Colonel Frank Seely School
3.8.1.1 Rutherford Scattering
Q1.(a) Scattering experiments are used
to investigate the nuclei of gold atoms.In one experiment, alpha
particles, all of the same energy (monoenergetic), are incident on
a foil made from a single isotope of gold.
(i) State the main
interaction when an alpha particle is scattered by a gold
nucleus.
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(1)
(ii) The gold foil is replaced with
another foil of the same size made from a mixture of isotopes of
gold. Nothing else in the experiment is changed.
Explain whether or not the scattering distribution of the
monoenergetic alpha particles remains the same.
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(1)
(b) Data from alpha−particle scattering
experiments using elements other than gold allow scientists to
relate the radius R, of a nucleus, to its nucleon number, A.The
graph shows the relationship obtained from the data in a graphical
form, which obeys
the relationship R = r0
(i) Use information from the
graph to show that r0 is about 1.4 × 10–15 m.
(1)
(ii) Show that the radius of a V
nucleus is about 5 × 10–15 m.
(2)
(c) Calculate the density of a V
nucleus.
State an appropriate unit for your answer.
density ......................................... unit
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(3)
(Total 8 marks)
Q2.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 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 potential energy is least at P.
D
Its speed is least at P.
(Total 1 mark)
Q3. In an
experiment to investigate the structure of the atom, α particles
are directed normally at a thin metal foil which causes them to be
scattered.
(a) (i) In
which direction will the number of α particles per second be a
maximum?
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(ii) State what this result suggests
about the structure of the atoms in the metal.
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(2)
(b) A small number of α particles are
scattered through 180°.
Explain what this suggests about the structure of the atoms in
the metal.
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(2)
(c) The figure shows the path of an α
particle passing near a nucleus.
(i) Name the force that is
responsible for the deflection of the α particle.
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(ii) Draw an arrow on the diagram in the
direction of the force on the α particle in the position where the
force is a maximum.
(iii) The nucleus is replaced with one
which has a larger mass number and a smaller proton number.
Draw on the diagram the path of an α particle that starts with
the same velocity and position as that of the α particle drawn.
(4)
(Total 8 marks)
Q4.(a) (i)
Why is it necessary to remove
the air from the chamber in a Rutherford scattering experiment?
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(ii) Give two conclusions that can
be deduced about the nucleus from the results of such an
experiment.
conclusion 1
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conclusion 2
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(iii) What force or interaction is
responsible for Rutherford scattering?
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(4)
(b) The figure shows three α particles,
all with the same kinetic energy, directed at a nucleus. The path
followed by α particle 2 is given.
Draw lines on the figure to show the paths followed by α
particles 1 and 3.
(2)
(Total 6 marks)
Q5.The diagram below shows the apparatus used to investigate
Rutherford scattering, in which α particles are fired at a gold
foil.
(a) Why is it essential for there to be
a vacuum in the chamber?
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(2)
(b) What observations made with this
apparatus support each of the following conclusions?No explanation
is required.
(i) The nuclear radius of
gold is much smaller than its atomic radius.
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(ii) Most of the mass of an atom of
gold is contained in its nucleus.
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(3)
(c) The drawing below shows α particles
incident on a layer of atoms in a gold foil.
On this figure draw the complete path followed by each of the α
particles shown.
(3)
(Total 8 marks)
Q6.The figure below represents an experiment on Rutherford
scattering in which α particles are directed at a gold foil. The
detector is shown in two positions in the evacuated chamber.
(a) Why is it necessary to remove the
air from the apparatus?
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(b) Explain why the gold foil should be
very thin.
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(c) Explain why the count rate from the
α particle detector in position 1 is much greater than that in
position 2.What can be deduced from this observation about the
structure of the atom and the properties of the nucleus of
gold?
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(Total 6 marks)
Q7.(a) An α particle source of half-life
3420 years has a rate of decay of 450 kBq. Calculate
(i) the decay constant, in
s–1,
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(ii) the number of radioactive
atoms in the source.
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(4)
(b) A narrow beam of α particles is
directed at a thin gold foil target in an evacuated vessel. Only a
very small proportion of the α particles scatter backwards at an
angle greater than 90° to the direction from which they came
(i) Describe what happens to
the majority of the α particles incident on the gold foil.
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(ii) Several deductions may be made
about the structure of gold atoms from the results of α– particle
scattering. Write down two of these deductions.
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(3)
(Total 7 marks)
Q8.In an experiment to investigate the structure of the atom, α
particles were aimed at thin gold foil in a vacuum. A detector was
used to determine the number of α particles deflected through
different angles.
(a) State two observations about the α
particles detected coming from the foil.
