AMERICAN ACADEMY LARNACAVII PHYSICS: EXERCISE 4( A) [Date: ]

NAME I IGRADE I

BLANI(PAGE

TURN OVER FOR QUESTION I

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-2-

Fig. 1

Ca) Describe:

the principle of an experiment that led to the revision of this theory;(i)

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(ii) the conclusions from this experiment.

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.........~.\.~ ~ :h.~..t !M.P,..S.Si.~ c.h.-.~ ..~~ .I:y:\.~

(b) State one later development in our knowledge of the composition of atomic nuclei. [1]

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[6]

(Total for Questions 1 = 7 marks)

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~ Alpha particles are fired at a thin gold film in a vacuum.

The alpha particles suffer negligible deflections when colliding with the electrons ofthe gold atoms but about 1 in 8000 are deflected through more than 90° by the goldnuclei.

(a) Suggest why the electrons do not deflect the alpha particles. [I]\ I ~, I r.........:e..s. ~.~ v.: :?:~,.~\:\ ':'0..~?>. 5.:::.~.: ~ .

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Cb) Explain:

(i) why the gold nuclei deflect the alpha particles; [2J

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(ii) why the proportion of alpha particles suffering large deflections is verysmall. [2]

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3) This question is about CL, [) and 'Yradiaticns.

The charge and mass of emissions from radioactive substances may be given in terms of thecharge of an electron -e and the mass me of an electron or the mass mp of a proton. Using these symbols orotherwise, complete the following table. [4-J

Radiation Charge Mass

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r 0 0

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(5)

-4--Li) Explain 'why an electron beam can be used to determine the diameter of atomic nuclei.'f/

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The table shows the radius r of various atomic nuclei of nucleon number A.

Nucleon Nuclear radius !

Element number A r1lO-15m

Boron 10 2.69

Silicon 28 3.93I

Strontium 88 5.34 I I

II ITin 120

I5.99

IUranium 238 7.74

It is predicted that for most nuclei r = roA l!3 where 1'0 is a constant.

Plot-a suitable graph to verify this relationship. You may wish to use the blank column inthe table above for your calculated data.

Use your graph to determine a value of 1'0.

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-6-The mass of a nucleus is directly proportional to its nucleon number. Assuming the shape ofa nucleus can be approximated to a sphere, and that r = roA 113, show that the density of nucleiof different elements should be the same .

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..............................v. ~ ..C\ ..r.CI & 1..(\.r<>~ .

A nucleus of fluorine containing 17 nucleons has a radius of 5.50 xlO-15m. Use your graphto predict how its density compares to that of other nuclei .

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........................................................................... -:7 3.: \6 >.{ ~v. ~ .

..........................c&b.o.~ ~ f.k ~.~ ~.>. ~~ :hr-.\.~ ..(2)

(Total 18 marks)

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(2)

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-f--This question is about the different experiments where small particles are fired at targetsand the scattering of these small particles is then observed. The information gained inthese scattering experiments can tell us about the structure of the targets, which areoften too small to be investigated in any other way.

Rutherford's team directed alpha-particles at gold foil and observed their deflections.Summarise their observations, and state the conclusions Rutherford reached about thestructure of gold atoms.

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To find a value for the diameter of a nucleus, high energy electrons can be used. TheStanford Linear Accelerator (SLAC) produces electrons with energy 190 Me V for thispurpose.

Magnetic field into page

-------x xk-------Electron beam x x x x Linear accelerator-----+--~- x (e.g. SLAC)

Detector

Beam focusScattering chamber

Target nucleiScattering angle

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------ ----------------

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U se the formula /...,= he / E to calculate the de Broglie wavelength of electrons with thisenergy. (E is the energy of the electrons in joules.)

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/...,= b·.~.>.c .. \0.-.' ~..~ .(2 marks)

Explain why it is necessary to use such high energy electrons to make precisemeasurements of the nucleus .

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Give one reason why an electron is more useful than an alpha-particle for investigatingthe structure of nucleons .

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(1 mark)

Experiments in the last ten years have been able to investigate the structure of nucleonsby using even higber energies. Usually these experiments (e.g. SLAC and CERN) areinternational collaborations. Suggest two reasons why international collaborations arenecessary for experiments of this sort .

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(2 marks)

(Total 10 marks)

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-7-~ This question is about the use of electrons to probe the structure of protons.

The diameter of a proton has been determined by recording the angular distribution of high speedelectrons scattered from a hydrogen target, as shown in Fig. 11.1.

hydrogen sample

~..particle accelerator 1--------_i+H!oH+!----.---.- electron beam

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Fig. 11.1

When the de Brog/ie wavelength of the electrons is comparable to the diameter of the protons,there is evidence of diffraction.

