1
(a)
Complete the following equation for beta minus (β−) decay of
strontium-90 (
Sr) into an isotope of yttrium (Y).
(3)
(b)
During β− decay of a nucleus both the nucleon composition and the quark composition
change.
State the change in quark composition.
........................................................................................................................
(1)
(c)
A positive kaon consists of an up quark and an antistrange quark
. This kaon decays
by strong and weak interactions into three pions. Two of the pions have quark compositions
of
(i)
. The third pion has a different quark composition.
Name the unique family of particles to which the kaon and pions belong.
...............................................................................................................
(1)
(ii)
Tick the box corresponding to the charge of the third pion.
positive
negative
neutral
(1)
(iii)
Positive kaons have unusually long lifetimes.
Give a reason why you would expect this to be the case.
...............................................................................................................
...............................................................................................................
(1)
(iv)
Name the exchange particles which are involved in the strong and weak interactions
of the kaon.
strong interaction ......................................
weak interaction ......................................
(1)
(Total 8 marks)
Page 1 of 25
2
Leptons, mesons and baryons are three classes of sub-atomic particles.
(a)
Some classes of particles are fundamental; others are not. Circle the correct category for
each of these three classes.
leptons
fundamental/not fundamental
mesons
fundamental/not fundamental
baryons
fundamental/not fundamental
(1)
(b)
Name the class of particles of which the proton is a member.
........................................................................................................................
(1)
(c)
By referring to the charges on up and down quarks explain how the proton has a charge of
+1e.
........................................................................................................................
........................................................................................................................
........................................................................................................................
(2)
(Total 4 marks)
3
(a)
State the combination of quarks that makes up a neutron.
........................................................................................................................
(1)
(b)
When a neutron decays, a down quark changes into an up quark as shown by the following
reaction.
d→u+
(i)
Show, in terms of the conservation of charge, baryon number and lepton number, that
this transformation is permitted.
(3)
(ii)
State the products arising from the decay of an anti-down quark,
.
...............................................................................................................
...............................................................................................................
(1)
(Total 5 marks)
Page 2 of 25
4
A radium-288 nuclide (
) is radioactive and decays by the emission of a β– particle to form
an isotope of actinium (Ac).
(a)
Complete the equation for this decay.
(3)
(b)
β– decay is the result of a neutron within a nucleus decaying into a proton. Describe the
change in the quark sub-structure that occurs during the decay.
........................................................................................................................
........................................................................................................................
........................................................................................................................
(1)
(Total 4 marks)
5
A negative pion (π−) is a meson with a charge of −1e.
State and explain the structure of the π− in terms of up and down quarks.
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
(Total 3 marks)
6
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)
Page 3 of 25
(ii)
Describe how the quark substructure of a meson differs from that of a baryon such as
a neutron.
...............................................................................................................
(1)
(Total 4 marks)
7
(a)
State the quark substructure of a neutron.
........................................................................................................................
(2)
(b)
Circle the terms below that can be used to describe a neutron.
antiparticle
baryon
fundamental
particle
hadron
lepton
meson
(2)
(Total 4 marks)
8
Electron capture may occur inside a radioactive atom to stabilise its nucleus. The electron
combines with a proton to form a neutron.
(a)
Complete the equation below for electron capture in argon-37.
(3)
(b)
How does the quark substructure of the neutron compare with that of the proton?
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(3)
(Total 6 marks)
Page 4 of 25
9
A carbon-14 nucleus undergoes β– decay, forming a new nucleus, releasing a β– particle and one
other particle which is difficult to detect.
(a)
Write down the proton number and the nucleon number of the new nucleus.
proton number ...............................................................................................
nucleon number .............................................................................................
(b)
Name the particle which is difficult to detect.
........................................................................................................................
(c)
Name the baryons and leptons involved in the decay.
baryons ...........................................................................................................
leptons .............................................................................................................
(d)
Give the quark structure for the neutron and the proton.
neutron ...........................................................................................................
proton .............................................................................................................
