Download Appendix A A Simple Approach to the Concept of Capacitance

Appendices
Appendix A
A Simple Approach to the Concept of Capacitance
Consider two insulated conductors well separated from each other, one of which carries positive
charge and the other negative charge of equal magnitude. The potential of the positively charged
conductor, A, will be positive owing to the positive charges on it, and that of the negatively
charged capacitor, B, will be negative due to the negative charges on it.
Now bring the two conductors close together; the potential of A (VA) will be reduced owing to the
nearby negative charges on B, and the potential of B (VB) will be raised owing to the nearby
positive charges on A. The potential difference (VA - VB) will therefore be reduced, and if the two
conductors are very close to each other, it will require much larger amounts of charge to give
(VA - VB) its original magnitude. Such a combination of conductors in close proximity is called a
capacitor. The ratio Q/V of the magnitude of the charge on each to the potential difference (P.D.)
between them is called the capacitance C. Thus,
C = Q/V.
The capacitance, C, of a capacitor depends on the distance, d, between its conductors and the
area, A, they present to each other. The functional relationship between C, A and d depends only
on the geometrical shape and arrangement of the conductors, but the smaller d and the larger A
are, the larger is C. For the case of the very simple geometry of two parallel plates:
C  1/d
and
C  A.
Charging a capacitor with a battery
Since V = Q/C, if the capacitor is originally uncharged, the P.D.
between its plates is zero.
Therefore,
i
VB = VA,
A
C
B
and VA is the same potential as that of the positive terminal of the
battery. The P.D. (VB - VD) across the resistance, R, is therefore
initially equal to the P.D. between the terminals of the battery, V.
A current, i, given by:
i
(V B - V D )
R
=
V
,
R
V
+
-
R
i
D
therefore flows in the direction shown, and, as a result, charge
begins to build up on the plates, +ve charge on A and negative charge on B at a rate given by:
dq
(
) V
= i= VB VD = ,
dt
R
R
and the P.D. (VA - VB) starts to increase. Since VA is fixed (at the potential of the +ve terminal of
the battery), VB must fall, and hence (VB - VD) must fall (as VD is fixed at the potential of the
negative terminal of the battery). Hence,
dq
(
)
= i= VB VD
dt
R
steadily reduces as the capacitor charges up. Eventually we reach a stage where VB = VD and
i = 0: the P.D. between the plates of the capacitor is V.
Physics 121/2 and 141/2 Laboratory Manual
A-1
Appendix B
The Junction Diode
Semiconductors and Doping
Germanium and silicon are semiconductor materials commonly used for diodes and transistors.
Both are elements of valence four; that is, in the crystalline state an atom is held by bonds formed
by sharing its four valence electrons with four other atoms. At absolute zero all these bonds
would be intact, but at room temperature a few will fracture due to thermal vibrations, and some
electrons will be free to move throughout the crystal. The "hole", or absence of electric charge, left
by the electron also effectively moves. For example, if an electron in a neighbouring atom moves
under the action of the electric field to fill the gap, then the hole will appear to have moved in the
opposite direction as if positively charged. The energy required to produce such a "electron-hole"
pair is 0.7 eV for germanium and 1.1 eV for silicon. Therefore, equal numbers of electrons and
holes can act as negative and positive charge carriers, respectively, in the conductor.
If then the semiconductor is "doped", that is, controlled amounts of a selected impurity are added,
then the balance between the positive and negative mobile charge carriers can be upset and the
conductivity of the semiconductor can increase dramatically. For example, if a small amount (say
one part in 108) of an element of valence five, e.g. phosphorus or arsenic, were added then the
impurity atoms would try to fit into the semiconductor lattice. However, at each impurity site
there would be one valence electron over, and at room temperature nearly all these weakly bound
electrons would be free to move throughout the lattice. The conductivity would have increased by
more than a factor of ten. The remaining impurity atom would be positively charged but it is not
a free hole since it cannot accommodate any neighbouring free electrons. (All four bonds with the
lattice are already filled.) This type of doped semiconductor is known as an n-type (for negative)
semiconductor because the current is mostly carried by electrons, known as the "majority
carriers". The phosphorus or arsenic is called a donor impurity because it donates an electron to
the conduction process.
Alternatively, one can form a p-type (for positive) semiconductor by adding an acceptor impurity,
which would be an element of valence three, e.g. indium or aluminium. Its atoms would also try
to fit into the semiconductor lattice but for each atom there would be one valence electron too few
to form all four bonds. An electron from a neighbouring atom would be attracted to the impurity
site. The result would be a hole where the electron came from which would be available for
conduction, and a fixed, negatively-charged ionized acceptor atom at the impurity site. Therefore,
holes are majority carriers in a p-type semiconductor.
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Physics 121/2 and 141/2 Laboratory Manual
The Junction Diode
A semiconductor junction diode is formed at the junction between a p-type and a n-type region in
the same crystal. Initially, mobile electrons near the junction flow from the n-type region to the
p-type region to combine with positively-charged holes there, and holes near the junction "move"
in the opposite direction. This current will stop when a large enough potential barrier is formed
across the junction - holes moving towards the n-type region will be repelled by the electric field
created by an excess of positive charge there, and, similarly, electrons moving towards the p-type
region will be repelled by the electric field set up due to the electrons which have already
migrated there. The p-type region is left with an overall negative charge, and the n-type region is
left with an overall positive charge. The net result is a P.D. across a region around the junction
containing no mobile carriers - the "depletion region".
