 3 [9] 6. (a) time for half of (active) nuclei (of radioactive substance) to decay 1 (b) t/minute number of counts in 30s, C ln C Correct values of ln C above 1 (c) (i) seven points correctly plotted [six points correct ] 4.5 graph of InC against time In C In C Linear (In C) Linear (In C) 3.5 y = 0.941x t/min (ii) best straight line through points sensible scale

5 PhysicsAndMathsTutor.com 5 (iii) from sensible triangle on graph gradient = [0.94] (min 1 ) (min 1 ) max 5 (d) (i) C = C 0 e t, ln C ln C 0 = t hence using y = mx + c, = ( )gradient (ii) half life = ln = 3 min (e) count over longer period than half minute [or repeat experiment] use stronger source use background count correctly max (f) for 14 C, = T 1 = (year) R 5. t ln ln = 0.3 R t = = 1840(year) [16] 7. (a) (i) 40 19K + e 40 18Ar + (e) (+Q) (ii) m = = u Q(= ) = 1.5(MeV) (iii) orbital electron vacancy due to electron capture outer electron fills vacancy and emits X ray photon max 5

6 PhysicsAndMathsTutor.com 6 (b) (i) 40 19K 40 0Ca + e + v (e) (ii) use of beta emission 8 times more probable than electron capture use of number of potassium atoms equals 5 times number of argon atoms leading to evaluation of 36% use of the decay equation correct answer for example: 14 atoms of K 40 originally becomes 8 atoms of Ca atom of Ar atoms K 40 unchanged 36% of K 40 not decayed use N = N 0 e t to give t = T 1 ln 0.36 ln = yr max 4 [9] 8. (a) (i) alpha (ii) two different track lengths short range particles have lower energy than long range particles particles in each range have same energy 4 (b) (i) Pu U + (+Q) (ii) 35 9U 31 90Th + (+Q) (iii) U 35 (iv) because of the inverse relationship between half life and alpha particle energy because the Th 90 nucleus is neutron rich compared with U 35 [or Pu 39] 5 [9]

7 PhysicsAndMathsTutor.com 7 9. (a) (i) T 1/ = 50 s (from graph) (ii) = ln 50 = 0.014s 1 (iii) N = A 0 = = (b) (i) elapsed time = 50s = 1 half-life N 30 = N 0 e 30 = e = no. decayed from t = 30s to t = 80s is = [alternative (b)(i) N 30 = N 0 e 30 and N 80 = N 0 e 80 give and number decayed (= ) = ] (ii) energy released = = J max 4 [9] 10. (a) N Z straight line between (Z = 0, N = 0) to (Z = 0, N = 0) curving upwards to Z = 80; N =

8 PhysicsAndMathsTutor.com 8 (b) (i) A = any region below the line of stability but N > 80and Z > 60 (ii) B = any region above and close to the line of stability (iii) C = any region below and close to the line of stability 3 (c) mode of decay change in proton number, Z change in neutron number, N emission emission emission 1 +1 e capture 1 +1 p emission 1 0 n emission 0 1 lose one mark for each row in error 3 [8] 11. (a) (R 3 3 = R0 A) plot R 3 against A with axes labelled units on axes scales chosen to use more than 50% of page element R/10 15 m A R 3 /10 45 m 3 carbon silicon iron tin lead calculate data for table plot data lose one mark for each error calculation of gradient

9 PhysicsAndMathsTutor.com e.g. gradient = 13 1 r 0 (= gradient) 3 = ( ) 3 45 (= m 3 ) = 1.1() m alternative: plot R against A 1/3 with axes labelled units on axes scales chosen to use more than 50% of page element R/10 15 m A A 1/3 carbon silicon iron tin lead calculate data for table plot data lose one mark for each error calculation of gradient 15 e.g. gradient = = (1.1() m 3 ) 6.0 r 0 = gradient = 1.1() m [or plot lnr against lna...] max 8 (b) assuming the nucleus is spherical ignoring the gaps between nucleons assuming all nuclei have same density assuming total mass is equal to mass of constituent nucleus any one assumption

