· Web view2021. 3. 14. · In part (b) the calculation of the radius of curvature was usually correct although some candidates did not use the correct mass value for the proton

Colonel Frank Seely School

Exampro A-level Physics (7407/7408) 3.2.1.3 Particles, antiparticles and photons

Name:

Class:

Author:

Date:

Time: 137

Marks: 112

Comments:

Page 1


Q1. Neutrons were discovered when beryllium, Be, was bombarded with alpha particles.

An alpha particle knocked a neutron out of a beryllium nucleus producing a carbon nucleus, C.

(a) Write down the equation that describes this reaction.

........................................................................................................................(2)

(b) (i) Describe the quark substructure of a neutron.

...............................................................................................................

...............................................................................................................(1)

(ii) Describe how the quark substructure of a meson differs from that of a baryon such as a neutron.

...............................................................................................................(1)

(Total 4 marks)

Q2. (a) State the name of the antiparticle of a positron.

........................................................................................................................(1)

(b) Describe what happens when a positron and its antiparticle meet.

........................................................................................................................

........................................................................................................................(2)

(Total 3 marks)

Page 2


Q3. The following is an incomplete equation for the decay of a free neutron.

(a) Complete the equation by writing into the space, the symbol for the missing particle.(2)

(b) Use the principles of conservation of charge, baryon number and lepton number to demonstrate that the decay is possible.

Conservation of charge ..................................................................................

Conservation of baryon number .....................................................................

Conservation of lepton number ......................................................................(3)

(Total 5 marks)

Q4.(a) (i) State two differences between a proton and a positron.

difference 1 ...........................................................................................

...............................................................................................................

difference 2 ...........................................................................................

...............................................................................................................

(ii) A narrow beam of protons and positrons travelling at the same speed enters a uniform magnetic field. The path of the positrons through the field is shown in Figure 1.

Sketch on Figure 1 the path you would expect the protons to take.

Page 3


Figure 1

(iii) Explain why protons take a different path to that of the positrons.

...............................................................................................................

...............................................................................................................

...............................................................................................................

...............................................................................................................

...............................................................................................................

...............................................................................................................(5)

(b) Figure 2 shows five isotopes of carbon plotted on a grid in which the vertical axis represents the neutron number N and the horizontal axis represents the proton number Z.Two of the isotopes are stable, one is a beta minus emitter and two are positron emitters.

Page 4


Figure 2

(i) Which isotope is a beta minus emitter?

...............................................................................................................

(ii) Which of the two positron emitters has the shorter half-life? Give a reason for your choice.

...............................................................................................................

...............................................................................................................

...............................................................................................................(3)

(c) A positron with kinetic energy 2.2 MeV and an electron at rest annihilate each other. Calculate the average energy of each of the two gamma photons produced as a result of this annihilation.

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................(2)

Page 5


(Total 10 marks)

Q5.Protons and pions are produced in a beam from a target in an accelerator. The two types of particles can be separated using a magnetic field.

(a) State the quark composition of

(i) a proton,

...............................................................................................................

(ii) a positive pion, π+

...............................................................................................................(2)

(b) A narrow beam consisting of protons and positive pions, all travelling at a speed of 1.5 × 107 m s–1 , is directed into a uniform magnetic field of flux density 0.16 T, as shown in the diagram.

(i) Calculate the radius of curvature of the path of the protons in the field.

...............................................................................................................

...............................................................................................................

...............................................................................................................

...............................................................................................................

...............................................................................................................

Page 6


...............................................................................................................

...............................................................................................................

(ii) Sketch, on the diagram above, the path of the pions from the point of entry into the field to the point of exit from the field.

(iii) If the magnetic field were increased, how would this affect the paths of the particles?

...............................................................................................................

...............................................................................................................

...............................................................................................................(7)

(Total 9 marks)

Q6.The circuit diagram shows a light-emitting diode connected in series with a resistor R and a 3.0 V battery of negligible internal resistance. The potential difference across the terminals of the diode is 2.0 V and the current through it is 10 mA. The diode emits photons of wavelength 635 nm.

