83 AL Physics/Essay Marking Scheme/P.1
PLK VICWOOD K.T. CHONG SIXTH FORM COLLEGE
83’ AL Physics : Essay
Marking Scheme
1.
(a)
Molecules move about in random directions colliding with
other molecules fairly frequently due to their finite size.
Thus inspite of their relative fast speeds - say A  A’
the molecules, in fact, take a long time to travel from,
say, A  B.
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(b)
Tube is first evacuated by connecting via rubber tube to
pump. With capsule attached as shown, tap closed, end
of capsule broken. Tap opened and time t taken for
‘half-brown’ level to move a certain distance S up tube
is measured.
(c) (i) If the r.m.s. speed of the molecules = v and that
on average molecules suffer n collisions in time t,
average distance between collisions (mean free
path),
 = vt/n .......... (1)
Random walk statistical rule gives
S = n  ........... (2)
Hence,  = S2/vt
where v = rate of diffusion of Br2
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(ii)
Let diameter of molecule = d. Collisions will take
place for centre separations  d. On average there
is one gas molecule in a volume d2.
In liquid molecules are packed like ‘touching
spheres’ i.e. 1 molecule occupies a volume d3.
If ratio of volumes is known, say R
R = d2/d3, hence we may estimate
d = /R.
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(d)
For molecules of masses m1, m2 with r.m.s. speeds u1, u2
at the same temperature T.
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1
3
u
m1u12  m2u22  kT and 1 
2
2
2
u2
m2
m1
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Natural uranium contains isotopes 235U and 238U. In diagram
235
UF6 diffuses more through the porous wall due to the
greater average speed of these molecules and B becomes
enriched in this. Since masses only differ slightly
(238/235) thousands of cascade stages needed, any residue
from one stage being pumped back to the previous one.
2.
(a)
Hall probe
Force on current carriers (of charge Q) due to a magnetic
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83 AL Physics/Essay Marking Scheme/P.2
field B. F = BQv. Carriers drift downwards (if -ve) or
upwards (if +ve) giving rise to charged upper/lower
surfaces. When force on carrier charges, QE = F charge
flow stops and a p.d. VH can be measured.
Now E = VH/d and since QE = BQv, VH = Bvd.
If I is kept constant so will v and VH  B.
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[Diagram not required]
In measurement need to
(i) keep constant current through specimen.
(ii) adjust balance away from the magnetic field to
make sure no p.d. across X/Y contacts of the
semiconductor probe - no current through A.
(iii) move probe into position and rotate to obtain
maximum VH p.d.
( N.B. it seems common practice to use A meter for the
Hall probe measurements in schools - in fact no current
should be taken and it is best to use milli-voltmeter/
d.c. amplifier etc.)
Accuracy factors
(i) uniform (through) probe standard known field for calibration.
(ii) area of probe restricts spatial resolution if
field gradient.
(iii) may be probe not exactly perpendicular to field.
(iv) correction for temperature essential since the
mobility (and v) increases significantly with
temperature increase.
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(b)
Search coil
For the search coil shown, orientated  to alternating
magnetic field B, the induced e.m.f. across terminals
dB
PQ is E = nA
dt
i.e. E = nAB0 cos t
In measurement
(i) connect P/Q to the input terminals of a C.R.O.,
(ii) rotate coil until amplitude of
wave trace is
a maximum.
(iii) measure amplitude  B0.
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Accuracy factors
(i) uniform, known calibration field (e.g. from
Helmholtz coils),
(ii) C.R.O. of sufficient sensitivity high
enough to give large amplitude trace.
(iii) Effect of stray fields
could be comparable to field being measured.
(any 2 correct)
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83 AL Physics/Essay Marking Scheme/P.3
3.
(a) A dormant physical system A can be excited into
forced oscillations by coupled energy transfer from
a sustained oscillating system B, though the induced
oscillation amplitude will, in general, be small.
If the oscillation frequency of B is adjusted to the
natural oscillation frequency of A maximum power
transfer will occur and the amplitude of the induced
oscillations in system A will maximize - this
phenomenon is called resonance.
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(b) (i) Mechanical
e.g.(long) simple pendulum
oscillating spring
If hand is moved slightly
in direction shown when
body is at extreme position
P the oscillation of the
pendulum can be sustained.
Vibrator consists of soft
iron metal strip which is
alternately attracted by
soft iron core in a
solenoid connected to an
a.c. source.
Frequency of oscillator
adjusted to resonance
1 g
,
2 l
where l is pendulum length
and g acceleration of free
fall.
Frequency, f0 
1 k
,
2 m
where m is mass of body and
k force constant (extension/
force) for spring.
Frequency, f0 
83 AL Physics/Essay Marking Scheme/P.4
Damping of body by viscous force of medium in
which oscillation takes place will reduce
sharpness of frequency response (e.g. replace
air by water).
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4.
(ii) Acoustical
Glass tube is lowered slowly into the beaker of
water until the air inside the tube is heard to
vibrate loudly (with the frequency of the tuning
fork). [Then a stationary wave motion of the air
in the tube is produced form the superposition of
the incident and reflected waves from the air/
water surface.]
Resonant frequency, f0 = v/4l,
where l is the air column length and v velocity
of sound.
Damping of the oscillations would reduce sharpness
of the frequency response and this could be produced
by e.g. an increase in the humidity of the air.
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(iii) Electrical
Oscillator frequency varied until a maximum
current observed in the LCR circuit. If the
resistance R ~ 0 the
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Resonant frequency, f0 =
,
2 LC
where L is the inductance and C the capacitance.
Damping of the induced current would reduce the
sharpness of the frequency response and this
would be produced by increasing the resistance R.
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(iv) Atomic
e.g. Fraunhofer absorption lines in the sun’s
electromagnetic wave spectrum.
Resonant frequencies determined by the
characteristic energy levels of the constituents
of the sun’s atmosphere.
Width of absorption lines due to
(1) Doppler shift due to temperature/molecule
movement,
(2) broadening of energy levels due to neighbour
atomic interactions.
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(a) (i)
According to Huygen’s wave theory waves are sent out
from centres of disturbance along the interface line
OD and these produce a plane wavefront BD in the water.
Since the time t taken A  D is the same as that O  B,
AD OD sin i ct


