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

(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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