(a) Calculate the resistance of R.

........................................................................................................................

........................................................................................................................

(b) Calculate the electrical power supplied to the diode.

........................................................................................................................

Page 7


........................................................................................................................

(c) Calculate the energy of a photon of wavelength 635 nm.

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

(d) Estimate the number of photons emitted per second by the diode.

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

(e) State an assumption you made in your estimation in part (d).

........................................................................................................................

........................................................................................................................(Total 8 marks)

Q7.An atom of argon is ionised by the removal of two orbiting electrons.

(a) How many protons and neutrons are there in this ion?

....................................... protons

...................................... neutrons(2)

Page 8


(b) What is the charge, in C, of this ion?

........................................................................................................................

........................................................................................................................(2)

(c) Which constituent particle of this ion has

(i) a zero charge per unit mass ratio,

...............................................................................................................

...............................................................................................................

(ii) the largest charge per unit mass ratio?

...............................................................................................................(2)

(d) Calculate the percentage of the total mass of this ion that is accounted for by the mass of its electrons.

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................(3)

(Total 9 marks)

Q8. (a) (i) Give an example of an exchange particle other than a W+ or W– particle, and state the fundamental force involved when it is produced.

exchange particle ................................................................................

fundamental force ...............................................................................

(ii) State what roles exchange particles can play in an interaction.

.............................................................................................................

Page 9


.............................................................................................................

.............................................................................................................(4)

(b) From the following list of particles,

p e+ μ– π0

identify all the examples of

(i) hadrons, .............................................................................................

(ii) leptons, …...........................................................................................

(iii) antiparticles, .......................................................................................

(iv) charged particles. ...............................................................................(4)

(Total 8 marks)

Q9. Under certain conditions a γ photon may be converted into an electron and a positron.

(a) What is this process called?

......................................................................................................................(1)

(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.

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

Page 10


(ii) Using values from the data sheet calculate this minimum energy in MeV.

.............................................................................................................

.............................................................................................................(3)

(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.

......................................................................................................................(1)

(Total 5 marks)

Q10. (a) An unstable nucleus, , can decay by emitting a β– particle.

(i) What part of the atom is the same as a β– particle?

.............................................................................................................(1)

(ii) State the changes, if any, in A and Z when X decays.

change in A .........................................................................................

change in Z ..........................................................................................(2)

(b) In the process of β– decay an anti-neutrino is also released.

(i) Give an equation for this decay.

.............................................................................................................(1)

(ii) State and explain which conservation law may be used to show that it is an

Page 11


anti-neutrino rather than a neutrino that is released.

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................(2)

(iii) What must be done to validate the predictions of an unconfirmed scientific theory?

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................(2)

(Total 8 marks)

Q11. (a) Hadrons are a group of particles composed of quarks. Hadrons can either be baryons or mesons.

(i) What property defines a hadron?

.............................................................................................................(1)

(ii) What is the quark structure of a baryon?

.............................................................................................................(1)

(iii) What is the quark structure of a meson?

Page 12


.............................................................................................................(1)

(b) State one similarity and one difference between a particle and its antiparticle.

similarity .......................................................................................................

......................................................................................................................

difference ......................................................................................................

.......................................................................................................................(2)

(c) Complete the table below which lists properties of the antiproton.

charge / C baryon number

quark structure

antiproton

(2)

(d) The K– is an example of a meson with strangeness –1. The K– decays in the following way:

K– → µ– +

(i) State, with a reason, what interaction is responsible for this decay.

.............................................................................................................

.............................................................................................................

.............................................................................................................

.............................................................................................................(2)

(ii) State two properties, other than energy and momentum, that are conserved in this decay.

.............................................................................................................

.............................................................................................................

Page 13


.............................................................................................................

.............................................................................................................(2)

(Total 11 marks)

Q12. (a) Pair production can occur when a photon interacts with matter. Explain the process of pair production.

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................(2)

(b) Explain why pair production cannot take place if the frequency of the photon is below a certain value.

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................(3)

(c) Energy and momentum are conserved during pair production. State two other quantities that must also be conserved.