Junction
p
n
Depletion Region (shaded)
Increasing
V
+
Figure 1
Now consider the effect of connecting an external P.D., for example a battery, across the diode.
-
+
p
n
+
V
Figure 2
If a battery is connected so as to increase the P.D., then no net number of majority carriers will be
able to cross the junction and almost no current will flow. Only the small number of thermally
released minority carriers (holes in the n-type region, electrons in the p-type region) will be able
to cross the junction and form a current, which typically is microamps at most.
If a battery is connected with opposite polarity to that shown above, and the E.M.F. is gradually
increased from zero, it will decrease and then reverse the internal P.D. across the diode. Majority
carriers on either side would then be able to cross the junction and a relatively large current
would be established. As the E.M.F. is increased, the resistance of the diode drops to near zero
and the current increases rapidly.
Physics 121/2 and 141/2 Laboratory Manual
A-3
Appendix C
The Spark Generator
The circuit used for the generation of sparks is as follows:
Secondary
Winding: S
Primary
Winding: P
C
A
B
K
Car
Battery
Spark
Plug
Figure 1
The low resistance primary winding P consists of a few turns of insulated copper wire wound over,
but insulated from, an iron core. This primary coil is in series with a high-current power supply
and the switch AK, which is opened and closed by rotating the cam B. The secondary winding S
consists of a large number of turns wound around P, but insulated from it, and connected to the
spark plug. (In cars the spark plugs are connected to the secondary via a distributor, which
delivers a voltage to the right spark plug at the right time.) When AK is closed a steady current
flows and a magnetic flux is induced in the primary. (The iron core amplifies the magnetic flux
density.) When AK is opened this current is interrupted (i.e. the current is now changing) and a
corresponding change in the magnetic flux through P is induced. This changing flux also threads
the coils of S, and hence induces a voltage in the secondary circuit according to the transformer
equation:
V2=
n2
V1 ,
n1
where V2 and V1 are the induced voltages across the secondary and primary coils, respectively,
and n2 and n1 are the number of turns in the secondary and primary coils. Due to the fact that
n2»n1, the secondary voltage is sufficiently high to cause a spark to appear across the gap in the
circuit at the plug tip.
Finally, the capacitor C prevents a spark occurring between the points A and K as they are being
separated, which would soon damage them. If C was not in the circuit, the voltage of the battery
would appear immediately across AK when they are separated, thus causing a spark across the
narrow gap. With C in the circuit, however, the capacitor begins to charge as soon as AK is
opened, and so initially the voltage of the battery appears across the resistance of the winding and
not AK.
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Physics 121/2 and 141/2 Laboratory Manual
Appendix D
Mechanism of the Breakdown of a Neon Diode
There are a number of processes going on inside the envelope of a neon diode before it is
connected in a circuit.
1.
There are always some electrons being released from the electrodes or the gas atoms by
background radiation such as:
(i)
Ultra violet light, if it gets through the glass envelope, can eject photoelectrons from
the metal cathode. If the metal surface is not atomically clean, visible light may
suffice.
(ii)
-rays from the surroundings, e.g. bricks in the building, can release electrons from
the electrodes or from gas molecules. These photoelectrons are energetic enough to
pass through several millimetres of gas, knocking electrons from gas atoms.
(iii)
An occasion
-particle from radioactive contamination of the electrodes or the
envelope will pass through the gas leaving a dense track of ionized atoms.
(iv)
A cosmic ray particle, usually a muon, may pass through the gas leaving a thin trail
of ionized atoms. Cosmic ray ionization is likely to be only about 25% of that
produced by other sources.
Note: Some luminous watches are a considerable source of -rays. You may notice a change
in the behaviour of the tube if you put your watch close to it. (Room lighting may also
have to be excluded.)
2.
If a voltage much lower than VS is applied across the electrodes, these ions will be collected
constituting a current, but it is much too small to be measured without specially sensitive
equipment. If the voltage is raised, electrons accelerating towards the anode may acquire
enough energy in one mean free path to knock an electron out of the next gas atom they hit.
To do this they require an energy of 21.47 electron volts, corresponding to the ionization
potential of neon. In this way one electron can grow quickly to an avalanche, the number of
electrons nearly doubling with each mean free path. The current, however, is still too small
to be detected except by the use of an amplifier.
3.
To produce a glow discharge and appreciable current, an avalanche must be able to breed
more avalanches. This it can do by means of ultra violet light from excited atoms in the
avalanche, or by electrons extracted from the cathode by electrostatic forces as positive ions
approach just before they are collected. The probability of this is very low, and
consequently the avalanches have to be large enough or numerous enough to ensure that at
least one secondary electron is always extracted from the cathode to continue the discharge,
thus making it self-maintaining. If the average number of secondary electrons resulting
from an avalanche was only one, then frequently the number of secondaries would be zero,
but occasionally it would be several. The first avalanche would then usually fail to breed.
