Download Current Electricity and Elastic Properties of Solids

Physics
AS/ unit 1 2011
1
Current Electricity
Charge, Current, and Potential Difference
Electric current is a flow of charge in a conducting material.
For there to be conduction, there have to be charge carriers that are free to move about.

In a metallic wire the charge carriers are always negatively charged, they are
electrons. In all solid conducting materials, the flow of charge is entirely due to the
movement of electrons. Positive charge carriers in a solid metal do not move.

In liquids and solutions (electrolytes) current is due to movement of positive ions
and negative ions.

In gases, current is due to the movement of positive ions and electrons.
When discussing electricity care is needed. Electrons actually flow from negative to
positive. We regard the flow of conventional currents as being from positive to negative.
We will always regard the direction of currents as conventional unless otherwise stated.
Activity: Draw a simple circuit below showing conventional and actual current using an
arrow to indicate direction
Conventional current
Actual current
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We regard metallic conductors as being a lattice of fixed positive ions in a sea of free
electrons.
Positive ions
Free electrons
In metals the electrons move about randomly at around 3  105 ms-1. When an electric
current starts to flow, the movement is still random, at 3  105 ms-1, but there is an overall
drift from the negative end to the positive. This speed is no more than a few millimetres per
second.
If the electrons are tied up in covalent or ionic bonds, they cannot move and the material is
an insulator. The best conductors, silver and copper are 1023 times better at conducting
than the best insulators, because they have lots of free electrons. Between these are the
semi-conductors with a few free electrons.
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Current and Charge
Current is rate of flow of charge




Current I is measured in ampères, or amps (A)
Charge Q is measured in coulombs (C)
time t is measured in seconds (s)
1 coulomb is the quantity of charge carried past a given point if a steady current of
1 amp flows for 1 second.
1 electron carries a charge of -1.6  10-19 C symbol e (this can be found on the formula
sheet)
Therefore 1 coulomb of charge is equivalent to 6.2 1018 electrons.
Activity: if a current of 3.2A flows through a circuit find the number of electrons passing a
point in the circuit per second.
If the current varies at all, we can still measure the charge by plotting a graph of the current
against time.
 The area under the graph is the charge. You may need to find the area using the
counting squares approach if the graph is curved and not linear.
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Potential Difference
In any circuit, electrical energy is converted to other forms of energy.
Activity: write down the energy transformations present in a torch.
The potential difference between two points in a circuit is the amount of electrical
energy changed into other forms of energy when a unit charge (1 coulomb) passes
from one point to the other.
Activity: in the diagram below if 4C of charge passes through the bulb entering with a total
energy of 12.6J and leaving with 3.4J then what is the potential difference?
Current
12.6J
3.4J
Potential difference is work done or energy transferred per unit charge



V is the potential difference (voltage) measured in Volts (V)
Charge Q is measured in coulombs (C)
W is the work done or energy tranferred measured in joules (J)
Using the definition above, we can define the volt as joules per coulomb.
1 V = 1 JC-1

1 volt is the potential difference (p.d.) between two points if 1 joule of energy is
converted for each coulomb of charge that passes between the points
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Resistance
Resistance is the opposition to the flow of an electric current. Resistance in a
conductor arises due to the collisions between the charge carriers and the ions in
the lattice. In each collision energy is transferred from the charge carries to the
lattice ions. The internal energy rises, so the conductor gets hot. The hotter the
conductor, the greater the vibration of the lattice ions. The probability of a collision
between an ion and an electron therefore increases.

The resistance of a metallic conductor increases with temperature.
The resistance of a conductor is the ratio between the potential difference and the
current.



