Particle Physics HW Questions 409 minutes 405 marks Q1.An atom of calcium, , is ionised by removing two electrons. (i) State the number of protons, neutrons and electrons in the ion formed. protons............................................ neutrons........................................... electrons.......................................... (3) (ii) Calculate the charge of the ion. charge ........................................... C (1) (iii) Calculate the specific charge of the ion. specific charge ................................... C kg −1 (2) (Total 6 marks)
Transcript
Particle Physics HW Questions
409 minutes
405 marks
Q1.An atom of calcium, , is ionised by removing two electrons.
(i) State the number of protons, neutrons and electrons in the ion formed.
specific charge ................................... C kg−1
(2)(Total 6 marks)
Q2.A positron is emitted from a nucleus when a proton changes to a neutron in the nucleus.The Feynman diagram for the quark interaction is shown in the diagram below.
(a) Identify the particles labelled A, B, C and D in the diagram.
A ....................................................
B ....................................................
C ....................................................
D ....................................................(3)
(b) (i) State the interaction responsible for this process.
(c) Energy and momentum have to be conserved in this process. State two other quantities that need to be conserved and show that they are conserved in the process.
Q3.(a) Hadrons and leptons are two groups of particles.Write an account of how particles are placed into one or other of these two groups.Your account should include the following:
• how the type of interaction is used to classify the particles
• examples of each type of particle
• details of any similarities between the two groups
• details of how one group may be further sub-divided.
The quality of your written communication will be assessed in your answer.
(b) An unstable isotope of neodymium, , decays into an isotope of cerium, Ce, by emitting an α particle.
(i) Complete the following decay equation.
(1)
(ii) The α particle is emitted from a stationary nucleus at a speed of 9.3 × 106 m s−1. Calculate the recoil speed of the daughter nucleus.
recoil speed ........................... ms−1
(2)
(iii) Show that, when a stationary nucleus decays, the kinetic energy of the recoiling cerium nucleus is only about 3% of the kinetic energy of the emitted α particle.
(ii) Calculate the number of neutrons in this isotope.
answer = .....................................(3)
(Total 10 marks)
Q9. (a) Protons can interact with electrons by gravity and by two other fundamental interactions. In the following table identify these interactions and name the exchange particle involved.
(ii) In the space below draw a Feynman diagram representing electron capture.
(3)
(Total 9 marks)
Q10. The diagram shows the path of an α particle deflected by the nucleus of an atom.Point P on the path is the point of closest approach of the α particle to the nucleus.
Which one of the following statements about the α particle on this path is correct?
A Its acceleration is zero at P.
B Its kinetic energy is greatest at P.
C Its speed is least at P.
D Its potential energy is least at P.(Total 1 mark)
Q11. (a) The table gives information about some fundamental particles.
Complete the table by filling in the missing information.
Q19. Under certain circumstances, a photon moving through a material can interact with the nucleus of an atom of the material to produce an electron and a positron.
(iii) Make use of the Data and Formulae booklet to show that the minimum energy of the photon required for this process is 1.02 MeV.
(1)
(iv) Photons whose wavelength exceeds a certain value will not cause this process.Calculate the maximum wavelength for the process to occur stating your answer to an appropriate number of significant figures.
Q20. (a) The photoelectric effect suggests that electromagnetic waves can exhibit particle-like behaviour. Explain what is meant by threshold frequency and why the existence of a threshold frequency supports the particle nature of electromagnetic waves.
The quality of your written communication will be assessed in this question.
(c) The theoretical work of Dirac suggested that for every particle there should exist a corresponding antiparticle. The first to be antiparticle to be discovered was the positron.
(b) (i) Explain why there is a minimum energy of the γ photon for this conversion to take place and what happens when a γ photon has slightly more energy than this value.