Alternatively, after waiting for several primary avalanches, one of them may give several
secondaries leading to a few generations of avalanches which would then peter out.
However, larger avalanches giving a larger average number of secondary electrons could
ensure that, in spite of fluctuations, there will always be one or more secondaries to produce
the next generation of avalanches. Since the avalanche size increases with the applied
voltage, breakdown will occur when the voltage is made high enough. This is the
breakdown voltage, VS.
4.
You can now see why the breakdown voltage is variable. There have to be enough positive
ions or U.V. photons reaching the cathode to give a guaranteed continuing supply of
secondary electrons. This can be achieved in two ways: either by waiting for a large enough
group of electrons to be released by chance by the background radiation, giving many
Physics 121/2 and 141/2 Laboratory Manual
A-5
avalanches, or by raising the voltage to get big enough avalanches even if they arrive one at
a time. Thus, if the voltage is building up quickly it may go higher before breakdown than
it would do otherwise. Again, if the background is increased with U.V. light or a -source,
breakdown will occur earlier, at a lower voltage.
5.
Now, once avalanche breeding sets in, there is a copious supply of secondary electrons and
the discharge can be maintained at a much lower voltage than the breakdown voltage. At a
slightly lower voltage the supply of secondary electrons will be inadequate (smaller
avalanches) and the discharge will go out. This is the quenching voltage, Vq.
6.
The instant the discharge goes out there will be some positive ions still uncollected, and
secondary electrons released during their collection will make it easier to start the
discharge again if the voltage rises again immediately.
A-6
Physics 121/2 and 141/2 Laboratory Manual
Appendix E
X-Ray Production
Bremsstrahlung
In the photoelectric effect, a photon transfers all its electromagnetic energy to a bound electron;
the photon's energy appears as the binding energy and kinetic energy of the photo-electron. The
inverse effect is that in which an electron loses kinetic energy and, in so doing, creates one (or
more) photons. This is an important process in the production of X-rays.
Consider the situation where a fast moving electron comes close to the positively charged nucleus
of an atom and thus is deflected by it (Figure 1). The electron experiences a large attractive force
as a consequence of its interaction with the heavy, positively charged nucleus; hence it is diverted
from its straight line path (i.e. accelerated). Quantum theory predicts that an accelerated electric
charge (as in the case of the electron) will radiate electromagnetic energy in the form of discrete
photons. It is therefore expected that a deflected electron will radiate one or more photons and
thus it will leave the site of the collision with less kinetic energy than it had, such that:
(K1 - K2) = Ephoton.
K1
-
nucleus
+
K2
photon
Figure 1
The radiation produced in such a collision is referred to as bremsstrahlung.
X-Ray Tubes
The X-rays you will use for your experiments are produced in an X-ray tube known as the
hot-cathode type. This refers to the use of a heated tungsten filament as the electron source (the
cathode). The anode is a heavy copper rod. An electric current through the tungsten filament
heats the cathode to a high enough temperature so that the electrons have sufficient kinetic
energy to overcome their binding to the cathode surface, and thus be released in thermionic
emission.
When applying a large voltage between the cathode and the anode (in this case either 20 or 30
kV), the electrons from the tungsten filament are accelerated through a vacuum towards the
copper target. On striking the target the electrons are decelerated and essentially brought to rest
in collisions. Although most of this appears as thermal energy in the target, a small fraction goes
into the production of electromagnetic radiation through the previous bremsstrahlung process.
Physics 121/2 and 141/2 Laboratory Manual
A-7
Figure 2 shows a typical spectrum arising from bremsstrahlung collisions of electrons with atoms.
Note the continuous nature of the spectrum.
Relative
Intensity
fmax
frequency (Hz)
Figure
Figure22
Ionization
Another process present in production of X-rays from the X-ray tube is excitation or ionization.
When atoms are bombarded with high energy electrons, an inner electron from the atom may be
excited or removed. When such an inner electron is displaced, a vacancy is created within the K
shell which may be filled by the transition of an electron from a higher shell (e.g. the L or M
shell).
The transition to the more bound state of the atom is accompanied by emission of a photon. The
energy of this photon is dependent upon its initial state:
a transition from the L shell to the K shell produces a K  photon;
a transition from the M shell to the K shell produces a K ß photon.
The actual energies of the K, Kß, ..., photons are determined by the spacing of the atomic energy
levels and, hence, will be different for different atoms. In your case the target atom is copper and
the characteristic X-rays are:
Note:
A-8
K:
 = 0.154 x 10-9 m
K ß:
 = 0.138 x 10-9 m.
K photons are of negligible intensity and therefore one would only expect to see
X-rays of energies corresponding to K and Kß contributing to the total spectrum of
the X-ray tube.)
Physics 121/2 and 141/2 Laboratory Manual
Appendix F
Mounting the Crystals

Select the crystal to be mounted and place one of the short edges onto the step in the crystal
post.

Ensure that the major (long, broad) face having the "flat-matt" appearance, is sitting butted
against the chamfered protrusion of the post (see Figure 1, below).

