1. AMERICAN ACADEMY LARNACA
VII PHYSICS: EXERCISE 4( A) [Date: ]
NAME I IGRADE I
BLANI(PAGE
TURN OVER FOR QUESTION I
.. ./2

2. -2-
Fig. 1
Ca) Describe:
(i) the principle of an experiment that led to the revision of this theory;
.... ~~j.~~
: ~..:..?~k~
- ?:S.{A;.~.. k.~ .
·····.···~ ~ bQ.~ ~~ ············································c·
(ii) the conclusions from this experiment. [6] I
..........~~ x~ ~.':V1!r.?. ~.k.~~ ~.~ !.f.~~
......... ~
~..~ :h.~..
t !M.P,..S.Si.~ c.h.-.~ ..~~ .I:y:.~
I
(b) State one later development in our knowledge of the composition of atomic nuclei. [1]
...........
~b.':'s. ; .
(1-)
~
(Total for Questions 1 = 7 marks)
I
'"
... /3

3. ! Leave
I ~ms
margin
~ Alpha particles are fired at a thin gold film in a vacuum. ![Plank
The alpha particles suffer negligible deflections when colliding with the electrons of
the gold atoms but about 1 in 8000 are deflected through more than 90° by the gold
nuclei.
(a) Suggest why the electrons do not deflect the alpha particles. [I]
.........:e..s. I
~.~ v.: ~,
:?:~,.~:
I
':'0..~?>. 5.:::.~.:
r ~ .
~ •••••••••••••••• 0 •••••••.••••••••••••••••• ~ • ., •• ~ ••••••• ~ ••••••• 0 ••••••••••••••••• o •••••.• ~ ••••••. c •• ~ ••••• 0 ••••••••••••••••• ~ ••••••• ~ ••••• G •••••
Cb) Explain:
(i) why the gold nuclei deflect the alpha particles; [2J
.....ri. Q..{.~.~~~
~
L. ~ ~~ l;J.q,.~J
.
...... ( ~r.r.Y..,- ~ ~ #.~.">. r.4L
~.~ .v.~.
~':;. .
(ii) why the proportion of alpha particles suffering large deflections is very
small. [2]
........
~~ D v. ~.~.~.t .
(5)
3) This question is about CL, [) and 'Yradiaticns.
The charge and mass of emissions from radioactive substances may be given in terms of the
charge of an electron -e and the mass me of an electron or the mass mp of a proton. Using these symbols or
otherwise, complete the following table. [4-J
Radiation Charge Mass
CL t'l..e... 4-W.. ~ I
[)+ ~e.. tv e.
-e...
I ~- !Me.
r 0 0
I
.01'
0,"/ /

4. -4--
Li) Explain 'why an electron beam can be used to determine the diameter of atomic nuclei. Leave
/
'f blank
......... -»;
o ~.~ ~.~ ~... ~ ~ ~.~.~ .
.......... ~ ~.I.~ ~~ R.~.~ ~.~ ~ ~.~.M.., .
(2)
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 3.93
I
I
Strontium 88 5.34 I
I I I
Tin 120 5.99
I I
Uranium 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 in
the table above for your calculated data.
(9)
Use your graph to determine a value of 1'0.
~
I( - / A. J.
................... :":". :. V"
. J.~ .
............................................................. c).. ~ ..:~ ~ y. ~ ~ .
...... f~Q~ ~.~"- 4. r.:- A
0.-.~~~.~.
-'7
............................................................................ ro..:~ ~ :7 .J."'.4.:f.. ~.<?
. ~ .
(3)
------------ ---- .

5. --_ .. _---
I
CD
~
I
I
T'"""
11
>- I
L()
~
I
I
i
I
,
I
I -e
i
I -
-
M
I
I -
"l"""
<
«
("')
~
I. N
!
I
-f--
I 0
L() N o
WS~-dX3 U! J
-----_ _
... .. -._-_ ....
._--_ .. __ ..