(c) Under suitable conditions, a γ photon may be converted into two other particles rather than an electron and positron.Give an example of the two other particles it could create.
specific charge = 4.0 × 106 C kg−1 Allow 1.66Allow CE from (ii)First mark is for mass if miss out electron mass and do not justify lose first mark
2[6]
M2.(a) A = down B = W+ C = positron and D= (electron) neutrino
symbols OKNOT neutronC and D either way round
3
(b) (i) weak 1
(ii) B / W(+) 1
(iii) W+ / B / exchange particle is charged / γ no charge OR W+ / B / exchangeparticle has (rest) mass / γ has zero (rest) mass OR photon has infinite range
exchange particle must be clearly identifieddon’t accept W+ more mass or shorter range
1
(c) Any two pairsQuantity: lepton number e+(−1) + v(e)(1) = 0 after same as before Quantity: charge u( +2/3) before 1−d(1 / 3) = +2 / 3 after decay Quantity: baryon number proton 1 and neutron 1 (can be shown through quarks)
can use p(+1) and e+(+1)to show charge conservedEach number must be correctly linked to a particle at least once for second markStrangeness not allowed
4[10]
M3.(a) The candidate’s writing should be legible and the spelling, punctuation and grammar
should be sufficiently accurate for the meaning to be clear.The candidate’s answer will be assessed holistically. The answer will be assigned to one of three levels according to the following criteria.
High Level (Good to excellent): 5 or 6 marksThe information conveyed by the answer is clearly organised, logical and coherent, using appropriate specialist vocabulary correctly. The form and style of writing is appropriate to answer the question.
Top BandBoth have rest massMention electromagnetic interaction Correct quark structure of mesons and baryonsBoth hadrons and leptons interact/decay through weak interactionFor 6 marks must have last two points
Candidate gives correct examples of hadrons and leptons. Identifies the differences between hadrons and leptons (hadrons affected by strong nuclear reaction and are made of quarks). Leptons are fundamental and do not experience the strong nuclear reaction. Hadrons are divided into baryons and mesons. Baryons three quarks, mesons quark anti-quark pair. Similarities between groups all experience weak interaction and if charged the electromagnetic interaction. All have rest mass.
Intermediate Level (Modest to adequate): 3 or 4 marksThe information conveyed by the answer may be less well organised and not fully coherent. There is less use of specialist vocabulary, or specialist vocabulary may be used incorrectly. The form and style of writing is less appropriate.
Middle bandOnly hadrons experience strong nuclear interaction (need this to get in middle band)Hadrons are mesons or baryons. Examples of each
Candidate gives correct examples of hadrons and leptons. Identifies one difference between hadrons and leptons (e.g. hadrons affected by strong nuclear reaction or are made of quarks). Leptons are fundamental. Hadrons are divided into baryons and mesons.
Low Level (Poor to limited): 1 or 2 marksThe information conveyed by the answer is poorly organised and may not be relevant or coherent. There is little correct use of specialist vocabulary. The form and style of writing may be only partly appropriate.
Lower band1 or 2 correct facts about hadrons leptons eg Leptons are fundamental / hadrons made of quarks
Identifies two correct properties of hadrons and leptons.
The explanation expected in a competent answer should include a coherent selection of the following points concerning the physical principles involved and their consequences in this case.example of hadron and leptonmention of strong interactionmention of quark structure hadronsleptons are fundamentalidentify baryons and mesonsgives quark structure of baryons and mesonssimilarities e.g. all have rest massall affected by weak interactionif charged both experience electromagnetic interaction
6
(b) (i) a correct example of particle e.g. electronand correct example of antiparticle e.g. positron
Allow correct symbolsAllow antielectron for positronAlso allow pi zero and gamma
1
(ii) correct difference e.g. opposite charge/other named quantum number must be consistent with (i)
1[8]
M4.(a) (i) neutron accept symbolssymbols e.g. n
1
(ii) electron accept symbols
1
(iii) neutron accept symbols
1
(b) (i) antineutrino V (e)
1
(ii) A=99 Z= 44
2
(iii) specific charge = 43 × 1.6 × 10−19 / 99 × 1.66 × 10−27 specific charge = 4.2 × 107 C kg−1
Correct answer no working −1If include mass of electrons lose 2 and 3 mark
4[10]
M5.(a) (i) three OR qqq1
(ii) mesons 1
(iii) experience the strong interaction made up of quarks OR not fundamental (eventually) decay to proton
2 max
(b)
interaction exchange particle
electromagnetic (virtual)photon OR
weak W+ or W −or Z(0)
W must have superscript2
(c) (i)
If no arrow on W boson line then must be clearly slanting in correct direction for second marke must have - superscriptIf no clear junctions lose second markIf no arrows on sides −1
3
(ii) lepton number must be conserved (+1 on lhs must be +1 on rhs)
1[10]
M6.(a) Similarity: momentum is conserved (in both cases)
Difference: kinetic energy is conserved in an elastic collision but not in an inelastic collision
For 2 nd mark allow ke is only conserved in elastic collision, or ke is not conserved in an inelastic collision.