10 PhysicsAndMathsTutor.com 10 M = 3 4 R 3 4 M R a 7 3m 3 4R = (1.110 ) 3 = kgm 3 4 [1] 1. (a) (i) (inner) orbiting electron [or electron surrounding the nucleus] captured by a proton (in the nucleus) converted into a neutron QWC (ii) daughter nuclide/nucleus/atom might be excited and energy given up as electromagnetic radiation [or orbiting electrons drop down to fill space (left by captured electron)] QWC (iii) 03Bi Pb (e) (+Q) [allow 0 e 1 for 1 + ] max 5 (b) (i) (use of N = N o e t and N activity gives) 90 = 100 exp( ) ln(100/ 90) = (= s 1 ) ln (ii) (use of T ½ = ln / gives) T ½ = = 4.(3) 10 4 s (= 11.(7) hr) (use of = s 1 gives T ½ = s or 1 hr) (iii) N (use of = N gives) ( )100 = ( ) N t N = 7.3() 10 7 (nuclei) (use of = s 1 gives N = (nuclei)) max 5 [10]

11 PhysicsAndMathsTutor.com (a) induced fission: (large) nucleus splits unto two (smaller nuclei) brought about by bombardment or collision thermal neutrons have low energies or speeds (< 1 ev) 3 (b) (i) N = 3 (ii) released neutrons have high(er) energies or speeds (iii) m = ( ) ( ) = u (if last term in m omitted or incorrect number of neutrons used in calculation, treat answer as C.E.) energy released = = 173 MeV (allow C.E. for m) 5 [8] 14. (a) (i) (radiation) (ii) (radiation) (b) (i) the radiation needs to pass through the body (to be detected) (ii) (otherwise) the activity of the source becomes too weak (during measurements) (iii) the decaying source may remain in the body for a long time and could cause damage [or the activity of the source will be low unless a large quantity is used (T 1/ 1/)] 3

12 PhysicsAndMathsTutor.com 1 (c) corrected count rate at 0. m (= ) = 500 (c min 1 ) corrected count rate at least distance (= ) = 5950 (c min 1 ) use of I I k o (or in the form I1 x x ) I x 1 (allow C.E. for using uncorrected count rate) 1/ gives least distance = least distance = 0.13 m 5 [10] 15. (a) (i) thick high density material giving minimal fatigue problems after irradiation any other sensible property e.g. withstands high temperature any two (ii) (reinforced) concrete 3 (b) effect of shielding: rays - intensity (greatly) reduced neutrons - some absorption (or speed or energy reduced by collisions) neutrinos - very little effect why shielding becomes radioactive: neutron absorption by nuclei or atoms makes nuclei (not particles) neutron rich or unstable become emitters and/or emitters max 4 QWC [7] 16. (a) (use of isotope instead of nucleus not accepted) there is equal probability of any nucleus decaying, it cannot be known which particular nucleus will decay next, it cannot be known at what time a particular nucleus will decay, the rate of decay is unaffected by the surrounding conditions, it is only possible to estimate the proportion of nuclei decaying in the next time interval any two statements () QWC

13 PhysicsAndMathsTutor.com 13 (b) continuous curve starting at Bq plus correct 1st half-life (.6 yrs, Bq correct nd half-life (5. years, Bq) (allow C.E. for incorrect 1st half-life) (c) (i) (use of T 1/ = ln ln gives) = = (s 1 ) ( (s 1 )) (ii) dn (use of = N gives) N = 9 dt = (atoms) (allow C.E, for value of from (i)) 5 (iii) (use of N = N 0 e t and A N gives) t 5 5 ln( A 0 / A ln( / = = (s) (allow C.E. for value of from (i)) 6 [10] 17. (a) (i) C B A Z X A correct arrows: A B C (ii) e 1 + A Z X A Z 1Y + v e 4

14 PhysicsAndMathsTutor.com 14 (b) (i) (( ) ) = (J) (ii) (J) (J) for 3 correct values (J) 13 (iii) (use of E = hf gives) f = Hz (allow C.E. from (b)(ii)if largest value taken) 3 (c) (i) (for each precaution with reason to max ) (ii) handle with (long) (30 cm) tweezers because the radiation intensity decreases with distance store in a lead box (immediately) when not in use to avoid unnecessary exposure to radiation [or any sensible precaution with reason] QWC γ rays are more penetrating and are therefore more hazardous (to the internal organs of the body) β particles are more hazardous because they are more ionising (for any argued case for either radiation) 3 [10] 18. (a) 10 (on grid: first arrow to start from 8 Pb; arrows must be consecutive; 06 last arrow must end on 8 Pb) arrow showing the change for an emission arrow showing the change for a emission correct and two emissions in any order (b) (positron emission) 9 Cu 8 Ni v e (+Q) (electron capture) 64 9 Cu e 8 Ni + v (e) (+Q) 4