Screw the clamp until the crystal is held securely by the rubber jaw.
Note:
The experimental face of the crystal is the face in contact with the chamfer on the
post.)
Cubic crystal
smooth face of
crystal faces the
x-rays
chamfered post
Clamping jaw
Clamping screw
crystal post
Figure 1: Mounting of Cubic Crystals
Figure 1: Mounting of cubic crystals
Physics 121/2 and 141/2 Laboratory Manual
A-9
Appendix G
Reading a Vernier Scale
The Vernier Scale is used whenever one needs to make a measurement of distance or angle to an
accuracy greater than that obtainable through direct visual reading of a linear scale.
The exact geometry of the Vernier Scale will often depend on the situation in which it is
employed. Despite this, the principle of its working remains the same.
In using the Vernier, it is useful to realise that the measurement can be broken down into two
parts. These are:
the visual: this part of the measurement proceeds normally (where the ‘pointer’ of the
measurement may be the ‘zero’ of the Vernier scale). The measurement is made to the limit of
reading of the scale
the Vernier: this is the new part of the measurement: by reading the Vernier an extra significant
figure can generally be obtained in the measurement.
Construction of the Vernier
The Vernier uses the linear reading scale of the measuring apparatus along with another scale
which is scaled by a factor of 9:10 compared to the linear scale.
Vernier Scale
2
3
0
1
4
5
2
6
3
4
7
5
8
9
mm.
Linear Scale
Figure 1
In the above situation, two markings from the Vernier line up with the linear scale. This is only
because the reading is exactly 4mm. You can see that the ten markings on the Vernier span the
space of only nine markings on the Linear scale. This means that generally only one of the
Vernier markings will align with the linear scale. The figure that lines up most closely provides
the next significant figure in your measurement.
Notice that if the pointer (the zero) was moved from 4 mm to 4.5 mm each of the markings on the
Vernier scale would line up with a marking on the linear scale only once and that they would do
this in turn from left to right. Thus the Vernier indicates faithfully the last significant figure of
accuracy. Understanding this is understanding the functioning of the Vernier scale.
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Physics 121/2 and 141/2 Laboratory Manual
Example:
0
2
3
1
4
2
5
3
6
4
7
5
8
mm.
9
Figure 2
In order to read this scale we might employ the following method:
1. Read the linear part of the measurement, in this case, from the ‘zero’ of the Vernier. Doing this
returns a result of 3.5 mm.
2. Next, determine which marking on the Vernier scale most nearly lines up with the markings
on the linear scale. Personally, I do this by scanning my eye across the scale and judging
whether the Vernier scale is to the left or the right of the linear scale. When I cannot decide
‘left’ or ‘right’, I know that I have alignment. In the above measurement I would thus say:
“right, right, right, right, don’t know, left, left...”, and thus determine that it is the 2 which
most closely lines up with the linear scale. This means that I need to add 0.20 mm to my
earlier, linear reading.
3. As the Vernier scale has a limit of reading of 0.05 mm, my uncertainty for this reading is
0.025 mm, which would possibly, most fairly be rounded to 0.03 mm. Thus my final result
would be 3.70  0.03 mm.
Exercises:
Try reading the following scales for practice:
1
mm. 2
3
mm. 2
Solutions:
0
1
3
2
4
0
5
3
3
5
10
4
6
15
4
1: 2.65  0.03 mm.
2
5
7
20
8
9
25
5
2: 4.75  0.03 mm.
Physics 121/2 and 141/2 Laboratory Manual
0
mm. 2
4
3
0
mm. 2
1
4
5
2
4
2.5
3: 2.65  0.03 mm.
2
3
6
6
7
8
4
8
5
9
10
3
3.5
4: 2.23  0.0005 mm.
A-11
Appendix H
S.I. Units
Quantity
Name of S.I. Unit
Symbol
S.I. Base Units
frequency
hertz
Hz
1 Hz = 1/s
force
newton
N
1 N = 1 kg m / s2
energy
joule
J
1J = 1Nm
power
watt
W
1 W = 1 J/s
quantity of electric charge
coulomb
C
1C = 1As
electric potential,
potential difference, tension,
electromotive force
volt
V
1 V = 1 W/A
electric capacitance
farad
F
1 F = 1 A s/V
electric resistance
ohm

1  = 1 V/A
inductance
henry
H
1 H = 1 V s/A
Note:
A-12
The S.I. units have been expressed in terms of the S.I. base units, namely metre (m),
kilogram (kg), second (s) and ampere (A). These are, of course, the units for the
following respective quantities: length, mass, time and electric current.
Physics 121/2 and 141/2 Laboratory Manual
Appendix I
Detector Construction and Operation
The basic feature of the operation of
the detectors is the production of an
electrical signal when radiation is
detected. We therefore start with a
simplified version of how the geiger
counter and the scintillation counter
work.