2
(b) (i) in the Ce nucleus A = 140 Z = 58 and for α A = 4 and Z = 2 All four correct values required
1
(ii) 0 = 140 v – 4 × 9.3 × 106 Allow 140 v = 4 × 9.3 × 106 for 1stmark.Allow ecf from values in (b)(i).
gives v = 2.6 (6) × 105 (m s−1) Allow inclusion of mass of 58 electrons in recoil atom when shown.
Ekof Ce = ½ × 140 × 1.66 × 10−27 × (2.66 × 105)2 (= 8.22 × 10 −15 J)
= 0.0286 or 2.86% For 3rd mark, answer must be evaluated to at least 2SF (3% alone is insufficient); note that use of vd = 2.7 × 10 5 m s−1 gives 0.0295 or 2.95%.
[or gives = 0.0286 or 2.86% ]Allow ecf from values in (b)(ii).
[or = = 0.0286 or 2.86% ]When ecf is applied, 3rd mark is only available for answers between 2.5% and 3.5%.
3[8]
M7. (a) (i) quark antiquark pair OR qq OR named quark antiquark pair 1
(ii) 0 1
(iii) us 1
(b) (i) Weak any of the following also score 1 mark:
weak interaction
weak interaction force
weak nuclear
weak nuclear interaction
weak decay
weak force
weak nuclear force1
(ii) conserved: baryon number, charge, lepton number, spin
not conserved: strangeness 3
(iii) K – → π0 + e– + v(e)
OR K– → π0 + µ– + v( µ )
2[9]
M8. (a) (i) nucleon number is the number of protons and neutrons OR mass numberproton number is the number of protons OR atomic number
(v) will encounter an electron and the two particles will annihilate (1)
releasing (two high energy/gamma) photons/quanta (1)2
[10]
M20. (a) The candidate’s writing should be legible and the spelling, punctuationand grammar should be sufficiently accurate for the meaning to beclear.
The candidate’s answer will be assessed holistically. The answer will beassigned to one of the three levels according to the following criteria.
High Level (good to excellent) 5 or 6 marks
The information conveyed by the answer is clearly organised, logical andcoherent, using appropriate specialist vocabulary correctly. The form andstyle of writing is appropriate to answer the question.
The candidate provides a comprehensive and coherent description whichincludes a clear explanation of threshold frequency and why this cannot beexplained by the wave theory. The description should include a clearexplanation of the photon model of light and this should be linked to theobservations such as threshold frequency, the lack of time delay ormentions 1 to 1 interaction, the could not be explained by the wave model.
Intermediate Level (modest to adequate) 3 or 4 marks
The information conveyed by the answer may be less well organised andnot fully coherent. There is less use of specialist vocabulary, or specialistvocabulary may be used incorrectly. The form and style of writing is lessappropriate.
The candidate provides an explanation of threshold frequency and workfunction. The candidate explains the photon model of light and how this can
provide an explanation of threshold frequency, eg relates energy of photonto frequency or talks about packets of energy.
Low Level (poor to limited) 1 or 2 marks
The information conveyed by the answer is poorly organised and may notbe relevant or coherent. There is little correct use of specialist vocabulary.The form and style of writing may only be partly appropriate.
States what is meant by photoelectric effect. Knowledge of photons/packetsof energy.
The explanation expected in a competent answer should include acoherent account of the significance of threshold frequency and howthis supports the particle nature of electromagnetic waves.