........................................................................................................................

........................................................................................................................(2)

(Total 7 marks)

Page 14


Q13. (a) The table gives information about some fundamental particles.

Complete the table by filling in the missing information.

particle quarkstructure

charge strangene baryonnumber

uud 0

Sigma + uus + 1

ud 0 0

(7)

(b) Each of the particles in the table has an antiparticle.

(i) Give one example of a baryon particle and its corresponding antiparticle.

particle ..................................................................................................

antiparticle ............................................................................................(1)

(ii) State the quark structure of an antibaryon.

...............................................................................................................(1)

(iii) Give one property of an antiparticle that is the same for its corresponding particle and one property that is different.

Same ....................................................................................................

...............................................................................................................

Different ................................................................................................

...............................................................................................................(2)

(Total 11 marks)

Page 15


Q14.(a) Complete the table to show the four fundamental forces and their corresponding exchange particles.

fundamental force corresponding exchange particle

strong nuclear gluon

electromagnetic

W+W− Z0

gravitational graviton

(2)

(b) Name the physical quantity that a particle must have for the electromagnetic force to act on it.

........................................................................................................................(1)

(c) Name the particle believed to be responsible for mass.

........................................................................................................................(1)

(Total 4 marks)

Q15.(a) The positive kaon, K+, has a strangeness of +1.

(i) What is the quark structure of the K+?

...............................................................................................................(1)

Page 16


(ii) What is the baryon number of the K+?

...............................................................................................................(1)

(iii) What is the antiparticle of the K+?

...............................................................................................................(1)

(b) The K+ may decay into a neutrino and an antimuon in the following way.

K+ → vµ + µ+

(i) Complete the table using ticks and crosses as indicated in the first row.

Classification K+ vµ µ+

lepton × ✓ ✓

charged particle

hadron

meson

(3)

(ii) In this decay, charge, energy and momentum are conserved.Give another quantity that is conserved in this decay and one that is not conserved.

Conserved ............................................................................................

Not conserved .......................................................................................(2)

(c) Another possible decay of the K+ is shown in the following equation,

K+ → π+ + X

(i) Identify X by ticking one box from the following list.

Page 17


electron

muon

negative pion

neutral pion

neutrino

neutron

positron

(1)

(ii) Give one reason for your choice in part (i).

...............................................................................................................

...............................................................................................................

...............................................................................................................

...............................................................................................................(1)

(Total 10 marks)

Page 18


M1. (a) Be + α C + n

(condone N; any other symbol must be defined as a neutron)

B1

(Condone other symbols if Z and A correct)

B12

(b) (i) udd (1 up quarks and 2 down quarks)

B11

(ii) A meson has only two quarks(whereas a baryon has three)

B11

[4]

M2. (a) electron

B11

(b) they annihilate (condone disappear/destroy or eliminate eachother)

B1

forming (two) gamma ray(s)/radiation or photon(s)(i.e. condone singular)NOT just energy

B12

[3]

Page 19


M3. (a) any neutrino

C1

electron anti neutrino

A12

(b) 0 → 1 + (-1) + 0

B1

1 → 1 + 0 + 0

B1

0 → 0 + 1 + (-1)

B13

[5]

M4.(a) (i) including, for example:positron is an antimatter particle; proton is a matter particle (*)positron is a lepton; proton is a hadron (*)positron has a smaller rest mass than a proton (*)positron is not composed of other particles; proton is made up of quarks (*)(*) any two [1] [1]

(ii) proton path has greater radius of curvature than positron (1)

(iii) radius of curvature r = and υ, B and e are constants (1)

therefore r proportional to m (1)mass of proton is (much) greater than massof positron (at same speed) (1)

5

Page 20


(b) (i) C - 14 (1)

(ii) C - 10 (1)as this is furthest from stability (1)

3

(c) rest mass of electron = 0.51 MeV therefore total energy available= (2.2 +2 × 0.51)= 3.22 (MeV) (1)

gamma photons produced have average energy = = 1.6 MeV(1)2

[10]