OB OD sin r vt
and, n = sin i/sin r = c/v
Since n > 1 for water v < c
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(ii)
e.g. Young’s two slit interference experiment. S is a
monochromatic light source. A and B are two slits,
T being a screen. Alternate dark and bright equi-spaced
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83 AL Physics/Essay Marking Scheme/P.5
parallel (to slits) fringes are observed on the screen
due the superposition of waves from A and B. When these
are in phase a bright fringe is produced and when they
differ in phase by  (or path difference /2)
cancellation occurs producing a dark fringe.
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(N.B. no need for mathematics provided explanation of
fringe production correct.)
(b) incident on alkali metal at A and ejected
photo-electrons travel to gauze cylinder G and
current observed in electrometer E. Potential H
varied until electrons stopped and current
drops to zero. Use light of different frequencies 
Then eVs = ½mvmax2 = Elight - W0
where W0 is the work required to
move a free electron out of the surface.
Form experiment, energy of light
photon (or particle) Elight = h
Thus maximum K.E. of emitted electrons does not depend
upon the intensity of the light (expected from
wave theory) but the frequency (expected from
photon/particle theory).
(c) The probability of finding a particle id proportional to
the square of the amplitude of the ‘wave’ - i.e. the
‘waves’ are not waves of matter or fields but of
probability. Thus in the dark fringes/spots produced by
electron diffraction there is a very low probability that
an electron can be found, while for the bright fringes/spots
the probability is very high.
5.
(a) Microphone
Note :(i) Only 2 turns of a large no. turns voice coil shown.
(ii) Diaphragm has to be able to move but there must be
a restoring force produced by e.g. corrugation
annular ring connecting it to the main body frame
of the microphone ('loosely' coupled).
(iii) There is a need for a hole to equalise pressure
each side of the (vibrating) diaphragm.
(iv) Stop prevents diaphragm being moved too far
inwards - might not be able to move back and
microphone would be damaged.
Working :
Movement of air due to the change of pressure of a sound wave
incident upon the diaphragm will cause it to move together
with the voice coil into magnet gap. Since the coil turns
cut across a magnetic field an e.m.f. is induced in them and
a current flows through coil in the direction shown in
diagram - clockwise looking into microphone. Direction is
given by Lenz's law - force on this induced current acts
oppositively to the force causing displacement. Considering
a sound wave of a single frequency the pressure increase
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83 AL Physics/Essay Marking Scheme/P.6
will be followed by a rarefaction and diaphragm would then
move outwards - thus a sinusoidal time - varying voltage of
the same frequency would be generated across the ends of the
voice coil.
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[Diagram + description - 2 M ; Working - 2 M; current, etc. direction - 1 M]
(b) Loudspeaker
Note :
(i) Construction similar to microphone but cone larger area.
(ii) This is firmly but loosely coupled to main frame gap between pole pieces narrow (larger field) and
coil attached to cone has to slide freely without
touching.
Working :
Reverse of microphone - a.c. current through coil - is
subjected to an alternating force along axis (force
direction given by Fleming L.H. rule or ( V  B ) - produces
a compression of the air in front of cone followed by
rarefaction as cone move back and this is repeated with
frequency of the a.c. giving rise to a sound wave of the
same frequency.
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[diagram + description 2 M, Working 2 M, current etc direction 1 M]
Reasons for poor reproduction
(i) Frequency response depends upon mass/size smaller enhances high frequencies;
longer enhances low frequencies.
(ii) Natural resonance of diaphragm/cone may produce
'ringing' effects
(iii) Not possible to re-produce a large range of sound
levels (which can be detected by ear).
- devices inefficient at low sound levels
(iv) In loudspeaker wave from back of cone is in antiphase with that from front - could lead to
cancellation (may use baffle board or correctly
designed cabinet to prevent this).
(v) Distortions will occur at high sound levels due to
the non-linearity of the devices-causing the
production of harmonics.
N.B. Give credit to any reasonable suggestions (1 M each)
6.
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(a)
On closing key K a current I flows in circuit as shown
and at any instant
E - (IR + Q/C) = 0 ........ (1)
where Q is the charge stored in capacitor - initially
Q = 0 and finally when p.d. across capacitor = E
(no further current flow) Q0 = CE.
(i) Total work done in charging up capacitor,
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83 AL Physics/Essay Marking Scheme/P.7
Wc 
Wc 