Hence state the quark transformation that occurs during β– decay.
........................................................................................................................
(Total 7 marks)
10
State the differences in quark structure between a meson and a baryon.
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
(Total 2 marks)
11
(a)
Give the number of nucleons and the number of electrons in an atom of
Na.
nucleons ..............................................
electrons ..............................................
(2)
Page 5 of 25
(b)
The isotope Na is a positron emitter. In positron emission an up quark undergoes the
following change,
u → d + β+ + ve.
Show that charge, lepton number and baryon number are conserved in this decay.
charge ...........................................................................................................
lepton number ..............................................................................................
baryon number ..............................................................................................
(3)
(c)
Describe what happens when a positron collides with an electron.
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 7 marks)
12
(a)
(i)
How do hadrons differ from all other subatomic particles?
...............................................................................................................
...............................................................................................................
(ii)
Give the quark composition of the following particles.
neutron .................................................................................................
neutral pion ...........................................................................................
...............................................................................................................
(iii)
Classify the following as either leptons, baryons or mesons.
kaon ......................................................................................................
muon .....................................................................................................
(5)
(b)
Which is the most stable baryon?
........................................................................................................................
(1)
Page 6 of 25
(c)
This table may be useful in answering the questions which follow.
particle
baryon
number
lepton number
strangeness
π–
0
0
0
p
1
0
0
p
–1
0
0
e–
–1
0
0
e+
0
1
0
νe
0
–1
0
The particle X, which is a strange particle, decays in the following way:
X → π– + p
(i)
State whether X is a meson, a baryon or a lepton.
...............................................................................................................
(ii)
Use conservation laws to decide whether each of the following decays of the π– is
possible. Give a reason for your answer.
(A)
π– → e+ + νe
Is this decay possible? ........................................................
reason ...................................................................................................
(B)
π– → p + e– + e+
Is this decay possible? ........................................................
reason ...................................................................................................
(5)
(Total 11 marks)
Page 7 of 25
13
(a)
Quarks may be combined together in a number of ways to form sub-groups of hadrons.
Name two of these sub-groups and for each, state its quark composition.
sub-group 1 ..................................................................................................
......................................................................................................................
sub-group 2 ..................................................................................................
......................................................................................................................
(3)
(b)
A free neutron is an unstable particle.
(i)
Complete the following to give an equation that represents the decay of a neutron.
n→
(ii)
Describe the change that occurs to the quark structure when a neutron decays.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(4)
(Total 7 marks)
14
The equation represents the collision of a neutral kaon with a proton, resulting in the production
of a neutron and a positive pion.
K° + p
(a)
n + π+
Show that this collision obeys three conservation laws in addition to energy and
momentum.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(3)
Page 8 of 25
(b)
The neutral kaon has a strangeness of +1.
Write down the quark structure of the following particles.
K° ..............................................
π+ ...............................................
p .................................................
(4)
(Total 7 marks)
15
Leptons, mesons and baryons are three classes of sub-atomic particles.
(a)
Some classes of particles are fundamental; others are not. Circle the correct category for
each of these three classes.
Leptons
Mesons
Baryons
fundamental/not fundamental
fundamental/not fundamental
fundamental/not fundamental
(1)
(b)
Name the class of particles of which the proton is a member.
......................................................................................................................
(1)
(c)
By referring to the charges on up and down quarks, explain how the proton has a
charge of + 1e.
......................................................................................................................
......................................................................................................................
(2)
(Total 4 marks)
16
(a)
The Σ+ particle is a baryon with strangeness –1.
(i)
How many quarks does the Σ+ particle contain?
.............................................................................................................
.............................................................................................................
answer ..........................
(1)
Page 9 of 25
(ii)
How many of the quarks are strange?
.............................................................................................................
.............................................................................................................
answer ..........................
(1)
(b)
The Σ+ decays in the following reaction
Σ+ → π+ + n
(i)
State two quantities that are conserved in this reaction.