M5.(a) (i) uud (1)

(ii) (1)2

(b) (i) = Bev [or r = ] (1)

m = 1.67 × 10-27 (1)

(1)

= 0.98 m (1)

(ii) pion path more curved than proton path (1)

(iii) path more curved [or radius (of path) smaller] (1) for both paths (1)

7[9]

M6.(a) VR = (3.0 – 2.0) = 1.(0) (V) (1)

R = = 100 Ω (1)

Page 21


(b) (use of P = IV gives) Pdiode (= 10 × 10–3 × 2.0) = 0.02(0) W (1)

(c) (use of c = fλ gives) ) = (4.7 × 1014Hz) (1)

(use of E = hf gives) E (= 6.63 × 10–34 × 4.7 × 1014) = 3.1 × 10–19 J (1) (allow C.E. for A.E. in value of f)

(d) energy supplied in 1 sec = 0.02(0) (J) (1) (allow C.E. for value of P from (ii))

number of photons emitted in 1 sec = = 6.5 × 1016 (1)

(allow C.E. for value of E)

(e) all the energy supplied converted to light energy [or 100% efficient] [or monochromatic light] [or all photons (emitted by LED) have the same energy] (1)

[8]

M7.(a) 18 (protons) (1) (37 – 18 gives) 19 (neutrons (1)

2

(b) (charge) = 2+ or 2– (1) Q = 2 × 1.60 × 10–19 = 3.2 × 10–19 (C) (1)

2

(c) (i) neutron (1)

Page 22


(ii) electron (1)2

(d) (2) (for correct nuclear mass and substitution)

(= 2.36 × 10–4) = 2.36 × 10–2 (%) (1)3

[9]

M8. (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]

M9. (a) pair production (1)1

Page 23


(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]

M10. (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

Page 24


(iii) hypothesis needs to be tested by experiment (1)

experiment must be repeatable (1)

or hypothesis rejected2

[8]

M11. (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

Page 25


(ii) any two

eg charge

baryon number

(muon) lepton number2

[11]

M12. (a) photon interacts with (orbital) electron/nucleus/atom

energy of photon used to create particle antiparticle pair

to conserve momentum photon needs to interact with interacting particle 2

(b) energy of photon depends on frequency

if energy/frequency is below a certain value there is not enough energy

to provide mass/rest energy of particles 3

(c) any two

eg charge

lepton number

baryon number

strangeness2

[7]

M13. (a)

Page 26


particle quark structure

charge strangeness baryon number

proton uud + 1 0 1

sigma+ uus +1 -1 1

π+ ud +1 0 0

7

(b) (i) examples:proton, antiquarks

1

(ii) consists of 3 antiquarks 1

(iii) same (rest) mass (energy)

difference eg baryon number/charge 2

[11]

M14.(a) Photon(right-hand box) TO for listingMust state name

Weak (nuclear) / weak interaction / weak nuclear interaction / weak force

B1(left-hand box) TO for listing

2

(b) Charge / (electric) charge

B1TO for listing any other physical quantity

Page 27


Must be word; do not accept symbol1

(c) Higgs (boson) / Higgs (particle) / Higgs (boson particle)Not graviton

Accept Higg / Higs / Hig

B1TO for listing

1[4]

M15.(a) (i) / up and anti-strange ✓In any orderBar must be over s only

1

(ii) 0 / zero / nothing ✓1

(iii) K– / negative kaon / ✓1

(b) (i)

classification K+ vμ μ+

lepton ✕ ✓ ✓

charged particle

✓ ✕ ✓

hadron ✓ ✕ ✕

meson ✓ ✕ ✕

1 mark for each correct row3

Page 28


(ii) conserved: baryon number OR lepton number ✓ not conserved: strangeness / kinetic energy ✓

Mass in either loses mark2

(c) (i) neutral pion ✓Indicated clearly in table in any way e.g. circled or cross. If more than one box used then must be a tick with neutral pion only

1

(ii) must be neutral / no charge / 0 charge to obey charge conservation OR cannot be baryon to obey conservation of baryon number OR cannot be lepton to obey conservation of lepton number ✓

Can show by using equation and appropriate quantum numbers

1[10]

Page 29


E1. (a) Responses here were very disappointing and relatively few correct answers were seen. The question demanded only conversion of a text description into an equation but many were unable to produce an equation with the correct particles in either side of the equation. Those who could often failed to insert correct Z and A numbers.