• threshold frequency minimum frequency for emission of electrons
• if frequency below the threshold frequency, no emissioneven if intensity increased
• because the energy of the photon is less than the work function
• wave theory can not explain this as energy of waveincreases with intensity
• light travels as photons
• photons have energy that depends on frequency
• if frequency is above threshold photon have enough energy
• mention of lack of time delaymax 6
(b) (i) use of Ek =
½ × 6.6 × 10–27 (1) × v2 = 9.6 × 10–13 (1)
v2 = 2.91 × 10–14 (or v = √2.91 × 10–14) (1)
(v = 1.7 × 107 m s–1)3
(ii) (use of p = mv)
p = 6.6 × 10–27 × 1.7 × 107 (1)
p = 1.1 × 10–19 (1) kg m s–1/N s (1)3
(iii) (use of λ = )
λ = 6.63 × 10–34/1.1 × 10–19 (1)
λ = 5.9 × 10–15 m (1) (6.03 × 10–15 m)2
[14]
M21. (a) neutrino (1)1
(b) proton number = 10 (1)
nucleon number = 22 (1)2
(c) baryon = neutron (1)
lepton = positron (1)
lepton = neutrino (1)3
(d) ddu and uud (1)1
(e)
–1 for each error3
[10]
M22. (a) repulsive then attractive (1)
short range (if distance quoted must be of order fm) (1)
correct distance for cross over (accept range 0.1 – 1.0 fm) (1)3
(b) (i) a helium nucleus (accept 2p and 2n) (1)1
(ii) (↓92↑238) U → (↓90↑234)Th(+↓2↑4)α (1)2
(c) (i) same atomic number/proton number (1)
different number of neutrons/nucleons (1)2
(ii) evidence of subtraction of mass number or atomic number (1)
(thus atomic number decreases to) 76 (1)
(atomic number of lead is 82 therefore) 6 (82 – 76) beta decays (1)3
[11]
M23. (a) (i) particles that experience the strong (nuclear) force/interaction (1)1
(ii) particles composed of three quarks (1)1
(iii) particles composed of a quark and an antiquark (1)1
(b) similarity: but the same (rest) mass or rest energy (1)
difference: opposite quantum states eg charge (1)2
(c)
charge/C baryon number
quark structure
antiproton –1.6 × 10–19 –1
–1 for each error2
(d) (i) weak interaction (1)
strange not conserved or there is a change/decay of quark(flavour) (1)
2
(ii) any two
eg charge
baryon number
(muon) lepton number2
[11]
M24. (a) (i) an electron (1)1
(ii) change in A = 0 (1)
change in Z = +1 (1)2
(b) (i) (1)
or n → p + e– +
or d → u + e– + 1
(ii) lepton number must be conserved (1)
lepton number before decay equals zero
hence after decay lepton number of electrons cancels with lepton
number of anti-neutrino or zero on both sides (1)2
(iii) hypothesis needs to be tested by experiment (1)
(1)(1)(1) if all correct – lose one for each error
(ii) the proton (1)4
[8]
M27. (a) n (1)p (1)ve (1)
3
(b) (i) γ photon (1)
(ii) γ is masslessγ has infinite rangeγ does not carry charge
(1)(1) any two3
(c) (i) all properties/quantum numbers (e.g. charge, strangeness)are opposite (1)
but the masses are the same (1)
(ii) π° (1)
(1)
γ (1)5
[11]
M28. (a) (i) 94 (protons) (1)
(ii) 145 (neutrons) (1)
(iii) 93 (electrons) (1)3
(b) same number of protons[or same atomic number] (1)
different number of neutrons/nucleons[or different mass number] (1)2
[5]
M29. (a) pair production (1)1
(b) (i) the γ ray must provide enough energy to providefor the (rest) mass (1)any extra energy will provide the particle(s) withkinetic energy (1)
(ii) (0.511 + 0.511) = 1.022 (MeV) (1)3
(c) any pairing of a particle with its corresponding
antiparticle (e.g. p + ) (1)1
[5]
M30. (a) n + v(e) (1)(1)
μ– (1)
K+ (1)4
(b) d → u + β– + v(e) (1)(1)2
(c) (i) weak interaction (1)
(ii) lepton (1)
(iii) electromagnetic and gravitational (1)3
[9]
M31. (a) (1)1
(b) 2e (1)
= (2 × 1.6 × 10−19) = 3.2 × 10−19 C (1)2
(c) (1)
= 4.1(1) × 107 C kg−1 (1)2
[5]
M32. (a) (i) Z0 with the weak interactiongluons or pions with the strong nuclear forceγ photons with electromagnetic interactiongravitons with gravity(any exchange particle (1) and corresponding interaction (1))
(ii) transfers energytransfers momentumtransfers force(sometimes) transfers charge any two (1)(1)
4
(b) p π0 (1)
Vee+µ− (1)
e+ (1)
pe+µ− (1)4
[8]
M33. (a) (atoms with) same number of protons/same atomic number (1)different number of neutrons/mass number/ nucleons (1)
2
(b) (i) 7 protons (1)8 neutrons (1)
(ii) (1)
= 4.5 × 107 (C kg–1) (1) (4.47 × 107 (C kg–1))(allow C.E. for incorrect values in (b) (i))
correct number of quarks and antiquarks in each (1)4
[7]
E1.This question required a knowledge of atomic structure and specific charge and part (i) was unsurprisingly, extremely well answered.