.............................................................................................................
.............................................................................................................
(2)
(ii)
State a quantity that is not conserved in this reaction.
.............................................................................................................
(1)
(iii)
What interaction is responsible for this reaction?
.............................................................................................................
(1)
(iv)
Into what particle will the neutron formed in this reaction eventually decay?
.............................................................................................................
(1)
(Total 7 marks)
17
(a)
Name three types (or flavours) of quark.
........................................................................................................................
........................................................................................................................
(2)
Page 10 of 25
(b)
By referring to the charges on quarks, explain why the neutron is uncharged.
........................................................................................................................
........................................................................................................................
(2)
(Total 4 marks)
18
(a)
Give the name of a particle that is a hadron.
......................................................................................................................
(1)
(b)
Pions are mesons.
Give a possible quark structure for a pion.
......................................................................................................................
(1)
(Total 2 marks)
19
(a)
The table gives information about some fundamental particles.
Complete the table by filling in the missing information.
particle
quark
structure
charge
uud
Sigma +
uus
strangene
baryon
number
0
+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)
Page 11 of 25
(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)
20
Which of the following is not true?
A
Each meson consists of a single quark and a single
antiquark.
B
Each baryon consists of three quarks.
C
D
The magnitude of the charge on every quark is
A particle consisting of a single quark has not been observed.
(Total 1 mark)
Page 12 of 25
Mark schemes
1
(a)
(90,39)
B1
(0,-1)
B1
B1
3
(b)
d u
or
Number of u quarks increases by 1 and number of d quarks decreases by 1
B1
1
(c)
(i)
Meson
Do not allow hadron
B1
1
(ii)
Negative box ticked
B1
1
(iii)
Characteristic of particles with strange quarks / they contain the strange quark /
they have strangeness
B1
1
(iv)
Gluon, W (+ or -) ( boson) or Zo
B1
1
[8]
2
(a)
lepton fundamental
meson, baryon not fundamental
allow underline or crossing out wrong options
B1
(1)
(b)
(i)
baryon / hadron
B1
(1)
Page 13 of 25
(ii)
uud
B1
= +1(e)
B1
(2)
[4]
3
(a)
d+d+u
B1
(1)
(b)
(i)
conservation of charge: –1 / 3 = +2 / 3 + (–1) + 0
B1
conservation of baryon number: 1 / 3 = 1 / 3 + 0 + 0
B1
conservation of lepton number: 0 = 0 + (+1) + (–1)
B1
(3)
(ii)
anti up–quark plus positron plus electron neutrino
B1
(1)
[5]
4
(a)
Ac
B1
β
B1
suitable anti - neutrino indication (anti - neutrino not required)
B1
(b)
Down quark changes to up quark
B1
[4]
5
2 quarks
M1
down and anti-up
A1
–1 / 3 + (–2 / 3) = – 1
A1
[3]
Page 14 of 25
6
(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)
B1
2
(b)
(i)
udd (1 up quarks and 2 down quarks)
B1
1
(ii)
A meson has only two quarks
(whereas a baryon has three)
B1
1
[4]
7
(a)
Three quarks mentioned; at least one u, one d
C1
udd A1
2
(b)