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(2)
(b) State two features of the structure
of the atom which can be deduced from these observations.
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(2)
(Total 4 marks)
Q9. The
diagram below shows a single atomic nucleus that is part of a thin
foil. A, B and C are the paths of three α-particles directed at the
foil as shown. All three paths are approaching close to the
nucleus.
(a) Complete the diagram carefully
showing the subsequent paths of the α-particles.
(3)
(b) Suggest two pieces of scientific
information that can be gained by bombarding matter with particles
in this way.
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(2)
(Total 5 marks)
Q10.(a) Draw a labelled diagram to
illustrate the main features of the apparatus used in the
scattering experiment that provided evidence for the existence of a
positively charged nucleus.
(3)
(b) Explain how the outcome of this
experiment supports the model of atoms having a small positively
charged nucleus.
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(2)
(Total 5 marks)
Q11.In the Rutherford alpha particle scattering experiment,
alpha particles having the same energy were fired at gold nuclei.
The diagrams below are intended to represent encounters between two
alpha particles and a gold nucleus N, the alpha particles arriving
at different times. Which one best represents the possible
encounters?
(Total 1 mark)
Q12.A beam of α particles irradiates a metal foil. The paths of
four α particles near the nucleus of a metal atom are shown in the
diagram. Which one of the paths must be incorrect?
(Total 1 mark)
M1.(a)
(i) electromagnetic /
electrostatic / Coulomb (repulsion between the alpha particles and
the nuclei) ✓
The interaction must be named not just described.
1
(ii) the scattering distribution
remains the same (because the alpha particles interact with a
nucleus) whose charge / proton number / atomic number remains the
same or the (repulsive) force remains the same
The mark requires a described distribution and the reason for
it.
Orthe scattering distribution changes / becomes less distinct
because there is a mixture of nuclear masses (which gives a mixture
of nuclear recoils) ✓(owtte)
A reference must be made to mass and not density or size.
1
(b)
(i) use of graph to find r0e.g.
r0 = 6.0 × 10-15 / 751/3 ✓(or 8.0 × 10-15 / 1751/3 )( r0 = 1.43 ×
10-15 m)
Substitution and calculation t must be shown.
Condone a gradient calculation on R against A1/3 graph (not
graph in question) as R ∝ A1/3
1
(ii) Escalate if clip shows Al in
the question giving R ≈ 4 × 10-15 m.
(using R = r0 A)R = 1.43 × 10-15 × 511/3 ✓R = 5.3 × 10-15 (m)
✓(R = 5.2 × 10-15 m fromr0 = 1.4 × 10-15 m)
First mark for working.
Second mark for evaluation which must be 2 or more sig figs
allow CE from (i) R = 3.71 × (i).
Possible escalation.
2
(c) Escalate if clip shows in the
question and / or the use of 27 in the working.
density = mass / volumem = 51 × 1.67 × 10-27(= 8.5 × 10-26
kg)
Give the first mark for substitution of data into the top line
or bottom line of the calculation of density.
v = 4/3π (5.3 × 10-15)3(6.2(4) × 10-43 m3)
In the second alternative the mark for the substitution is only
given if the working equation is given as well.
Ordensity = A × u / 4/3π (r0 A1/3)3= u /4/3π (r0 )3
51 × 1.67 × 10-27 would gain a mark on its own but 1.66 × 10-27
would need u / 4/3 π(r0)3 as well to gain the mark.
top line = 1.66 × 10-27
bottom line = 4/3π (1.43 × 10-15)3
✓ for one substitution
density = 1.4 × 1017 ✓(1.37 × 1017)kg m-3 ✓
Expect a large spread of possible answers. For exampleIf R = 5 ×
10-15 V = 5.24 × 10-43 and density = 1.63 × 1017.
Possible escalation.
3
[8]
M2.D
[1]
M3.