6. -6-
The mass of a nucleus is directly proportional to its nucleon number. Assuming the shape of Leave
a nucleus can be approximated to a sphere, and that r = roA 113, show that the density of nuclei blank
of different elements should be the same .
................ :;:: ~ ~ I.v..: ~ ~ 2.~ :: ~~
.............................. ~ ..C..r.CI &
v. 1(.r<>~
.. .
(2)
A nucleus of fluorine containing 17 nucleons has a radius of 5.50 xlO-15m. Use your graph
to predict how its density compares to that of other nuclei .
.................. :::: ~..6:)...k~~
r: tf:!:": ~~.~ .
.................. ~~:.~ ::r
~ 7::!. v.-: .. ~ ~.~.~ ~ .~ ~ .
-~
........................................................................... -:7 3.: 6 >.{ ~v. ~ .
..........................
c&b.o.~ ~ f.k ~.~ ~.>. ~~ :hr-..~ ..
(2)
(Total 18 marks)
...
~

7. -f--
This question is about the different experiments where small particles are fired at targets Do Dot write
in this margin
and the scattering of these small particles is then observed. The information gained in
these scattering experiments can tell us about the structure of the targets, which are
often 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 the
structure of gold atoms.
~'~~J~" .~ ... rd,...-: .~.G:v..~J...h..... ~~ ... ~ ... ~~ ..
........ ':>9~ r. ~
;--. .
. ~ .. ~- {) fJ-.s. ~~ W ~~ ~~~~ 4.C- ~.~"'t? JJ >
.~ .. .v. >~~ ~ W:-~~ ~ .
..... ~.~c,.~ .
. .~ .. (k~ ~; ... ~ ... ~~~~ ... ~.~ ... ~-.~CfL< .
..... ~'M.- ~ ~~?... t ..~(A>.5.~ .. ) <A-.~~ .
..... ~~ .
(4 marks)
To find a value for the diameter of a nucleus, high energy electrons can be used. The
Stanford Linear Accelerator (SLAC) produces electrons with energy 190 Me V for this
purpose.
Magnetic field into page
-------x
Electron beam
x
xxxx
k-------
Linear accelerator
-----+--~- x (e.g. SLAC)
Beam focus
Scattering chamber
Detector
Target nuclei
Scattering angle
.../8
------ ----------------

8. -g-
=
U se the formula /..., he / E to calculate the de Broglie wavelength of electrons with this Do not write
in this margin
energy. (E is the energy of the electrons in joules.)
1 ~" -~tt:"'- -.: - "Er_
· P.- .. ~ : .. 'Y ~(.,) ~ .. -:-b <? .. ~ .. ~:~ .~. ~Q .. ~ ~ .
· ~.o.c.. t 0.b. », ~'.b »< ~0. ~~~ 3"
} ~ .
/...,
= b·.~..c .. 0.-.' ~..~
> .
(2 marks)
Explain why it is necessary to use such high energy electrons to make precise
measurements of the nucleus .
...... .~.{.t~ A..~ ..'?~.~ o.~AA ~ .
....... ~ .. 9>~.~~~>: .
(1 mark)
Give one reason why an electron is more useful than an alpha-particle for investigating
the structure of nucleons .
....... ~~~ t-<f ~~ ~" -~.~~S "
(1 mark)
Experiments in the last ten years have been able to investigate the structure of nucleons
by using even higber energies. Usually these experiments (e.g. SLAC and CERN) are
international collaborations. Suggest two reasons why international collaborations are
necessary for experiments of this sort .
....... .~ ~J...~.~ .
· 'i- ~~~ __
.S_~_ .. ~_. ~:.;: ..5. ~t4.~ .
• •••••••••••••••••••••••••••••••••••• #; •••••••••••••••••••••••
(2 marks)
(Total 10 marks)