Part (ii) caused more problems with a significant proportion of candidates either giving a charge equivalent to 20e or 18e. The calculation of specific charge has often proved to be quite discriminating with the specific charge of an ion causing candidates the most problems. On this occasion candidates performed slightly better partly due to them having been asked for the charge in part (ii) and not being penalised when carrying their answer into part (iii).
A significant proportion of candidates completely ignored the mass of the electrons and although their mass does not significantly alter the specific charge they were required to include it or to justify it being disregarded.
E2.Feynman diagrams often prove to be somewhat discriminating and in line with this, the performance in this question was quite patchy. On this occasion candidates were not required to draw or complete a diagram and this tends to make the question more accessible.
In practice less than 50% of candidates were able to correctly identify the particles with the commonest errors being the identification of the positron and the neutrino – confusion with β−decay being the most frequent mistake.
Parts (b) (i) and (ii) were very well answered but this was not the case with (b) (iii). Less than 40% of candidates were able to give a difference between the exchange particle and a photon or gave one word answers such as charge or mass. Their responses were required to be completely clear, matching a stated property with the relevant exchange particle or photon.
Most candidates were able to state two other conserved quantities in part (c) but the demonstration of conservation were often less convincing. As with part (b) (iii) there was often a lack of clarity with things such as lepton number, charge or baryon number not being related to particular particles.
E3.This question on particle classification generated some very impressive responses. Many candidates proved to be quite confident in their extended writing and top band answers were seen more frequently than has been the case in the past, particularly when questions refer to the photoelectric effect or line spectra
The main confusion that weaker candidates seem to have was an appreciation of which groups are affected by the strong nuclear force – a significant proportion seemed to think that this was only baryons
The most common omission in good answers was the identification of a similarity between hadrons and leptons. Overall however, the question worked well and candidates clearly enjoy this aspect of the specification and evidence for this is found in the confidence shown in many of the answers.
E4.This question was concerned with atomic structure and radioactive decay. The majority of candidates did not really have any problems with part (a) which required them to identify the
constituents of the atom and state which had the largest specific charge.
The performance in part (b) was not quite as strong although only 25% of candidates had real issues with the equation for beta decay. The weakest answers were seen in (b) (iii) which required a specific charge calculation. Questions on this topic tend to be quite discriminating and this was certainly the case this time. Common mistakes were the use of incorrect masses for the technetium nucleus and dividing the mass by the charge rather than the charge by the mass. The unit for specific charge seemed to be well known although a significant minority gave the incorrect answer: coulomb.
E5.Part (a) of this question required candidates to understand the classification and quark structure of hadrons. This proved to be very accessible and well over 90% of candidates were able to state how many quarks there were in a baryon and were also familiar with mesons. When it came to properties of hadrons the majority were able to state one property but only about half were able to come up with two properties. A common error was to state the same property twice, an example of this being: hadrons interact by the strong interaction and leptons interact with the weak interaction. It was also quite common to see answers that referred to baryon numbers and this was not an acceptable answer as hadrons do not all have the same baryon number.
In part (b) candidates were required to identify the exchange particle in two interactions. A high proportion of candidates were able to identify one of these but only about half were able to give two correct exchange particles. Many lost marks with the weak interaction exchange particle by omitting the relevant charge (W+ or W-).
Part (c) was concerned with electron capture. Candidates were required to draw a Feynman Diagram that represented electron capture. Full marks for this were comparatively rare and common errors were the omission of arrows on the lines representing the proton, the electron, the neutron and the neutrino or the omission of an arrow on the exchange particle. The latter was only penalised if the candidates showed the exchange particle horizontally (when an arrow pointing in the correct direction was required). The final part of this question on lepton conservation was well answered. The only consistent error seen was when less able candidates tried to explain this in terms of charge conservation.
E6.In part (a) the expected responses were references to the conservation of momentum and to whether kinetic energy was conserved in the two types of collision. The facts were generally well known and answers were well rewarded. It was essential to refer to kinetic energy when writing about the difference. Most candidates also completed the α decay equation correctly in part (b). When errors were made in part (b)(i), marks were still available in part (b)(ii) by correct use of the nucleon number values written down in part (b)(i). A common error here was use of 144 for the nucleon number of the daughter nucleus. This was regarded as a physics error and so no marks could be credited for part (b)(ii).