Interaction
site: gas is
ionised,
enabling
current flow
Anode (+) Cathode
(-)
+ ion flow
The geiger counter consists of a
- ion flow
Incident
cylindrical case with an axial wire
radiation
running through it; the cylinder being Insulator
Gas Mixture
filled with a suitable mixture of gases
(see Figure 1). The axial wire is
Filament
insulated from the cylindrical case
Figure 1
and is held at a positive potential
relative to the case by means of a D.C.
power supply. When ionising radiation enters the counter, it ionises some of the gas molecules
along its path, and the negative ions and/or electrons so formed are attracted to the anode whilst
the positive ions are attracted to the cathode.
As the electrons are accelerated by the electric field between the electrodes towards the anode,
they have collisions with other gas molecules, thereby causing further ionisation. This process of
charge multiplication occurs many times. The net result is that a substantial negative charge is
eventually dumped on the anode.
PHOSPHOR
+
ANODE
CATHODE
DYNODES
Figure 2
The scintillation counter consists of a transparent substance, known as a scintillator or phosphor
(in your case a sodium iodide crystal impregnated with thallium), one face of which is optically
coupled to a photomultiplier tube, the other faces being coated with a reflecting material. (A
photomultiplier is an evacuated glass tube with an assortment of electrodes in it - see Figure 2).
When radiation interacts with the phosphor, it gives rise to tiny flashes of light which impinge on
the end of the photomultiplier. The light entering the photomultiplier strikes the cathode, which
is coated with a photosensitive material, causing it to emit photoelectrons. These are attracted to
the next electrode, called a dynode, which is held positive relative to the cathode. The dynode is
coated with a material which has the property that when one electron strikes it, more than one
electron is liberated. These electrons are then attracted to the still more positive next electrode,
where further electron multiplication occurs, and so on down the photomultiplier, until eventually
a substantial burst of electrons is deposited on the anode.
Thus, with both types of detector, the net result of radiation interacting with it is the dumping of
a burst of negative charge on the anode.
Physics 121/2 and 141/2 Laboratory Manual
A-13
Voltage Pulses
The anode of a detector is connected to a high voltage power supply via a resistor, R, known as the
load resistor, and is isolated from the preamplifier (the first piece of equipment connected to the
detector) by a capacitor C. This capacitor allows the input terminal of the preamplifier to remain
at a low voltage, i.e. the potential difference between the plates of C is normally close to V volts.
HIGH
VOLTAGE
POWER
SUPPLY
V volts
+
Resistance, R
C
PREAMPLIFIER
CATHODE
ANODE
Figure 3
In its normal state, the anode of the detector is at the same potential as the +ve terminal of the
power supply. This is because, in the absence of any current between the anode and the cathode,
no current flows through R. When the burst of negative charge is dumped on the anode, as a
result of a radiation detection event, the potential of the anode is lowered. There is, therefore, a
potential difference established across R, and a current flows through R, until the anode potential
eventually rises to that of the positive terminal of the power supply again. Physically, this
current is simply the escape of the burst of electrons which was dumped on the anode. These
electrons pass through the H.V. supply and on to earth.
The variation of the charge, and, therefore, of the
voltage, on the anode will be a function of time as
shown on the voltage- time graph. t is the time
during which the negative charge is dumped on
the anode - the time to produce the voltage drop.
The decay of the voltage drop is quite protracted
because, as more of the electrons escape through
R, the potential difference across R gets smaller,
hence the current gets smaller, and the decay of
the voltage drop gets slower. The complete
potential variation, arising from the radiation
detection event, is known as a voltage pulse.

Voltage
time
Figure 4
Since the left-hand plate of C is connected to the anode with virtually zero resistance in between,
this left-hand plate is essentially part of the anode, and the presence of negative charge on it
during the time of the voltage pulse lowers the potential of the right-hand plate of C. Thus, the
voltage pulse appears also on the right-hand plate of C, and hence, at the input of the
preamplifier. The function of your electronics system is to count these voltage pulses.
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Physics 121/2 and 141/2 Laboratory Manual
Scintillation Counter Electronics
If your scintillation counter has two or more cable sockets in its end, the block diagram of your
electronics is as follows:
SCINTILLATION
COUNTER
PREAMPLIFIER
AMPLIFIER
POWER
SUPPLY
SINGLE
CHANNEL
ANALYSER
COUNTER
POWER
Figure 5
However, if your scintillation counter has only one lead coming from it, your block diagram is as
follows:
SCINTILLATION
COUNTER
PREAMPLIFIER
AMPLIFIER
POWER
SUPPLY
SINGLE
CHANNEL
ANALYSER
COUNTER
POWER
Figure 6
In this arrangement, the load resistance, R, of your scintillation counter is in the high voltage
lead inside the preamplifier box.
The power lead between the amplifier and the preamplifier plugs into the back of the amplifier.
This lead carries the power needed to operate the preamplifier circuits. Notice that the power
leads between the power supply and the scintillation counter, including those which go via the
preamplifier in the second block diagram, have longer and more heavily insulated plugs on them
than have the signal cables. The corresponding sockets are also different. Never try to force one
type of plug on to the other type of socket.
Identify all the components of your electronics, then read on and make yourself familiar with each
"module".