9. -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 speed
electrons scattered from a hydrogen target, as shown in Fig. 11.1.
hydrogen sample
~..
particle accelerator 1--------_i+H!oH+!----.---.- electron beam
,/
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
~~ ~
-= -"). ~y 0 IV s:. '>cC 'J- 0 >c' 0 "V. '> ~
:: 1-" x D-It --s [3]
(ii) The electrons are given this energy in a particle accelerator, by repeatedly accelerating
them through a potential difference of 100 kV. Calculate the number of times each electron
has to pass through this potential difference to acquire an energy of about 4x 10-11 J.
e = 1.6x 1O-19C
-1-
4:- ' t ')£" () ;,
.".,.-----~.-...--~-------~
-6")<!" 0-'''> answer .;J..'?.rr!2
.....••
[2]
. .. /10

10. -/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.
10-6
10-7
-. <,
detector current! A
10-8
.~
r-,
10-9 <, r-,r-,
J
1 0-10 <,
r-,
10-11 <,
1 0-12
o 10 20 30 40 50 60 70 80 90
scattering angle e/ degrees
Fig. 11.2
State and explain the feature of the graph which shows that the electrons are being diffracted
by the protons.
~~t~ j1W-;~
~ i1> ~ I'.> Q,v..~Ul../ c:- o; ~ ~ s, h- (t.~ ('''t)I.
,u-..-~ ~ r-.. o: ~~>~ s:k~ Q.~W-
[2]
(c) At high enough electron energies, the experiment provides evidence for the internal structure
of the proton.
Describe what is observed and state what it reveals about the internal structure of the proton.
rO--Y k ~
c.- ~-.A~v..- r~~ ~
[3]
[rotal: 10]
... /Ir

11. r----- -//-
Leave
I The diagram shows the straight track of a cosmic ray passing through a detector. The
blank
I ()
curved track is made by an electron knocked out of an atom by the cosmic ray. Assume
that both the cosmic ray and the electron are moving in the plane of the paper.
I
I
r:
,-,osrmc
ray
y/'// /'
ACTUAL
-:
SIZE
I
I
I
I
(
I
I
I
/
Electron
I (a) The detector is within a magnetic field. Explain how you can deduce that the magnetic
field acts at right angles to the plane of the paper.
et g §i
.. __ L J J:1
~. ~y. .
I
............
r-, +.-, - "f .~ -
r- )
~ 'lA
I
',~
<.
CA· , :.If,..x. 't
lR". J! j/
:-::"
-:
:--.... 'f7
.>.
"
.
I ....... :-;.~~ ~!:}.-!?
.~ ~ e'.~~ C/k
.
y.~.#:C
.
I
I
!
I (2)
Ii
I
i
I
!i·
I
l~
.. _-----------------------

12. 10
-lL-
---------------------------. -----,,-------..
i Leave;
blank
Cb) (i) The magnetic flux density is 0.50 T. Determine a value for the speed of the
electron.
............... r::.
r. ~ e. .r ~ ~ t~s- .
...........................................................
f. .
- I -"'!
............................. r.::=: ~.~.Y. :: O.:.~.Q.~ ..~
. l-..~ ?':':' .. !.Q
.. ~ ~.). t ~ w1
10
~ er-r ~ (0 -1.1
...............................................................................................................
I<.
.,)..............
I
!
I
Speed = 3.. .Q.: ~s..~~
~ .
(4)
(ii) Discuss this value of speed .
? c
................. .
...............~
.~ f.~.~.~
5. >.~(. ~.~~.~.~ r- .~1:~.~
J.~ ~.~ t .
...... ..~.~.~.~~ .
(2)
(Total 8 marks)
I,
I
I
i
I
I
L _ ----------------------_._-------------_._---"----;---
, --/13
J