hadron
B1
Baryon
B1
2
[4]
Page 15 of 25
8
(a)
Electron
0, –1
correct positions
B1
Chlorine
37,17
B1
Neutrino symbol (ν or υ or similar)
Not anti-neutrino
B1
3
(b)
reference to both up and down quarks
C1
reference to 3 quarks per nucleon
C1
proton: uud, neutron: udd
A1
3
[6]
9
(a)
7,14 (1)
(b)
(anti) neutrino (1)
(c)
proton, neutron (1)
electron, (anti) neutrino (1)
(d)
udd (1)
uud (1)
d → u (1)
[7]
Page 16 of 25
10
meson has 2 quarks; baryon has 3 quarks/3 antiquarks
B1
good extra detail
B1
[2]
11
(a)
22 (nucleons) (1)
11 (electrons) (1)
2
(b)
charge: +
=–
+ 1 + 0 (1)
lepton number: 0 = 0 – 1 + 1 (1)
baryon number:
=
+ 0 + 0 (1)
3
(c)
the electron and the positron are annihilated (1)
photon(s)/ ray(s) are produced (1)
specifying two ( ) photons/rays (1)
masses converted into energy (1)
max 2
[7]
12
(a)
(i)
hadrons (are not fundamental) are composed of quarks
[or hadrons may interact through the strong nuclear force
(as well as all the other interactions)] (1)
(ii)
(neutron) udd (1)
(neutral pion)
(iii)
(1)
(kaon) meson (1)
(muon) lepton (1)
5
(b)
proton (1)
1
Page 17 of 25
(c)
(i)
(X) baryon (1)
(ii)
(a)
not possible (1)
charge not conserved (1)
(allow C.E. from previous line)
(b)
not possible (1)
baryon number not conserved (1)
(allow C.E. from previous line)
5
[11]
13
(a)
baryon
antibaryon
meson
qqq
qqq
qq
two names (1)
composition of each sub-group (1) (1)
3
(b)
(i)
n → p (1)
(ii)
a down (d) quark changes to an up (u) quark
[or udd changes to uud] (1)
+
(1) +
(e)
(1)
4
[7]
14
(a)
baryon number 0 + 1 = 1 + 0 (1)
lepton number 0 + 0 = 0 + 0 (1)
charge 0 + 1 = 0 + 1 (1)
3
(b)
K°
(1)
π+
(1)
p
udu (1)
correct number of quarks and antiquarks in each (1)
4
[7]
Page 18 of 25
15
(a)
lepton fundamental
meson, baryon not fundamental
allow underline or crossing out wrong options (1)
1
(b)
(i)
baryon/hadron (1)
(ii)
u u d (1)
+
+
–
= + 1(e) (1)
3
[4]
16
(a)
(i)
three (1)
one (1)
2
(b)
(i)
charge (1)
baryon number (1)
lepton number (1)
mass (1)
energy (1)
momentum (1)
max 2
(ii)
strangeness (1)
(iii)
weak interaction/(nuclear) force (1)
(iv)
proton (1)
5
[7]
Page 19 of 25
17
(a)
up, down, strange (allow charm, top, bottom)
any two (1) any three (1)(1) (not u, d, s etc)
B2
2
(b)
udd (1)
B1
+2/3(e) -1/3(e) -1/3(e) (1)
B1
2
[4]
18
(a)
one named hadron or obvious symbol
B1
1
(b)
d /u /u / u or words
B1
1
[2]
19
(a)
particle
proton
sigma+
π+
quark
structure
uud
uus
ud
charge
+1
+1
+1
strangeness
0
-1
0
baryon
number
1
1
0
7
(b)
(i)
examples:
proton, antiquarks
1
(ii)
consists of 3 antiquarks
1
Page 20 of 25
(iii)
same (rest) mass (energy)
difference eg baryon number/charge
2
[11]
20
C
[1]
Page 21 of 25
Examiner reports
1
2
4
(a)
This was generally well done. Common errors were to neglect to identify the antineutrino or
indicating that it was an electron antineutrino. There was a significant proportion who wrote
the equation as for positron decay.
(b)
Fewer than half the candidates realised that the change was a down quark to an up quark
(c)
(i)
This was known by most candidates.
(ii)
Well over half gave the correct response.
(iii)
A majority of the candidates appreciated that strangeness is responsible for longer
than usual lifetimes.
(iv)
Both parts had to be correct to score the mark which was gained by half the
candidates. It was essential that the gluon and not a pion was stated for the strong
interaction. The exchange particle in the weak interaction was more often correct.
This question was extremely well answered with the majority of candidates gaining at least three
of the four marks.
(a)
A sizeable minority of candidates circled the complete opposite of all the correct answers. It
is essential that candidates read the questions carefully.