Physics 121/2 and 141/2 Laboratory Manual
A-15
(i)
Preamplifier
The current through the load resistor, R, of the detector is small for most detectors, but for
pulses to propagate along long cables (as is often required), without severe loss of
amplitude, they must be generated by high current sources. It is, therefore, customary to
feed detector pulses into a preamplifier, a circuit which can generate large current through
the load resistor on its output terminal, in response to an input pulse. Such a circuit is not
concerned with amplification of the pulse: in fact, it may even reduce the amplitude. The
output pulse from the preamplifier is fed into the amplifier.
(ii)
Amplifier
Most modern pulse electronics are designed to handle pulses with amplitudes up to 10 volts.
An amplifier, as its name suggests, produces output pulses with larger amplitude than
those presented at its input, and its "gain" controls are normally adjusted so that the pulses
being studied are amplified to a size which conveniently covers this 10 V operating range.
Your amplifier has two gain controls: a coarse control which allows substantial gain
changes to be made in discrete steps, and a fine control which allows continuous control
over a range comparable to one step of the coarse control.
Your amplifier is also designed to accept either positive or negative input pulses, the choice
being made by a selector switch on the front panel. It gives output pulses regardless of the
input pulse polarity. However, there is a choice available, by another selector switch, for
unipolar or bipolar output pulses (see Figure 7). The choice between these depends on the
shape of the input pulses and the nature of the measurement being made.
Voltage
Voltage
Unipolar Pulse
Bipolar Pulse
Time
Time
Figure 7
(iii)
Single Channel Analyser
In many applications, including all the experiments in this
laboratory, one wants to count the pulses coming from the
amplifier, or to count just those whose amplitudes fall in a
particular voltage range. The single channel analyser
(S.C.A.) has two control knobs. When the selector switch
is set to "normal", the lower level knob sets the minimum
height (in volts) of pulses to which the S.C.A. will respond,
and the upper level or window knob sets the maximum
height. Thus an output pulse isgenerated only if the input
pulse has an amplitude between the settings of these two
knobs. All the output pulses are identical, and are about 5
V high. The operation of the S.C.A. with the selector
switch set to "window" will be described later, when this
mode of operation is needed.
A-16
V
5 Volts
t
SCA output pulse
Figure 8
Physics 121/2 and 141/2 Laboratory Manual
(iv)
Counter
All that remains to be done in the radiation detection procedure is to count the pulses from
the S.C.A. This is done with the counter (more often known as the scaler), which displays
the running total as red numbers in a small window in the front panel. It has three
controls which will be found useful: a selector switch to start and stop counting, a pushbutton to reset the display to zero, and a discriminator knob. The discriminator knob
behaves in the same way as the lower level knob on the S.C.A., and is generally used only
when pulses are fed directly from an amplifier into the counter. In our application, the
counter will be counting only the 5 V pulses from the S.C.A.; any setting below 5 will,
therefore, be satisfactory.
(v)
Power Bin
Your high voltage power supply, amplifier, S.C.A. and counter all plug into a standard bin
which has a power supply mounted along its back. This power supply provides all the
power needed by these units for their operation.
(vi)
Computer Interface
If you are using the computer to acquire your data, you first need to switch on the computer
and run the data acquisition program. To do this double click the left mouse button on the
Counter Icon in the Lab Tools Group. Make sure the counter is connected to the computer
and is switched on at

Once the data acquisition program starts a window called “Radiation Counter” will appear
(see Figure 9)
Counter Control
Data/Status
Start
Break
Count Data
4000
Waiting for user input...
3000
Counter Parameters
Number of Samples
5
2000
Sample Time (sec)
1
Samples Read
Counter Runs
0
0
1000
0
0
1
2
3
4
Data Storage
File
ON
Path:
0.00
DATALOG.TXT
(C:\DATA\)
Figure
Figure 9 7
Physics 121/2 and 141/2 Laboratory Manual
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
A-18
In a typical experiment the following procedure is recommended
(i)
Make sure the counter is connected to the computer and is switched on at the wall.
The transformer should be set to 7.5 Volts.
(ii)
Before testing the counter, your demonstrator should have setup the electronics so
that the pulses coming from your detector peak at about 9 Volts. This process should
be explained to you by your demonstrator in the first prac class. In later prac classes
you may wish to setup the electronics yourself.
(iii)
Before testing your computer counter make sure that the “Data Storage” button is off.
If this is left on all your test readings will be written to a file.
(iv)
Set some test parameters, (for example 5 samples with count time of 1 second) and
click on the “start” button. Your measurements should appear in the graph window
joined by a line, if data doesn’t appear in the graph window call your demonstrator.
(v)
Once the number of samples and count time have been determined for your
experiment these values need to be set in the appropriate boxes. (Note: Quite often
you may need to take a background radiation measurement before beginning the
experiment. In this case your sample number should be set to 1.) Remember to set the
“Data Storage” button to the “on” position before collecting data. It is usually a good
idea to change the name of the file in which the data is to be stored. The convention is
to use the .txt extension for data files of this type.
(vi)
When you have finished collecting data you can analyse and plot the data using
another software package like “Microsoft Excel”.