(a) (i) The energy E of a high-speed electron is given by

E=pc

where p is the momentum of the electron and c is the speed of light.Show that the energy of electrons which have a de Broglie wavelength of 4.8 xi 0-15 m(twice the diameter of a proton) is about 4x 10-11 J.

c= 3.0x 108ms-1

h = 6.6x 10-34 Js

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(ii) The electrons are given this energy in a particle accelerator, by repeatedly acceleratingthem through a potential difference of 100 kV. Calculate the number of times each electronhas to pass through this potential difference to acquire an energy of about 4x 10-11 J.

e = 1.6x 1O-19C

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-/0-(b) Fig. 11.2 shows how the detector current depends on the angle through which the detected

electrons are scattered. The graph shows evidence of diffraction.

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r-, <,J r-,r-,

<,r-,<,

10-7

detector current! A10-8

10-9

1 0-10

10-11

1 0-12 o 10 20 30 40 50 60 70 80 90scattering angle e/ degrees

Fig. 11.2

State and explain the feature of the graph which shows that the electrons are being diffractedby the protons.

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[2]

(c) At high enough electron energies, the experiment provides evidence for the internal structureof the proton.Describe what is observed and state what it reveals about the internal structure of the proton.

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The diagram shows the straight track of a cosmic ray passing through a detector. Thecurved track is made by an electron knocked out of an atom by the cosmic ray. Assumethat both the cosmic ray and the electron are moving in the plane of the paper.

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(a) The detector is within a magnetic field. Explain how you can deduce that the magneticfield acts at right angles to the plane of the paper.

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(2)

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Cb) (i) The magnetic flux density is 0.50 T. Determine a value for the speed of theelectron.

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Speed = 3..~ \.Q.: ~s..~~ .(4)

(ii) Discuss this value of speed .

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(Total 8 marks)

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(i) Write down an equation, in terms of these quantities only, relating the magnetlcl'forces on the ion to the required centripetal force.

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(ii) Hence show that the time T for one revolution of the ion 15 given by the. T Zttmexpression = -R .

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(5)Figs. ! and d" show plan and three-dimensional views of a simple form of particle!

accelerator known as a cyclotron. IIt consists of two semi-circular boxes called 'dees'. Hydrogen ions are injected near to the!

centre. The alternating potential difference is to accelerate the ions across the gap between the'dees'. The ions are constrained to move in semi-circular paths when within the 'dees' by amagnetic field perpendicular to the plane of Fig. i, A charged pia te P finally extracts the highspeed ions from the cyclotron.

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-- ~.---- ... - .__ .. _ ..._. __ .. ----------------------

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(b) For a particular cyclotron accelerating hydrogen ions the B field is 0.60 tesla,

(1) Calculate the time period for one revolution of a hydrogen ion.-, t: 7...11.Vt\ ;:: 'l..r\ ')< \.~ ~ 10 _•. -:l. ~_~

t3>r,.. 0-(.. -r y \.<Oyt6 -\'fc..

(ii) Why does the fact that this is independent of the speed of travel of the ion and the iradius of the orbit simplify the operation of the cyclotron? !

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(1,.<.1

Cc) If a hydrogen ion emerges with energy 2.4 x 10-12 J, at a measured speed"'6f5 x 107 m s -1, a simple calculation of the mass of the hydrogen ion gives a value of1.9 x lO-27 kg.

(i) Show how this value can be obtained.

(ii) Suggest a reason for the appar:,ent discrepancy between this value and the'databook' value of 1.7 x 10-21 kg.

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~~.,, The following extract is taken from an article about the Continuous Electron Beam~/Accelerator Facility (CEBA.F), which produces high-energy electrons for particleexperiments.

The sheer size of the magnets reflects a bizarre phenomenon at work within. CEBAF.At speeds close to the speed of light, Einstein's special theory of relativity predictsthat objects appear to gain mass. The electrons in CEBAF move so fast that they actas if they have gained 8000 times their normal mass, making them far more reluctantto change course - hence the need for powerful magnets.

The gain m mass of an electron is another way of saying that it has gained energyequivalent to 8000 electron masses. Calculate the voltage through which an electron hasto be accelerated from rest to gain this energy .

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Voltage = t..:.\.&..V .-=-- =

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The electrons are guided along a pathwhich has two straight sections with twosemicircular sections at each end, asshown.

A B

Explain the role of the magnets in thisparticle accelerator, including anapproximate calculation of field strength.You may wish to refer to the varioussections AB, BC, CD and DA along thepath.

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D C

Assume that the electrons are travellingclose to the speed of light so that they havea mass of 8000 times their nonnal mass .