13. (Do M!;
-, IvrrHe in
0)
0/ ()'h' yorogen IOD 01 mass m andich arge q travels witn speec v Hi
a A '- c. j'1.." '1 f" , !
a circ e or ramus r Hi a Ithis
magnetic field of flux density B, !margln
(i) Write down an equation, in terms of these quantities only, relating the magnetlcl'
forces on the ion to the required centripetal force.
~tr= Wl~~
u",
I
y
~ I
i
(ii) Hence show that the time T for one revolution of the ion 15 given by the
. T Zttm
expression = -R .
-q
.., T w,
'V -::: ~qv-
~v_ I -
I ~Y 11 tii'
,'> I IF
~
V
?..1. X- l t: "l.rt'v'..
r ';;;
)
-r
J
Et
(5)
Figs. ! and d" show plan and three-dimensional views of a simple form of particle!
accelerator known as a cyclotron. I
It 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 a
magnetic field perpendicular to the plane of Fig. i, A charged pia te P finally extracts the high
speed ions from the cyclotron.
P
I
Alternctinq supply
v
1 Fig. z
Alternating supply
Fig. I
-- ~.---- ... - . __ _.. ..._. __ .. ----------------------

14. -/iL-
1/
'!DQ not
write 1"
this
(b) For a particular cyclotron accelerating hydrogen ions the B field is 0.60 tesla, Imargin
(1) Calculate the time period for one revolution of a hydrogen ion.
-, t: 7...11.Vt ;:: 'l..r ')< .~ ~ 10 _•. -:l. ~_~ I
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 i
radius of the orbit simplify the operation of the cyclotron? !
'2'" cA. {.,:""'-tL ~
~U.~(A. ~ ~ l/t>U-V- ~
i; iJ,L.. '> ~ ~lJ.-.QA C. I
(1,.<.1
Cc) If a hydrogen ion emerges with energy 2.4 x 10-12
J, at a measured speed"'6f
5 x 107 m s -1, a simple calculation of the mass of the hydrogen ion gives a value of
1.9 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.
~u
lo.. e":i:· -«, A.s S (I d..."I.. 4..).a"t> ~' 4.
t
"- m..
.. /15

15. -15-
Leave ")
blank i
~~., The following extract is taken from an article about the Continuous Electron Beam
,
~/
Accelerator Facility (CEBA.F), which produces high-energy electrons for particle
experiments.
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 predicts
that objects appear to gain mass. The electrons in CEBAF move so fast that they act
as if they have gained 8000 times their normal mass, making them far more reluctant
to change course - hence the need for powerful magnets.
The gain m mass of an electron is another way of saying that it has gained energy
equivalent to 8000 electron masses. Calculate the voltage through which an electron has
to be accelerated from rest to gain this energy .
............
i~.E.. :7 ~~~ .. ~.~{-...<: ;:: ~ .. V .
• ~. _-..,[ ( • <;5 -,- ••••
............. ~
V.:~ -
~ q~ ..~0
..L~
- -
~ .../~ ~
•••.. ~.~:.Q.:r.:.: ~ ..~~).
~
..9. .
(.~ y It:> -~qL
I
!
i
Voltage = t..:..&..V
-=-- =
. I
(3) II
I
I
I
I
I
I!
I
!
I
!
I
!
I
I
! I
!

16. -/6- 0------.....
(
. Leave 1
blank
The electrons are guided along a path
which has two straight sections with two A B
semicircular sections at each end, as
shown.
~llom
Explain the role of the magnets in this
particle accelerator, including an
approximate calculation of field strength.
You may wish to refer to the various
sections AB, BC, CD and DA along the
D C
path.
Assume that the electrons are travelling
close to the speed of light so that they have
a mass of 8000 times their nonnal mass .
........ ~.:I ~..')
A g.~.> ~.k.~ k ~y.~ ~ C.~.~~ .
......... ~~ ~.~~.~.: ::;;~ ~.9. ~~ ~(.~ ..~ ~ .
.........
~~ C.. ..ll.
~ ~: .." .