There was a large number of possible routes to a successful answer in part (b)(iii), where a ratio of kinetic energies was required. For all three marks to be awarded the final evaluation of the percentage had to be worked out to at least two significant figures, so that it had been shown to be not exactly 3%. A few candidates quoted the ratio of the speed of the nucleus to the speed of the α particle as the final answer. This ratio turns out to be correct, but full marks were only awarded when the ratio was shown to be the ratio of kinetic energies.
E7. Students seemed quite familiar with the quark structure of mesons and were able to deduce the quarks found in the K−meson successfully. The questions relating to the Feynman Diagram were well answered and full marks were quite frequently awarded. A significant minority however, did have problems interpreting the information given to produce a correct equation of the decay as required in part (b)(iii).
E8. This proved to be one of the most accessible questions on the paper with many students securing full marks. The majority of explanations of nucleon number, proton number and isotope were clear although a minority did confuse number of neutrons with number of protons in there definition of isotope. The calculations and deductions pertaining to the nucleus and one of its isotopes were in the main well set out and in many cases this helped generate correct answers. A minority, as has been the case in previous sessions, did include the mass of electrons in the specific charge calculation even though the question clearly refers to a nucleus.
E9. The quark structure of the proton was well remembered but this was not the case with interactions and their associated exchange particles. A surprising number of students were unable to provide two consistent examples. Mixtures such as strong interaction and W+ were relatively common. It was also clear that a significant proportion of students were unfamiliar with the process of electron capture. A common problem seemed to be a misunderstanding of where the electron in the interaction comes from. The Feynman diagram proved to be quite discriminating but students who took a bit of care were generally more successful.
E10. This question was a re-banked question but the improvement in its facility was much less marked: from 62% to only 64% in fact.
E11. Previous papers have indicated that students have a good understanding of the quark structure of hadrons and this was certainly the case in this examination. The table in part (a) was completed well and full marks were frequent. The remainder of the question was also answered well and students now seem well aware that a similarity between particles and their corresponding antiparticle is rest mass.
E12. Part (a) was answered well and the evidence suggests that specific charge is a topic that is now much better understood. It has often been found in previous papers that explanations which go beyond standard definitions usually produce considerable discrimination.
This was certainly the case in part (b) (i) and it was quite common for less able students to write confused and contradictory answers. A common mistake was to assume that X and Y were isotopes. Some students also thought that the question was about ions rather than nuclei.
Part (b) (ii) produced better responses although the route to a candidate’s final answer was sometimes difficult to follow. A significant number of students gave answers with no working which is bad practice; especially for a question allocated four marks.
E13. This question was generally answered well although, while students explained the basics of pair production, it was quite rare for them to mention the necessity for the photon to interact with a nucleus. Momentum was referred to by some of the more able students, but this was more often related to the particle and antiparticle after production, rather than the initial photon.
The remainder of this question was answered well, with students confidently explaining why the frequency of the photon must not be below a certain value. They also were able to select appropriate quantities that need to be conserved during the process of pair production.
E14. This question was answered well and provided limited discrimination between candidates. Most were able to successfully identify two baryons and also deduce the quark structure of the pion, π+. Less able candidates found it hard to identify which of the K+ decays in part (b)(ii) were possible and they provided explanations that were not convincing.
Part (c) was answered very well with the majority able to identify the weak interaction and correctly apply charge and baryon conservation. Most candidates were well aware that the proton is the most stable baryon.
E15. This question was more discriminating. The majority of candidates were able to state what is meant by isotopes. However, less able candidates found it hard to complete the equation for alpha decay and the calculation for specific charge of the alpha particle also caused them problems.
A significant number of poor responses were seen to part (iv), these were mainly the result of the alpha particle being considered in isolation rather than describing the short range of the strong interaction and linking this to the effect of the nucleus, Y, on the alpha particle.
E16. Part (a) required candidates to complete the equation for positron decay and the majority were able to do this successfully. The only common error was the inclusion of an antineutrino rather than neutrino and confusion with β-- decay.