15 PhysicsAndMathsTutor.com 15 (c) (the following examples may be included) particles coulomb/electrostatic/electromagnetic repulsion [or K.E. converted to P.E. (as particle approaches nucleus)] information: any of the following: proton number, nuclear charge, upper limit to nuclear radius mass of nucleus is most of the mass of atom [alternative (high energy) electron (scattering) diffraction of de Broglie Waves by nucleus information: any of the following: nuclear radius, nuclear density ] 3 QWC [10] 19. (a) (i) origins of background radiation: cosmic rays ground, rocks and buildings air nuclear weapons testing/nuclear accidents nuclear power discharge/waste from nuclear power medical waste any three any two (ii) (use of C = C 0 e t gives) (84 3) = (110 3) e 600 ln(107/ 81) 600 = 4.6(4) 10 4 (s 1 ) (iii) (use of dn = N gives) N = 107 dt = (nuclei) (allow C.E. for value of from (ii) 7

16 PhysicsAndMathsTutor.com 16 (b) radiation is highly ionising, hence causes cancer/damage cells/ DNA/kill cells outside: less damage plus reason (e.g. absorbed by dead skin some s directed away from body) [or reference to burning] inside: more damage plus reason (e.g. all s absorbed living tissue will absorb radiation can reach vital organs) 3 QWC 1 [10] 0. (a) graph to show: electron intensity decreasing with angle of diffraction to a non-zero first minimum (b) (i) last column of table completed correctly with either or A 1/ R 3 /(10 45 m 3) axes cover more than 50% of graph sheet all points plotted correctly using labelled axes (i.e. x-axis A 1/3, y-axis R/10 15 m or x axis A, y-axis R 3 /10 45 m 3 ) (ii) gradient = r 0 [or gradient = r 0 3 ] gives r 0 = (1.1 ± 0.1) m 5

17 PhysicsAndMathsTutor.com 17 (c) electrons are not subject to the strong nuclear force (so) electron scattering patterns are easier to interpret electrons give greater resolution [or electrons are more accurate because they can get closer] [or particles cannot get so close to the nucleus because of electrostatic repulsion] electrons give less recoil (high energy) electrons are easier to produce [or electrons have a lower mass/ larger Q/m, so easier to accelerate] (in Rutherford scattering) with particles, the closest distance of approach, not R is measured max 3 QWC 1 [10] 1. (a) graph passes through N = 10/11 when Z = 10 and N increases as Z increases N = when Z = 80 and graph must bend upwards (b) (i) W at Z > 60 just (within one diagonal of a square) below line (ii) X just (within one diagonal of a square) above line (iii) Y just (within one diagonal of a square) below line 3 (c) working showing the change due to emission of four α particles four β particles

18 PhysicsAndMathsTutor.com 18 (d) Any two from the following list of processes: β + describe the changes to N (up by 1) and Z (down by 1) [or allow p change to n] α move closer to line of stability [or state the proton to neutron ratio is reduced] p only if nuclide is very proton rich [or electrostatic repulsion has to overcome the strong nuclear force] [or highly unstable] [or rare process] e capture describe the changes to N (up by 1) and Z (down by 1) allow p changes to n marking: listing two processes discussing each of the two processes 3 QWC 1 [10]. (a) reasons: α particle has much more mass/momentum than β particle α particle has twice as much charge as a β particle α particle travels much slower than a β particle any two QWC 1 (b) (i) energy absorbed per sec (= energy released per sec) = = (J) ( (J)) energy absorbed in 1minute (ii) temperature rise in 1 minute mass specificheatcapacity = (for numerator) (for denominator) = 0.90 K (or C) (allow C.E. for incorrect value in (i)) 5 [7] 3. (a) R (= r 0 A 1/3 ) = (38) 1/3 = 8.0(6) m