(a) (i)
straight on or deflection of zero degrees (1)
(ii) the atom consists mainly of open
space[or volume of nucleus is (very much) smaller than volumeof the
atom] (1)
2
(b) most of the mass of an atom is
contained in its nucleus[or the mass of the nucleus is greater than
the mass of the α particle] (1)the nucleus contains a positive
charge (1)the charge is concentrated at the nucleus (1)
max 2
(c) (i)
electrostatic (force)[or electromagnetic or coulomb] (1)
(ii) arrow pointing away from the
nucleus at the closest distance to the nucleus (1)
(iii) path showing less deflection at
all times
4
[8]
M4.(a)
(i) to prevent
absorption/deflection/interaction/collision
of
the α particle (by the air) (1)
(ii) (nucleus) has a positive
charge
(or
same charge sign as an α particle (nucleus) contains most of the
mass (or is very dense) (1)
(1) (any two)
(nucleus) is small compared to the separation between nuclei
(iii) electromagnetic or electrostatic or
Coulomb (1)
4
(b) (particle 1) path is straighter than
path of particle 2 (1) (particle 3) path is bent more than path of
particle 2, with minimum
radius of curvature near the minimum separation
and
in front of the nucleus (1)
2
[6]
M5.(a) to prevent the α particles being
absorbed or scattered (1)by air molecules (1)
(2)
(b)
(i) little or no deflection
(1)by a majority of α particles (1)
(ii) some α particles suffer large
deflection[or backscattering occurs] (1)
(3)
(c) first path continues undeflected
(1)third path shows backscattering (inside the dotted circle)
(1)second path undeflected or deflected downwards
and fourth
path undeflected or deflected upwards (1)
(3)
[8]
M6.(a) α particles have a short range in
air (3–5 cm) (1)(or to minimise collisions between α particles and
air molecules) (1)
(b) the α particles must not be absorbed
by the foil (1)(or the α particles must only be scattered once)
(1)
(c) a majority of α particles pass
straight through (1)most α particles do not pass close enough to be
deflected(or few pass close enough to be deflected significantly)
(1)
atoms consist mainly of open space (1)nuclei are very small (or
nucleus much smaller than the atom) (1)the nucleus is massive (or
most of the mass of the atom is contained in the nucleus)the
nucleus is positively charged
(or the nucleus and the α particle have the same charge) (1)
The Quality of Written Communication marks were awarded
primarily for the quality of answers to this part.
[6]
M7.(a)
(i) (1)
= 6.43 × 10–12 (s–1) (1)
(ii)
= 7.0 × 1016 (1)
(4)
(b)
(i) pass through with no [or
very small] deflection (1)
(ii) volume of nucleus <<
volume of atom (*)[or nucleus small and atom mostly empty space]
(*)most of mass in nucleus (*)nucleus has positive charge (*)size
of nucleus << separation (*)(*) any two (1) (1)
(3)
[7]
M8.(a) alpha particles undeflected
(1)some through small angles (1)(very) small (but significant)
number deflected through > 90° (1)
max 2
(b) atom mostly empty space (1)positive
charge concentrated (1)in a volume much less than total volume [or
radius] (1)
max 2
[4]
M9.
(a) A - repelled,
B1
B bends away from nucleus
M1
B & C would cross beyond nucleus
A1
3
(b) one piece of information
B1
second piece
B1
2
[e.g. substructure of atom / size of nucleus / charge onnucleus
/ density of nuclear material, atoms mostlyempty space / massive
nucleus / evidence for nucleus / alphaparticle]
[5]
M10.(a) source / scatterer / detector
labelled
M1
vacuum
A1
(thin / gold / metal) foil
A1
(3)
(b) some backscattered (> 90°) =>
α's and nuclei both +ve
B1
few deflections / most pass through ∴ nuclei small
B1
(2)
[5]
M11.A
[1]
M12.D
[1]
E1.The calculations involving the nuclear radius were done well
but the question parts on alpha particle scattering were not
answered as well as expected. In part (a)(i) a majority did refer
to electrostatic or electromagnetic repulsion. There were however a
significant number who chose to give the strong nuclear force or to
simply refer to like changes repel. Interestingly there seemed to
be a number of students, judging from their answers’, who did not
really understand the word ‘interaction’. The response to (a)(i)
was very polarised. Around half of the students understood that the
charge of the nucleus did not change and neither did the
scattering. The other half regarded the alpha particle as bouncing
physically from the nucleus and therefore the radius or the change
in nuclear size would have consequences. If contact had been made
between the alpha particle and the nucleus the SNF would have put a
stop to the scattering. In (b)(i) a majority of students had no
problem in using the graph. There were a handful who only showed
the equation without any working data. A few others incorrectly
thought that the gradient of the graph could give the value of the
constant. This last group should be distinguished from a number of
students who linearised the data before they found a gradient ie
the gradient of R against A1/3. The main stumbling block for some
in (b)(ii) was to not actually perform the calculation which they
set up. They simply quoted the radius given in the question.
Students found the calculation required very easy. The calculation
of the last part (c) was done well by a majority. A very small
number quoted the wrong units and a few made errors in the volume
calculation by either quoting the wrong formula for the volume of a
sphere or getting the powers of 10 wrong in the calculation.