V is the potential difference (voltage) measured in volts (V)
R is the resistance measured in ohms ()
I is the current measured in amps
The unit for resistance is ohm (). (The curious symbol ‘’ is Omega, a Greek capital letter )
Example:
A Bulb of resistance 25 has a potential difference of 8V applied across it.
a)
Calculate the current produced in the bulb
b)
Calculate the charge delivered to the bulb in 1 minute
c)
Calculate the number of electrons flowing through the bulb in 1 minute
d)
Calculate the energy dissipated in the bulb during 1 minute
Questions: P29 Q1,2,8,9,10,11,12,13,14,15
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Energy and power in a Circuit
Suppose that the charge that flowed through an electrical component was in the form of a
steady current that flowed for t seconds.
We know that Q = It and W = QV.
If we substitute Q in the second equation and make W the subject, we get
Now we know from module 2 that:
Power (W) = work done (J)
Time (s)
Substituting our first equation into the power equation gives us an equation for power
Power is measure in watts (W).
Example
An immersion heater is rated at 3 kW and is switched on for 2000 s. During this time a
charge of 25 000 C is supplied. What is the potential difference across the element?
For a given power, the lower the voltage, the higher the current.
The starter motor in a car has a power of about 2400 watts. This would require a current of
10 A at mains voltage (240V), but 200 A at 12 volts, the voltage of a car battery. The wire
leading to the starter motor is very thick to prevent it from overheating and melting due to
the high current passing through it.
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The Heating Effect of a Current
We have seen how resistance in a wire causes a heating effect. The rate of heat flow is, of
course, power. So we can relate the power to resistance.
We know that P = VI and V = IR by substituting the second equation into the first once for V
and then again for I we can get 2 further equations for power
As you can see to reduce power loss and therefore heat loss in cables and
machines the current should be kept as small as possible.
Example
What is the power dissipated by a 10  resistor if a p.d. of 20 volts is applied across it?
We can also find the result by finding out the current and then using P = VI to find out the
power.
Questions: P32 Q1,2,3,5-12, (4)
Ohm’s Law
We have seen how the resistance is the ratio of the voltage to the current, R = V/I.
In a metallic conductor, kept at constant temperature, we find that if we alter the voltage or
the current, the other variable changes in such a way that the ratio remains constant.
Ohm’s Law is a special case where I  V.
This is Ohm’s Law, which states:


The current in a metallic conductor is directly proportional to the potential
difference between its ends provided that the temperature and other
physical conditions are the same.
If the temperature does change, the resistance will change as well. In a light bulb the
change is quite marked because the change in temperature is large.
A conductor that obeys Ohm’s Law is called an ohmic conductor.
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Voltage Current Characteristics
You should know and understand the voltage current graphs for an ohmic conductor, a
semiconductor diode, a filament lamp and a thermistor.
We can easily measure voltage and current, using the data to plot current against voltage
graphs (called characteristics). Be careful to note which way round the axes are.
In the exam you will need to be able to draw the graphs and
explain clearly why each graph has that specific shape,
commenting on shape and symmetry.
For an ohmic conductor:
Current
A
Voltage V
The straight line shows a constant ratio between voltage and current, for both positive and
negative values. As voltage increases current increases at the same rate. Ohm’s Law is
obeyed by the object.
The graph shows symmetry as object behaves the same regardless of the direction the
potential difference is applied across it.
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For a filament lamp
Current
(A)
Voltage V
The graph is not a straight line. As the voltage increases, the current increases at a lower
rate. The resistance rises as the filament gets hotter. This makes it harder for the current to
flow. Like the graph for the ohmic conductor, the graph is symmetrical. (It does not matter
which way round the p.d. is applied)
For a semiconductor diode
Current (A)
Forward bias
Reverse bias
//
1.0V
Voltage (V)
0.6V
Breakdown
voltage, about
–30 volts
This graph is not symmetrical. The diode starts to conduct significantly at a voltage of about
+0.6V. Thereafter the current rises rapidly for a small rise in voltage. (The voltage cannot
exceed 1V).after 0.6V the resistance falls away to almost zero. If potential difference is
reversed, almost no current flows until the breakdown voltage is reached. That will usually
end the useful life of the diode.
For an LED (light emitting diode) the graph is similar but conduction starts at about 1V and
does not exceed 2V. Break down on reverse bias occurs at about 5V. The light output of an
LED depends on the voltage applied to it.
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Thermistor
Current
(A)
Voltage V
For a thermistor (negative temperature coefficient or ntc) the current rises at a greater rate
than the voltage.
A thermistor is a special type of material that when heated releases more free electrons into
the material.
As current in a thermistor increases two things happen
1. More electrons collide with lattice ions in the material. This heats up the material
and causes the lattice ions to vibrate. This has the effect of increasing resistance.
2. As the material heats up more charge carries are released in the material. The
increased number of charge carries makes it easier to get a current to flow through
the material and so has the effect of reducing the resistance of the material.
The effect of releasing more charge carries in point 2 is stronger than the heating in point 1
and so the net effect is that the resistance of a thermistor decreases with and increase in
current and temperature making it easier for a current to flow.
Again the graph produced is symmetrical showing that potential difference can be applied in
either direction through a thermistor with equal results.
In other situations scientists may want to devise an experiment to investigate the variation
of resistance with temperature. This could be for a thermistor or any other material or wire.
Activity: Draw a circuit that could be used to obtain a graph to show the variation of
resistance with temperature.
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What would the student have to do with the circuit in order to obtain sufficient
measurements to show graphically the relationship between resistance and temperature.
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
Briefly describe the relationship between resistance and temperature for;
1. A copper wire …………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………..
2. A thermistor …………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………..
Light dependent resistors
LDRs are also semiconductors. As the light intensity (brightness) increases more charge
carriers are released and their resistance falls.
We will see uses of both LDR’s and thermistors later in this booklet.
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Resistivity
The resistance of a wire depends on three factors:
1.
2.
3.
We can say that the resistance is proportional to the length and inversely proportional to the
area. So we can write:
R  l/A
 R = ρ l/A
The constant of proportionality is called the resistivity, symbol ρ, ‘rho’ a Greek letter ‘r’.
 Resistivity is a property of the material itself.
 It has the units ohm metres ( m). (NB: NOT ohms per metre)
 It is defined as the resistance of a sample of material of unit length and unit area at a
certain temperature.