19 PhysicsAndMathsTutor.com 19 (b) (use of inverse square law e.g. I1 x I x 1 gives) 10 = x 0.03 x = m ( m) (c) (use of A = A o exp( t gives) 0.85 = 1.0 exp ( 5) 1n(100/ = 3.1(3) 10 3 s 1 3 (d) it only emits γ rays relevant properties of γ radiation e.g. may be detected outside the body/weak ioniser and causes little damage it has a short enough half-life and will not remain active in the body after use it has a long enough half-life to remain active during diagnosis the substance has a toxicity that can be tolerated by the body it may be prepared on site any three 3 [10] 4. (a) graph passes through N = 100 to 130 when Z = 80 and N = 0 when Z = 0 (b) (i) W at Z > 60 just below line (ii) X just above line (iii) Y just below line 3 (c) fission nuclei (or fragments) are neutron-rich and therefore unstable (or radioactive) neutron-proton ratio is much higher than for a stable nucleus (of the same charge (or mass)) β particle emitted when a neutron changes to a proton (in a neutron-rich nucleus) 3

20 PhysicsAndMathsTutor.com 0 (d) The marking scheme for this part of the question includes an overall assessment for the Quality of Written Communication (QWC). There are no discrete marks for the assessment of written communication but the quality of written communication will be one of the criteria used to assign the answer to one of three levels. Level Good 3 Modest Limited 1 Descriptor an answer will be expected to meet most of the criteria in the level descriptor answer supported by appropriate range of relevant points good use of information or ideas about physics, going beyond those given in the question argument well structured with minimal repetition or irrelevant points accurate and clear expression of ideas with only minor errors of spelling, punctuation and grammar answer partially supported by relevant points good use of information or ideas about physics given in the question but limited beyond this the argument shows some attempt at structure the ideas are expressed with reasonable clarity but with a few errors of spelling, punctuation and grammar valid points but not clearly linked to an argument structure limited use of information or ideas about physics unstructured errors in spelling, punctuation and grammar or lack of fluency 0 incorrect, inappropriate or no response 0 Mark range examples of the sort of information or ideas that might be used to support an argument: reduction of greenhouse gas emissions is (thought to be) necessary to stop global warming long term storage of radioactive waste is essential because the radiation from it damages (or kills) living cells radioactive isotopes with very long half lives are in the used fuel rods nuclear power is reliable because it does not use oil or gas from other countries radioactive waste needs to be stored in secure and safe conditions for many years

21 PhysicsAndMathsTutor.com 1 conclusion either nuclear power is needed; reduction of greenhouse gases is a greater problem than the storage of radioactive waste because 1 global warming would cause the ice caps to melt/sea levels to rise safe storage of radioactive waste can be done or nuclear power is not needed; storage of radioactive waste is a greater problem than reduction of greenhouse gases because 1 radioactive waste has to be stored for thousands of years greenhouse gases can be reduced using renewable energy sources [14] 5. (a) number of gamma photons per second = (= ) area of sphere of radius 1.50m (= 4πr = 4π 1.5 ) = 8.3m number of gamma photons per sec per cm = (= 1(.)) 3 (b) (i) decay constant = ( ln ) = s 1 t / 5 ( ) new no. of gamma photons per sec per cm = 1(.) e = 15(.0) (or 6 hours is 0.5 half-lives source activity decreases to 0.5 of initial activity in this time new no. of gamma photons per sec per cm = 1(.) 6/1 = 15(.0) ) (ii) any two of the following points beta particle range in air is less than 1.5m beta particle absorbed by air beta particles lose energy in air more rapidly than gamma photons beta particles ionise air much more than gamma photons 5 [8]

molar mass = 0.239kg (1) mass needed = = kg (1) [7]

molar mass = 0.239kg (1) mass needed = = kg (1) [7] PhysicsAndMathsTutor.com 1 1. (a) (i) proton number 82 and nucleon number 214 (ii) Pb 2 (b) (i) kinetic energy [or electrostatic potential energy] (ii) m = 8.6 E 2 c 1 10 = 8 2 (10 ) = 9.6 10 0 kg [5]