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/0) The photograph shows the path of an electron spiralling inwards anticlockwise in a bubble'./" - '-' .•. -

chamb er. 'The photograph I§ full size,

(a) (i) Explain bow the electron produces the white truck. You may be awarded 8 markfor the clarity of your answer.

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I1 (ii) Explain the origin of the centripetal force that is making the electron spiral in this i

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(4)

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(b) Theory shows that the momentum p of the electron at any point on its path is givenI by p = Ber, where B is the magnetic flux density perpendicular to its motion, r is theI radius of its path at that point and e has its usual meaning. I

I (i) The magnetic flux density in the bubble chamber is 1.2 T. By making suitable I1.1 measurements on the photograph, determine approximate values for the I

momentum of the electron at P, Q and R. If you are using a transparent ruler, it I

I may help to place a piece of white paper underneath it. (Take the centre of the .11:

spiral to be at S.)

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(ii) The speed v of the electron at ail three places P, Q and R on its spiral IS

3 0 X H18m cc-1 to ""0 siznificant 01r711res• _0.1.. u •... Lv" 1.61.1..1.. a .•..L ... L 5~ .

Deduce the effective mass of the electron. at each point and comment on yourresults .

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SYNOPTIC QUESTION

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The diagram shows part of a linear accelerator - a linac. Alternate metal tubes areconnected together and to opposite terminals of a high-frequency alternating potentialdifference of fixed frequency.

High frequencyalternatingpotentialdifference c

I B D~ \) \ ~~. p. ratanl~,-,,-)----.---,,-}<--) Ll:':~_) etc ~ beam

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Injectedprotons

(a) Describe how the protons are accelerated as they move along the linac and explainwhy the tubes get longer towards the right. You may be awarded a mark for theclarity of your answer.

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(5)

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r) A . 1" 1 A?~ " . , - < f h 'L·· 1(b _ parncu ar nnac nas q.~\J metal tubes and the peak voltage 0_ the a tematmg suppiyis 800 kV.

(i) Show that the emerging protons have zained a kinetic energy of about 5 x 10-' I J'"-' ••••.• 1.. t-i (",.....' ,

and express the mass equivalent of this energy as a fraction of the mass of astationary proton. Take the mass of a proton ri1p as 1.01 u .

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(ii) The frequency of the alternating supply is 390 MHz. Calculate how long it takesa proton to travel along the linac .

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(c) The emerging protons can be made to collide with

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(i) a target of fixed protons, e.g. liquid hydrogen, or

(ii) a similar beam of protons travelling in the opposite direction.

S· 1. f eith botl . 1 ( \tate some acvantages or eit er or otn expenmenta arrangement s) .

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(2)

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In a synchrotron, charged panicles are confined by magnets to a ring while beingaccelerated to high energies. The particles radiate electromagnetic waves. referred to assynchrotron radiation, as they move round the ring. The maximum kinetic energy of aparticle is limited by synchrotron radiation. For particles of the same energy, the syn-chrotron radiation is greater for lighter particles and for rings of smaller diameter.

(a) Explain why, after a particle has reached maximum energy, it is necessary tocontinue to boost its energy each time it passes round thering.

(ii) Suggest why it is more difficult, using a synchrotron, to accelerate electrons tothe same high energy as protons, (3)

(b) Why does a collision between a particle of kinetic energy E and an antiparticle ofkinetic energy E, moving in opposite directions. release more energy than a collisionbetween an antiparticle of kinetic energy 2£ and a stationary particle? (2)

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'13).,// (a) (i) Particle accelerators are used to increase the energy of charged particles. Circularaccelerators can accelerate charged particles to higher energies than can beachieved in linear accelerators. Discuss the principles of physics used in a circularaccelerator. You should refer to principles from more than one unit You may beawarded a mark for the clarity of your answer.

(ii) Show that, if the speed of a charged particle in a circular accelerator is increased,the radius of the circular path increases.

(3 marks)

(b) (i) A bubble chamber contains liquid hydrogen at high pressure. When the highpressure is suddenly released, visible tracks of particles moving through thechamber are produced. Describe the processes which lead to these tracks beingmade visible.

(ii) The photograph shows tracks in a hydrogen bubble chamber. The tracks associatedwith one particular interaction are reproduced as a diagram alongside. There is amagnetic field into the page.

Particle 5 trackI I

I

Particle 2 track

The tracks in the diagram show particle 1 decaying at A into two particles 2 and 3,with particle 3 leaving no track. What can you deduce about particle 2?

Suggest why particle 3 leaves no track.(3 marks)

(iii) Particle 3 subsequently decays at B into another pair of particles, 4 and 5. The sumof the masses of particles 4 and 5 is less than the mass of particle 3. Explain howthis can be the case.

(2 marks)

(Total 1i marks)

.../25

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