Q0
VdQ and,
0

Q0
0
Q
Q
1 1  0
1
1
dQ   Q 2   Q02 / 2C  CE 2  Q0 E
C
C  2 0
2
2
2
(ii) Need to solve equation (i)
Q0
1 t
dQ
dt 
0 (Q0  Q)
CR 0


Q  Q0 (1  e t/CR )
dQ Q0  t /CR
=
e
dt
CR
The total energy dissipated in the resistor,

Q 2   t /CR
WR  I 2 Rdt  20
e
dt
0
C R 0
Q 2 CR 1 Q02 1
i.e.
WR  20

 Q0 E
2 C
2
C R 2
At any instant, current I =

1

2
Comment :
WC = WR = ½Q0E, and WC + WR = Q0E
Q0E represents the work done inside the battery transferring charge Q0 from one plate to the other
against a constant p.d. (e.m.f.) of E and this internal
work is equal to the net total work done in the
external circuit.
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(b)
First of all neglect R, Current, I =
dQ d(CE 0 sin t)
=
dt
dt
and I = CE0cos t ........ (1)
If R considered, C neglected.
Current, I’ = E0/R sin t
Thus for capacitor effective impedance = I/C compared
with R for the resistor.
Given condition implies that R < 1/C, i.e.
p.d. across R can be neglected.
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Current in circuit at any instant is given by equation (1)
while the power, P = IE = CE02 sint cost
i.e. P = ½CE02 sin2t ........(2)
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Comment :
Power flows out and into the a.c. source alternately at
a frequency double that of the source.
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