17. t r::
-It-
i'.
/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 mark
for the clarity of your answer.
r !.' ""
.........h..tl!N~.0_
1
L :-:':i).y ~~,-"" .~A.{..~'>:~
~
.:>
"I
:,,',;."D:"':
~
.'~ ..l.U~ . i
"
B .". • J
"-
l
~""
...•.•....•. , ~".:.-> .•.•..•....••...•...•.•..•••...•..••.....•.•.•..•.••....•.•........•..•.•.•••.•.••..•••••.•...•.
P·J·tl ~
I
II
........
s~~A.~ ~:-!.~~.~ )~-."f')&.?~'~
. :7:7. -J~.P .~~ .
...........Q~ .-i':.~'Y.:'.~"""", 0'~~
i .~..
f'-,
)i ~.~ .~~ .p .~h'. ~)..1
f ..-r'(
i
I
v~.~
.................... ~..&? SA'D:lIf... ~~. V4)..r.:.~
- .
I
........................................................................... - ' .
.. ~
I
.I I
i
I I
I I
!...J
'_._ ..._._-_ ..... _ ..--.------.--. -----------------_ ... _. .__ i

18. ( Leave'1
i blank !
1 (ii) Explain the origin of the centripetal force that is making the electron spiral in this i
m~cr i
I
i I
·1 :.: .. ~~':~.~~::::::::~::~::':::.::':::::::::"::::::::::::::::::::::.:::::::::::.:::.::::::: I
I I
I ., ~~~s~~~r~~l~s ~f'~~'~;r~l~'l~' :~~~ ·l;;~·~~~~~·~~d~all~~e~;e~~e~ ....... I
I. . r2.~Q'Y.: .. d. ""..........................................................................
!
(4)
(b) Theory shows that the momentum p of the electron at any point on its path is given
il, ,.1,1'.:
I by p = Ber, where B is the magnetic flux density perpendicular to its motion, r is the
I 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 I
1.1 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.)
...1?: ?..~ ~.R ..r. , , I
,.........................................
..... ..~ :U ..Y. .k,,- ..Q~~'..(:, >:: ...' 'C.. I
I ::; :.~.2.~9.~.~~ :-I.~ ~
.. -
.. y.................................................... I I
I I
1
i
., 'C: "'1?. ..><.. LD.::'~ ,( ~ &:.?,.?.~.9~~".................. I i
i1 = .1."' ..~0..~:.oP5.................................................................. I I
1,1 ;~ .;~ ~.~.~.~.~ ~ ~~.................. I,I,!II 11,1
..... ~ .. ; -- "? ~ Y.: .q ~ -:-..:.h.$.- ~ .. K? ~ .
-.q ~
g.~' y ~ .-.~.. 9.
...... .... ~
1 J:.~ ~ 2.:.1. ~ .. ~p. ~
.~ .
I ~ S.·.~ y ...f.;?~"::.y.s
.. ···········..········..··(3) I I
I.~ --ll'---_.J
.. , /17
._-- ... _--------------

19. if).
-17-
;~----------------------------------------------------------------------~--~,
, Leave f
f
(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 015~ res .
• _0.1.. uLv" •... a .•.. L r711 1.61.1..1.. L ...
Deduce the effective mass of the electron. at each point and comment on your
results .
........ 9. :;. ~.~
;-:-:7. ~ .. :: o
..;... . ,
t
r:
'~
I
........ ~ ..?
.f..~ ~.7..:.~Q~.~.~.~?
-=- . .
.. ;; 4:.O' ~.!'O ..~~~ ~
::
.
I
e ~.,.,....~ ----
~ >'" 0 'Nt s" I!
-"t..q •
(
......... .:
~ ~
r:
7 }:~.?-::.~ ..
:.
I
:.~:'? ~
_'l..l .
~.?.:': ..~.q ~ .
"> >'" to "A:> I
R..
......... ~ .. : ~~:-- =:'
<; f
: ..~ .. ~ ~.Y>
- .•..11J
?: ::: -..1... :?': ~ 9.
-"ttt ~
~ .
!
..., ">./ 1 Q'. '<" ....• .,.. - -- . -
I
~ -- . ~,>
I
(4)
'~A.
I
I
l'----- -----------------------~ ~
./0<0