Physics 121/2 and 141/2 Laboratory Manual
Glossary
ammeter
An instrument for measuring electric current.
analogous
Similar to; showing analogy (process of reasoning from parallel cases).
attenuate
Reduce amplitude of (signal or current).
calibration
Determination of the absolute values of the indications of an instrument such
as, for example, the prism spectrometer.
capacitor
An arrangement of one or more pairs of conductors separated by insulators
between which an electric field can be produced.
coaxial cable A cable that consists of a central wire surrounded by an insulator with an outer
coaxial conducting cylinder. The outer conductor is often earthed. Coaxial
cables do not produce external fields and are not affected by them.
collimator
A system that produces a beam of parallel light or other radiation.
converge
(Of lines) tend to meet in a point; come together as if to meet or join.
criterion
Principle or standard that a thing is judged by.
damping
Of a free oscillation - progressively dying away due to an expenditure of energy
by friction, viscosity, or other means.
decade box
A chain of, usually, four resistors in series which, normally, increase
progressively in powers of ten and, in turn, are each adjustable from 0-9; thus
in the case given a resistance range of 0-9999.
deviation (angle of)
The angle between the incident ray and the refracted (or reflected) emergent
ray.
diatomic
Consisting of two atoms in a molecule; for example, hydrogen gas, H2.
diffraction
When a beam of light passes through an aperture or past the edge of an opaque
obstacle and is allowed to fall upon a screen, patterns of light and dark bands
(with monochromatic light) or coloured bands (with white light) are observed
near the edges of the beam, and extend into the geometrical shadow. This
phenomenon, which is a particular case of interference is due to the wave
nature of light and is common to all wave motions.
discrete
Separate, individually distinct, discontinuous.
dissipate
Disperse, dispel, (cause to) disappear, fritter away (energy).
diverge
Proceed in different directions from point; take different courses from each
other.
dry cell
A primary cell in which the active constituents are absorbed in some porous
material so that the cell is unspillable. (Primary cell - a cell in which the
current is produced directly from chemical action by the solution of one of the
plates.)
Physics 121/2 and 141/2 Laboratory Manual
G-1
electrolysis
The production of chemical changes in a chemical compound or solution by
causing its oppositely charged constituents or ions to move in opposite
directions under a potential difference.
electrostatic
Of electricity at rest; based primarily on forces between electric charges.
extrapolation
The estimation of the value of a function for a value of the variable lying
outside the range of those for which the function is known. This may be done
graphically or by calculation.
flux
A flow of something through a unit area in unit time.
full scale deflection
A reading on a meter which corresponds to the maximum value of the chosen
scale.
galvanometer
An instrument for measuring or detecting small currents, historically by the
mechanical reaction between the magnetic field of the current and that of a
magnet.
harmonic
An oscillation of a periodic quantity or a tone of a series constituting a note,
whose frequency is an integral multiple of the fundamental frequency.
histogram
A graphical representation of a frequency distribution: rectangular areas
standing on each interval into which the observations are grouped show the
frequency of observations in that interval.
impedance
If an alternating E.M.F. is applied to an electric circuit the alternating current
produced is controlled by the capacitance and inductance of the circuit as well
as its resistance. This extra opposition is the reactance of the circuit and the
total opposition to current flow is the impedance. (Symbol: Z)
impinge
(Cause to) make impact (on, upon).
induction (EM)
When the magnetic flux through a circuit changes, an electromotive force is
induced in the circuit. The induced E.M.F. is equal to the rate of decrease of
magnetic flux through the circuit. If the circuit is closed, this E.M.F. gives rise
to an induced current.
inductor
A coil or other piece of apparatus possessing electromagnetic inductance and
selected for use because of that property.
inference
(Logic) forming of conclusion from previous statements and/or results.
interpolation Estimation of the value of a function, y(x), for a value of the variable, x, which lies
between those for which the function is known. This may be done graphically
or by using an interpolation formula.
ionization
The process of forming ions. Ionization occurs spontaneously when an
electrolyte dissolves in a suitable solvent. Ionization in bulk materials requires
the action of some ionizing radiation, for example, X-rays.
isotopes
Two or more atoms having an identical nuclear charge (i.e. same atomic
number) but differing in atomic mass. Such substances have almost identical
chemical properties but differing physical properties, and each is said to be an
isotope of the element of given atomic number. The difference in mass is
accounted for by the differing number of neutrons in the nucleus.
key
Alternative name given to a switch as used in electric circuits.
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Physics 121/2 and 141/2 Laboratory Manual
lateral
In a sideways direction.
leakage current
Ideally a capacitor represents a break in a circuit, but in practice some current,
termed the leakage current, manages to pass through.
micrometer
Instrument for the accurate measurement of small distances.
multimeter
Meter which is capable of measuring current, potential difference, and
resistance simply by choosing the appropriate scale.
net
Total, ultimate, effective.
nominal value
Face value.
normal
The normal to any surface at a point is the line perpendicular to the tangent
plane at that point.
ohmmeter
An instrument for measuring resistance.
ordinate
In analytical geometry, the ordinate of a point is the perpendicular distance of
the point from the axis.
overload
Subject a piece of electrical equipment to conditions (e.g. excessive current)
beyond a specified, safe limit.
parallax
(Angular amount of) apparent displacement of an object, caused by an actual
change in the point of observation.
parameter
A variable on which a system depends.
peak-to-peak Difference between maximum and minimum (peak) values which have been obtained
graphically or from a visual display.
permeability
The property of a magnetic material controlling the field produced by a given
current. It has the units henry per metre. (Symbol: )
permittivity
The property of an insulator responsible for increasing the capacity of any
system in which it is placed. It is measured in farads per metre and has a
value greater than that for a vaccuum (o). (Symbol: )
phase
The fraction of the period that has elapsed, measured from a fixed point.