E3. Part
(a) was answered well by most candidates but in part (b) only the
better ones produced good answers. These candidates appreciated
that in order for backscattering to occur, the á particle must
collide with a particle of greater mass. The fact that repulsion
came from having both a positive nucleus and a positive á particle
was widely known.
Part (c) proved to be a good discriminator but it was common to
see the force, which was supposed to act on the á particle,
appearing to act on the nucleus.
E4.Difficulties occurred in this question because it required
some care in the candidate’s choice of words and also required the
candidate to think carefully about the drawing in part (b). In part
(a) the simple fact that air absorbs or deflects á particles was
frequently not stated and words like diffraction appeared in the
answers. The conclusions concerning the nucleus also lacked
sufficient detail in some cases to gain marks. Such examples were:
‘the nucleus has a big charge’ rather than a positive charge and
‘the atom is mainly open space’ when the question was specifically
about the nucleus and not the atom. In the final section of part
(a) the strong nuclear force and the weak interaction both featured
as possible answers, both being incorrect.
In part (b) the path of á particle 3 in particular was poorly
done because candidates did not address the physics of the
situation before drawing the path. Some thought should have been
given to the following: the force is repulsive so which way does
the path curve, where does the path curve the most, how much
curvature is there compared to path 2 and how close does the path
come to the nucleus.
E5.A clear majority of candidates were aware of what happens in
Rutherford scattering but failed to score well because of a lack of
precision in their answers. For example, in part (a) the answer was
frequently given as “so nothing would affect the α particles”.
Needless to say this type of answer gained no credit.
In part (b) there were some obvious misunderstandings of the
experiment, for example the answers to parts (i) and (ii) were
often interchanged, implying that candidates did not really
understand the conclusions arrived at.
Candidates lost marks in part (c) because they did not think
carefully enough about the paths followed by the α particles. It
was common to see the mistake of α particles being deflected in the
wrong direction, but in addition, examiners saw many subtle errors
such as the α particles being shown to hit the nucleus or the
smallest radius of curvature in the path occurring well away from
the repelling nucleus.
E6.This question produced a good spread of responses, ranging
from the vague to the highly articulate and technically correct.
There were very few conceptual misunderstandings but some
candidates found it very difficult to make simple correct
statements. For example, candidates who wished to state as an
answer to part (a) that ‘the α particles hit air molecules’ would
write ‘the a particles interfere with the air‘ or ‘the α particles
are aware of the air‘. Several candidates also slipped into using
electrons rather than α particles as the projectiles. If this
occurred it was penalised only once.
E7.Many candidates scored full marks on this generally high
scoring question. Most of those candidates who knew the meaning of
decay constant could complete the calculation in part (a). There
were some arithmetic errors, a few candidates did not change years
into seconds, and in part (a)(ii) some mistakenly introduced N = N0
e−λt.
In part (b) marks were often lost through careless wording. Most
candidates realised that the majority of alpha particles travelled
straight through the foil, but others said that they were deflected
through small angles, sometimes up to 90°. A statement that the
volume of the nucleus was small compared with the volume of the
atom was expected, but most candidates simply referred to a small
nucleus. This was accepted if it was accompanied by the statement
that most of the atom was empty space, which seemed almost a reflex
response. Other examples of lack of precision were to omit the word
nucleus completely, or to confuse nuclei with atoms, or to say that
the nucleus was highly charged, or a concentration of charge
instead of positively charged. Describing the nucleus as massive in
isolation was not accepted as a substitute for a statement that
most of the mass of the atom is concentrated in the nucleus.
E8.Most candidates recognised the physical situation correctly,
but marks were sometimes lost because they could not express their
knowledge in precise terms and used words like “some”, “few” and
“many” far too often.
E9.
(a) Although candidates had a reasonable
idea of the physics in this question, diagrams were poor and
scrappy. The head-on collision (A) was often represented as having
a huge deviation, whilst the remaining alpha particles frequently
failed to cross beyond the nucleus. Some candidates lost marks
because their drawings were so poorly drawn as to be
indecipherable.
(b) Many were able to produce two pieces
of information that is yielded by a scattering experiment of this
type and this question scored well.
E10.(a) Virtually no candidates gained
full marks for a description of the alpha scattering experiment.
Most candidates seemed unaware of the need for the chamber to be
evacuated and many failed to describe the scatterer as being a
foil. Many candidates simple regurgitated the well-love diagram of
alpha particles approaching a nucleus at different alignments.
(b) The description of the analysis of
the alpha scattering results was often incomplete and not helped
when, in many cases, candidates referred to the bombarding
particles as protons, neutrons, electrons or as having a negative
charge. This last version left candidates trying to describe the
repulsion of negative particles by positive nuclei – inevitable
doomed from the outset!
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