Parts (b)(i) and (ii) caused far more problems and the majority of candidates did not identify the decay as electron capture and were then unable to explain where the electron came from – most seeming to think that it was a free electron. The remainder of this question was answered well and many candidates were able to explain the conservation of lepton number and to successfully complete the
Feynman diagram. However, there was sometimes confusion over the exchange boson and some candidates did omit arrows from the lines representing the products of the decay.
E17. This question was answered well and candidates’ demonstrated a clear understanding of the distinction between baryons and leptons. The most common examples of these particles given were protons and electrons although a significant minority successfully opted for more exotic particles. When stating the difference between hadrons and leptons some candidates responded saying that hadrons experienced the strong nuclear force but then spoilt their answer by not contrasting this with leptons or by saying leptons experience the weak interaction. Although the latter statement is true, it is not a property exclusive to leptons.
The Feynman diagram in part (b) was well understood. Many candidates provided a stated conservation law using clear before and after statements. This made it a straightforward task to follow their logic.
E18. This question proved accessible to candidates of all abilities and consequently was not particularly discriminating. Some candidates did struggle to identify the particle with the highest specific charge, with a significant minority opting for the proton. The equation for β was answered well, although it was not uncommon to see an equation representing changes in quark flavours rather than showing what happened to the nucleus as a whole. The antineutrino was the most common omission in the equations given.
Part (b) was answered well with the majority of candidates opting for a mass number between 220 and 230.
E19. This question on pair production suggested that while candidates are for most part, familiar with the process they do have the tendency to become confused when more details are required. The majority correctly identified the process and were able to use lepton or charge conservation effectively to explain why a positron must be produced along with the electron. They did however, find the quantitative aspect more of a challenge and it was not uncommon to see overcomplicated answers or no attempt made to answer part (iii).
The calculation for maximum wavelength in part (iv) was answered well by the more able candidates but others found this difficult. Common errors were not converting rest mass energy to joules and the use of energy as momentum when the equation for the de Broglie wavelength was used in error. Good answers to part (v) were frequently seen, although some candidates are under the impression that the positron annihilates with the electron produced rather than another electron.
E20. Descriptive questions on the photoelectric effect have in the past caused candidates major problems, it was therefore good to see so many confident answers this series. There was strong evidence that the concept of threshold frequency is now understood much better. Many candidates correctly explained the term and also were able to give a detailed explanation of its significance in the particle model of light. The one to one interaction and lack of time delay in the emission of electrons was also explained well in a high proportion of answers. Some good responses were not fully developed however, as they did not contrast the behaviour of photons with the behaviour of waves. This question also assessed the quality of written communication and most answers were well structured and expressed with clarity and precision.
The calculations in part (b) were answered well, although some less able candidates were unable to correctly use the equation for kinetic energy. There was a dedicated mark for the unit of momentum in part (ii) and, as is often the case, candidates found this a difficult unit to recall.
E21. This question was well answered and candidates’ demonstrated a clear understanding of quark structure and were able to identify particles as baryons or leptons successfully. The only common error arose when there was confusion between β– and β+ decay. This resulted in candidates giving the wrong proton number and also incorrectly identifying an antineutrino as a lepton formed due to the decay. The questions on the quark structure of protons and neutrons and the Feynman diagram for the interaction were answered well by the majority of candidates.
E22. Candidates found part (a) quite challenging. The majority recognised that the strong interaction is repulsive at small distances and attractive at larger distances. However, many candidates tended to either not give quantitative answers or quoted distances that were not acceptable. Answers were often muddled making them difficult to interpret. Although many candidates stated the interaction was short range, it was frequently not clear what they understood by this. Responses such as ‘the force decreases to a small value’ were common.
Part (b) was answered much better and the majority of candidates identified the nature of the alpha particle, completed the equation correctly and explained what is meant by isotopes. The final part of the question was quite discriminating and it was clear that the better candidates found the deduction quite straightforward, arriving at a correct answer with the minimum of working.
E23. This question was well answered and candidates’ responses suggested that the structure of hadrons is well understood. In part (a), less able candidates tended to give specific examples for baryons and mesons rather than their general quark structure. They also stated that the defining property of hadrons was that they were composed of quarks despite the fact that this was stated in the stem of the question.
Responses to part (b) were generally good although some did state that particles and antiparticles had different charges rather than opposite charges.
The table in part (c) did cause a significant proportion of candidates’ problems. The most common error was to identify the charge of the antiproton as –1 even though the unit, C, was given in the heading of the table.