Points in the path of a wave motion are said to be points of equal phase if the
displacements at those points at any instant are exactly similar; i.e. of the same
relative magnitude and varying in the same manner.
photon
The quantum (discrete unit quantity) of electromagnetic radiation. It has an
energy of h where h is the Planck constant and  the frequency of the
radiation. For some purposes photons can be considered as elementary
particles travelling at the velocity of light (c) and having a momentum of h/c
or h/ (where  is the wavelength). Photons can cause excitation of atoms and
molecules and more energetic ones can cause ionization.
photosensor
Primarily a timing device which is either turned on or off by the blocking of a
light beam which passes into a light-sensitive sensor.
polarity
The distinction between the north and south poles of a magnet or the positive
and negative parameters (e.g. voltage, charge, etc.) in an electrical circuit or
device.
Physics 121/2 and 141/2 Laboratory Manual
G-3
potentiometer
A form of 3-terminal potential divider in which the fall of potential along a
uniform wire is used to tap off any potential difference less than that between
the ends of the wire. In electronic circuits a potentiometer can also be used as
a variable resistor.
propagation
Extend the operation of, transmit (by vibration, etc.).
qualitative
Dealing only with the nature, and not the quantities, of the substances under
consideration.
quantitative
Dealing with quantities as well as the nature of the substances under
consideration.
quantized
Formed into quanta.
quantum
Discrete unit. (Often quantity of energy proportional to the frequency of the
radiation.)
rarefied
Gas or solid with decreased density or solidity, respectively.
ratio box
A device consisting of two variable resistors, R1 and R2, both of which increase
in powers of ten so that their ratio is itself an integral power of ten.
rectifier
An electrical device that permits current to flow in only one direction and can
thus make alternating into direct current. The most common rectifiers are
semiconductor diodes.
refraction
(Of light.) The change of direction that a light ray undergoes when it enters
another transparent medium.
resonance
A condition in which a vibrating system responds with maximum amplitude to
an alternating driving force. The condition exists when the frequency of the
driving force coincides with the natural undamped oscillatory frequency of the
system.
saturation
Cause (substance, air, vapour, metal) to absorb or hold the greatest possible
amount of another substance, moisture, magnetism, electricity, etc.
short circuit
An electrical connection of relatively low resistance made intentionally or
otherwise between two points in a circuit.
shunt
In general, if two electrical circuits are connected in parallel either one is said
to be in shunt with the other. In an instrument a resistor, usually of low value,
which is connected in parallel with an instrument such as an ammeter so that
only a fraction of the current flows through the instrument, thereby increasing
the range of the latter, is called a shunt.
simulate
Imitate conditions of (situation, etc.).
spectrometer An instrument for producing, examining, or recording a spectrum.
spectrum
G-4
(1)
Any particular distribution of electromagnetic radiation, such as the
display of colours produced when white light is dispersed by a prism or
diffraction grating. The term is also applied to a plot of the intensity of
electromagnetic radiation against wavelength, frequency, or energy, or to
a photographic record of dispersed electromagnetic radiation.
(2)
Any distribution of energies, momenta, velocities, etc. in a system of
particles, as in a mass spectrum or an electron spectrum.
Physics 121/2 and 141/2 Laboratory Manual
superimpose Lay (thing) on or on something else.
tolerance
Permissible variation in dimensions, weight, resistance, etc.
torque
Two equal and opposite parallel forces (couple) acting upon a body, which will
tend to cause rotational motion. The moment of a couple is the product of
either force and the perpendicular distance between the line of action of the
forces.
trajectory
The path of a body thrown or projected.
transducer
Any device for converting a non-electrical parameter (e.g. sound, pressure,
light) into electrical signals, the variations in the electrical signal parameter
being a function of the input parameter, and vice versa.
uncertainty
Alternative term for confidence limits.
vernier scale
A short scale sliding (or rotating) relative to the main scale of a length or angle
measuring instrument. It is used for determining the fraction of the smallest
interval into which the main scale is divided. The instrument pointer is the
zero division of the vernier scale.
viscosity
The property of fluids by virtue of which they offer a resistance to flow.
voltmeter
A device for measuring voltage.
Wheatstone's bridge A set of four resistors connected with two resistors in each branch of the
circuit. A galvanometer joins the midpoint (the point at which a resistor is
positioned on both sides, e.g. R1 and R2) of each branch and will show no
deflection when the voltages in the four resistors is equal, so that:
R1 / R2 = R3 / R4.
Physics 121/2 and 141/2 Laboratory Manual
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