(b) (i) The structure was known by the vast majority of the candidates.

(ii) The majority knew the difference in substructure between a baryon and a meson.

E2. (a) The vast majority did this correctly. ‘Anti-positron’ was not an acceptable response.

(b) The majority knew that they annihilated (but few who tried to use the correct word could spell it). Many decided that disappear was an easier option. Relatively few appreciated that the result would be gamma radiation.

E3. (a) Most of the candidates identified the particle as a neutrino. Although many were able to say that it was an electron antineutrino, a lot missed the additional correct detail.

(b) Many candidates completed this part correctly but some had clearly not learned how to use the conservation laws to demonstrate the viability of the decay.

E4.Parts (a)(i) and (a)(ii) were found to be straightforward by most candidates, but only the best explained the ideas behind the trajectory with any rigour. This required the essential statement that B, v, and e are constants in the equation R = mʋ / Be.

Page 30


Part (b) discriminated well at the bottom end of the ability range.

Many more candidates than expected failed to include the rest mass of both particles in the total energy calculation in part (c).

E5.The majority of candidates were able to give the correct quark composition of the proton in part (a), but many were unable to give the correct quark composition of the positive pion, usually as a result of stating that the antiquark was strange.

In part (b) the calculation of the radius of curvature was usually correct although some candidates did not use the correct mass value for the proton. In part (ii) the majority of candidates knew the pion path was more curved and were thus able to score full marks. In the final part candidates often failed to state that the radius of curvature would be less for both types of particles.

E6.In part (a), a significant number of candidates obtained a value of 200 Ω or 300 Ω for the resistor through not using the correct pd across it. In part (b), the same candidates usually proceeded with an incorrect calculation of power in the diode by using in the expression I2R the resistance calculated in part (a). Some candidates were not aware of the correct value of the prefix m in mA.

The energy of the photon was usually calculated correctly in part (c), but a small minority wrongly considered 1 / λ as the frequency or used an incorrect equation. In part (d), most candidates knew how to proceed and gave a correct calculation. In the final part most candidates gave a correct assumption made in the previous estimation. Those candidates who were not specific in stating the assumption were not awarded this mark.

E7.Part (a) usually gave a good start to the majority of candidates. In part (b) there was an even split between candidates who gave the answer as +2 and those who gave the correct answer in coulombs. The final answer was also sometimes given a negative value. The results in part (c) were, in general, correct.

Page 31


In part (d) only the better candidates completed the calculation. The usual errors involved using the wrong number of electrons or nucleons or not using consistent mass units. In recent examinations it has been quite common for candidates to make errors when calculating percentages but in this question this error was not often seen.

E8. 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.

E9. 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.

E10. 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

Page 32


candidates’ responses suggest that they are quite familiar with the concept of validated evidence.

E11. 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.

E12. 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.

E13. 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

Page 33


particles and their corresponding antiparticle is rest mass.

E14.This question was well answered with most candidates scoring all 4 marks.

E15.This question on particles was well answered and not particularly discriminating. The majority of candidates were able to score high marks in parts (a) and (b) although less able candidates tended to lose a mark on the table, usually because they did not appreciate that a meson was a hadron.

Part (c) was less well done with only 54% of candidates identifying X correctly. The reason for their choice was also not well answered as many responses were far too vague. It was common to see statements such as ‘charge conservation’ but candidates were expected to write more of an explanation such as ‘X must be neutral so charge is conserved’. More able candidates wrote down the equation with appropriate quantum numbers and although not required, this was a sensible approach to adopt.

Page 34

Documents

· Web view2021. 3. 14. · In part (b) the calculation of the radius of curvature was usually correct although some candidates did not use the correct mass value for the proton