A is the cross sectional area measured in m2
R is the resistance measured in Ohms ()
L is the length the current travels through the object in m
ρ is the resistivity of the material in  m
1 metre is a reasonable length of wire, but 1 square metre is a very thick wire indeed. The
diameters of real wires are measured in millimetres or the area in square millimetres. The
equation will only work in SI units, so we must remember to convert square millimetres to
square metres.
1 mm2 = 1  10-6 m2.
Example
The cross-sectional area of a steel conductor rail is 25 cm2. What is the resistance of 1 km of
the conductor rail? The resistivity of steel = 2.0 10-7  m;
Activity:
1. If you increase the length of a wire the resistance will ………………………………..
2.
If you increase the diameter of a wire the resistance will ……………………………….
3.
If you increase the resistivity of a material the resistance will …………………………….
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Silver and gold are the best conductors. This means they have a low resistivity. They are
however very expensive. Copper has a low resistivity too, but is still quite expensive.
Aluminium has a higher resistivity, but much lower density, so is relatively cheap. Therefore
aluminium is widely used for power cables, wrapped around a core of steel for strength.
Some typical values for resistivity are:
Type of material
Conductors
Alloys
Semiconductors
Insulators
Material
Copper
Gold
Steel
Constantan
Nichrome
Carbon
Germanium
Silicon
Glass
Polythene
Resistivity @ 25 oC (m)
1.78  10-8
2.42  10-8
2.0  10-7
4.9  10-7
1.0  10-6
3.5  10-5
0.60
2300
1013
1014
Superconductors
Superconductors are materials whose resistance becomes zero when
they are cooled to or below a certain temperature, called the transition
temperature.
When a current passes through the superconductor the potential difference across it is zero
since it has no resistance and so there is no heating effect so no energy is lost in passing a
current through it.
Superconductors are therefore used to make high power electromagnets (which require
very large currents) producing very strong magnetic fields.
These are used in MRI scanners and in the accelerating magnets in the Large Hadron
Collider. They are also used in the maglev trains (the bullet train) which uses magnetic
levitation.
Because they can transfer power without wasting energy they can be used in power cables,
but the cost of keeping the superconductors cool can out weigh the savings made.
The highest transition temperature (sometimes called critical temperature) so far produced
is about -123º C (150K). The transition temperature is dependent on the elements used to
make the material.
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The following graph shows how the resistance of a superconductor varies with temperature.
The transition temperature is sometimes called the critical temperature.
Resistance
(Ω)
Make sure you
draw this drop
as vertical not
curved or
slanted
0ºC
Temperature ( ºC )
Transition
temperature
Series and Parallel Circuits
In all circuits both charge and energy are conserved