Part (d) was answered confidently although a significant proportion of candidates did seem to think that strangeness was conserved in this decay.
E24. This question was well answered and candidates seemed confident in their understanding of beta decay. They were for the most part well aware of the changes that occur during the decay. The equation for beta decay was only awarded one mark and a few candidates lost this mark due to careless errors such as missing out the bar on the anti-neutrino. There were many impressive explanations of why a neutrino was not produced, providing evidence of a good understanding of the conservation of lepton number.
Part (b) (iii) assessed candidates understanding of how science works and many candidates’ responses suggest that they are quite familiar with the concept of validated evidence.
E28. Over 50% of the candidates lost one or more marks on this easy opening question. The most common error was giving the wrong number of electrons, by mistakenly taking the charged ion as a neutral atom. Also, a worrying number of candidates did not answer part (b) correctly because they were confused between neutrons and protons. Many candidates did not refer to the number of protons when discussing isotopes but simply stated that isotopes were the same atom with different numbers of neutrons.
E29. A significant minority of candidates failed to score at all because they thought the whole question was set on the photoelectric effect. In part (b), only about a third referred to the fact that energy was required to create mass and even fewer said that the excess energy appeared as kinetic energy. Instead, candidates stated that more particles/different photons/heat etc was
given out or else they wrote that the process could not go ahead unless the energy had a specific value. Part (c) was more successfully tackled, but a minority gave the two emitted particles as anything they could associate together, e.g. β and ν or n and p.
E30. Part (a) discriminated very well and served to separate candidates who simply guessed from those who looked for something like conservation of charge, and from those who looked more carefully at everything, including the subscripts.
Part (b) proved to be difficult. Less able candidates did not appreciate what changes occurred in 3 decay and only the more able candidates could convert the nucleon change to a quark change. In part (c) many scored two or three marks. They lost marks by leaving out gravity as a possible force. A number of candidates failed completely on this part of the question by making reference to the strong nuclear force. To end on a more positive note, almost all candidates knew that an electron was a lepton.
E31. Answers to this question generated many errors. Less than 50% of the candidates gained full marks for what was really an easy starter question. In part (b), the incorrect answer of +4e appeared very frequently and likewise, in part (c), the incorrect inclusion of the electron mass was a very common occurrence. Additionally, calculation errors, failure to give the correct units and significant figure errors all contributed to an overall poor performance.
E32. Normally the question concerning fundamental forces and particles is answered well, but this time very few candidates scored full marks. Part (a) (i) gave rise to very few problems to the prepared candidate, but in part (a) (ii), the usual answer gave only one role played by the exchange particles in the interaction, thereby losing a mark by omitting to give a second role. Another common error was to suggest that the exchange particle somehow gave energy or momentum to the interaction, rather than transferred energy or momentum.
More able candidates had no trouble with part (b), but the less able candidates failed badly by not identifying all the examples given. The π0 particle was accepted as a possibility for an antiparticle, being its own antiparticle, but it does not appear as a required answer.
E33. Less able candidates failed on part (a) primarily because of statements such as ‘there are less neutrons in an isotope’, rather than stating that the number is different.
In part (b) (i), some candidates included electrons contained in the nucleus. As in previous examinations, the calculation of charge-to-mass ratio in part (b) (ii) often had just a ratio of 7/15
without the correct multiplying factors. Finally, many candidates did not realise that the ion had an imbalance of charge corresponding to the magnitude of the electronic charge. What was intended as a relatively easy opening question caused a majority of candidates to lose at least one mark.
E34. Responses to this question were slightly examination centre dependent. In part (a), a majority of candidates thought strangeness was conserved and, consequently, invented the strangeness number for each particle to conform with this idea. The other frequently seen error was for candidates not identifying the relevant quantum numbers but simply stating, without justification, which conservation laws were valid.
Part (b) discriminated quite well with about 50% of candidates obtaining the correct quark combinations and only about 10% failing to attempt the question.
E35. Responses to this question were slightly examination centre dependent. In part (a), a majority of candidates thought strangeness was conserved and, consequently, invented the strangeness number for each particle to conform with this idea. The other frequently seen error was for candidates not identifying the relevant quantum numbers but simply stating, without justification, which conservation laws were valid.
Part (b) discriminated quite well with about 50% of candidates obtaining the correct quark combinations and only about 10% failing to attempt the question.