(b)
Credit was given for those candidates stating that the proton is a hadron.
(c)
Answers were usually very clearly laid out and correct.
(a)
The equation was completed well by a large proportion of the candidates but there was a
significant number who could make no valid attempt. The β– was usually correct, but
common errors were to quote
together with an ambiguous symbol for the
antineutrino. Examiners required candidates to make it clear that the third particle was an
anti-neutrino.
(b)
5
6
This was well answered by the majority who knew that a down quark changes to an up
quark when the neutron decays to a proton.
Marks gained for this part hinged on whether or not candidates were aware that a meson
consists of a quark-antiquark pair. When this was known the candidate usually went on to
correctly assess that a negative pion could only be a down quark or an anti-up quark. A slight
minority were unable to access any marks, believing that a meson comprises of three quarks.
(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.
Page 22 of 25
7
(a)
Almost all were able to indicate the correct quark substructure of the neutron. However
these answers were often couched simply as, for example, ‘udd’ without any definition of
these symbols leaving the examiners to infer what candidates meant.
(b)
Again, many knew that the terms baryon and hadron are used to describe a neutron, but
far too many also suggested that the neutron is a fundamental particle. A small group of
candidates used the lepton response as an alternative to hadron.
8
Most candidates attempted to complete the equation but only a few gained all three marks and
many achieved no marks at all. However, the majority got full marks in part (b).
9
This question was very well answered and it was pleasing to see that many candidates were able
to recall most of the appropriate information from this relatively new part of the syllabus.
10
11
Many candidates were able to suggest that mesons have two quarks and that baryons have
three, but fewer were able to give good additional detail (for example, that mesons have a quark
and anti-quark structure). A sizeable minority reversed the quark count in the arrangement of the
two types of particle.
A minority of candidates failed to score the two marks in part (a) because they interpreted
nucleons as neutrons. Part (b) presented more of a challenge for the more able candidate
because the fractional charge and the fractional baryon number for quarks were concepts that
were not universally understood. Many candidates took this part of the question to mean, ‘Are the
quantities conserved or not?’ The other common error was failing to assign correct lepton
numbers. Because of these difficulties the question turned out to be a good discriminator
between candidates.
In part (c) the majority of candidates were aware that the positron and the electron suffered
annihilation but only the better candidates referred to the production of two photons. A noticeable
number of the less able candidates confused annihilation with pair production.
12
This question again showed good discrimination and in particular showed up the weaknesses of
the poorer candidates. Part (a) was usually performed well by most candidates whereas part (b)
was answered incorrectly by a large majority of candidates. It was a common misconception in
the answer to part (b) that the neutron was the most stable baryon.
It was common in part (c) for more than half the available marks to be earned, but often this was
due to consequential errors. It was interesting to note that candidates would often work through
conservation of lepton number, baryon number and strangeness but failed to consider
conservation of charge. Consequently, part (c)(i)(A) was a stumbling block for most candidates.
Page 23 of 25
13
The average candidate performed well on this question. Many candidates lost marks by
describing the meson as having two quarks rather than having a quark plus an antiquark. Other
candidates lost marks because of the ambiguous way in which antiquarks were included in their
description of a baryon.
In part (b) many of the weaker candidates were under the illusion that a lepton had a quark
structure and also that the change to the quark structure during the decay was a change to an
antiquark rather than a down quark changing to an up quark.
14
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.
16
This question was answered well with a number of candidates obtaining high marks. Quark
structure and the application of conservation laws seemed to be particularly well understood.
17
In part (a), the vast majority of candidates could name three flavours of quark with up, down and
strange being far from the only examples offered.
The substructure of the neutron was understood well by all but a very small number of
candidates in part (b).
18
Most candidates were able to answer part (a), with most common answers being proton/neutron.
Fewer candidates correctly answered part (b); here common errors included 3 quark
combinations and combinations of quark-antiquarks that included the strange quark.
Page 24 of 25
19
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.
Page 25 of 25