20. -2JJ-
---------~---
.. T
Leave ;
blank
SYNOPTIC QUESTION
/)') The diagram shows part of a linear accelerator - a linac. Alternate metal tubes are
I
connected together and to opposite terminals of a high-frequency alternating potential
difference of fixed frequency.
High frequency
I B D
alternating Injected ~ ) ~~. p.ratan
potential protons l~,-,,-)----.---,,-} <--) Ll:':~_) etc ~ beam
difference A c
(a) Describe how the protons are accelerated as they move along the linac and explain
why the tubes get longer towards the right. You may be awarded a mark for the
clarity of your answer.
.......
k······~·~·~;··~·····f······±·······~········
~.~.~.Ab :.?'1' .
.......... .~': !~ ~ ~ .. ~ ~ ~ '> ~~ ~.~ .
........~.~~.~ f!.,..~~~ (i...v..~ s.r-.p .
.........
h~ !~ ~.~~ ~ ~~ .
.........~ r:.1. '??'? ~ .. 1 ~ ~ $..~ ..
~ ~ ~
(5)
;
._---- --_/

21. .---------------~--. _. ------.-. -----~--.~~-- ._---.----
Leave
blank j
r)
(b _ parncu 1" nnac nas q.~J metal" tubes and. the peak voltage
A . ar A?~ 1 , - < f h
0_ the a 'L··
tematmg suppiy 1
is 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 a
stationary proton. Take the mass of a proton ri1p as 1.01 u .
.-
- il ' ,eg - I'{ J
.;:;:.. -:x .
....... ..
? L..x. :.b ..y.. j,0 ~ ~ ~ 'f':7 .I.D J/. .
-{
............'.'-;; S.:.4...~. J.b 3 < •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
r:: ~-=-- r -i~ ~
:; ?:1:.!5.1Q _----=- > ~
Ai «:
......... ..~.~~
:;,.,::: ?") ~.::: ~
c; " ..
: b:.Q ..;;...: .
C'- (1) »c: lOa-
................................................................................................................................
"1..>~') ". {O--...rr
~!
!
f 0 ~'"'l.£r!
......... :.. .. O
~.· ~ ~ ~.~ ~ 0:..1.6 .
, ib( )< . ,1.. y o-"..~~~
......................................... ~ .
(6)
(ii) The frequency of the alternating supply is 390 MHz. Calculate how long it takes
a proton to travel along the linac .
...........:+ hP .1 ;.: ~.AO ; It .~.Q
........-----=- .
>10>", 0&
""
0
Time = ...J:., ...
1
r....b>.~..•.............
~====~=.~
(2)
i
i
!1
i
I
!
_'-- __ .J
-- ._- -- -_ .... _- ---------------------

22. Leave
blank
(c) The emerging protons can be made to collide with
(i) a target of fixed protons, e.g. liquid hydrogen, or
(ii) a similar beam of protons travelling in the opposite direction.
S·tate some acvantages orf eit er or botl expenmenta 1 arrangement ( s) .
1. eith otn .
.... ) £.C1.....'S..i..
. rw..~ ,.,
.. ~D ~~ ~ S1.~.~.':1..~ .
...............
~~ ilil. .
.....~.)
~ ~.?.~ ..Q ~"? ~.. (..l.~ A~~ ~ .
. ..~.~ -:':"? ~ ~ ~~.~ t?{h-:-:~:.d:es '" .
(2)
(Tota115 marks)
I
i
l~ !
~------------------.----- ·------------------------.----------------------------------~--~--/
.. !.!.3