The total current flowing into a point is equal to the current flowing out of that
point. In other words, the current does not leak out or accumulate at that point.
Charge that flows away must be replaced.
5A
9A
4A
From this diagram we can see that there are 9A entering the junction and 9A leaving the
junction


Energy has to be conserved in any circuit
This implies that the energy supplied by the power supply in a circuit must be
transformed into other forms in the components in the circuit.
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Series Circuits
A
I
R1
R2
R3
V1
V2
V3
1. As current passes round the circuit it has only one path to take so the current is the
same at all points in a series circuit.
2. Energy must be conserved. As the electrons only have one path to take round the
circuit the potential difference across each resistor must add up to the potential
difference of the supply.
Therefore:
Vtot = V1 + V2 + V3
Now we know that V = IR from earlier
 IRtot = IR1 + IR2 + IR3
The currents is the same at
all points in a series circuit
so the I’s cancel out
 Rtot = R1 + R2 + R3
This is true for any number of resistors in series.
When combining resistors in series the total resistance will always
be higher than any one of the single resistors in the arrangement.
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Parallel Resistors
Atot
R1
I1
Itot
A1
R2
I2
A2
R3
I3
A3
1. In a parallel circuit as the current splits along the 3 branches of the circuit each
electron only passes through one of the resistors. It therefore only transforms
energy through one component. This means that in a parallel circuit the potential
difference is the same across each branch of the circuit.
2. Current and charge are conserved in any circuit. The current splits into 3 paths to
pass through the 3 resistors. In a parallel circuit the sum of the currents through
each branch of the circuit add up to the total current in the circuit.
Itot = I1 + I2 + I3
The potential difference is
the same along all branches
of a parallel circuit so the
V’s cancel out
From I = V/R, we can write:
V = V+ V + V
Rtot R1 R2 R3
𝟏
𝑹𝒕𝒐𝒕
=
𝟏
𝑹𝟏
+
𝟏
𝑹𝟐
+
𝟏
𝑹𝟑
+...........
This is true for any number of parallel resistors.
When combining resistors in parallel the total resistance will
always be less than the smallest resistor in the combination
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Activity: In the following questions find the total resistance of the combination shown.
Questions: P30 Q1-12 (13) questions
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Example
Three resistors are arranged in series and parallel as shown in the circuit below. They are
connected to a battery of negligible resistance whose terminal voltage is 12.0 V.
12 V
35
20 
48 
1. Calculate the total resistance of the circuit
2. Calculate the total current in the circuit
3. Calculate the potential difference across the 20 resistor
4. Calculate the current in the 35 resistor
5. Calculate the current in the 48 resistor
Take care with such problems:
 Make sure that the voltages across each path through the circuit add
up to the battery voltage.
 Make sure the currents in the parallel part of the circuit add up to the
battery current.
 If they don’t, go back and check what you’ve done wrong!
Questions: P30 Q14-18, P52 onwards Q3,4,6,7 past paper questions
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Cells in series and parallel
Series
Activity: If each of the cells in the diagram below is 9V what is the total Emf of the supply.
In general for cells connected in series, the total Emf
is ……………………………………………………........................
…………………………………………………………………………………
…………………………………………………………………………………
Total Emf = ……………………………….
Parallel
Activity: If each of the cells in the diagram below is 9V what is the total Emf of the supply.
In general for cells connected in series, the total
Emf is ……………………………………………………...............
………………………………………………………………………………
………………………………………………………………………………
Total Emf = ……………………………….
Example
Calculate the total emf and resistance if 3 cells of emf 1.5 V and resistance 0.2Ω are
connected i) in series ii) in parallel.
i)
In series. Total emf =................................................
Total internal resistance = ..........................................
ii)
In parallel. Total emf =.................................................
Total internal resistance =..................................................
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Ammeters and Voltmeters
In any electrical circuit a voltmeter should be connected in ………………………………… with the
component it is measuring.
This is because the voltmeter needs to record the potential difference across the component
so it needs to measure the difference in energy between the electrons arriving at, and
leaving the component.
A perfect voltmeter does not interfere with the current flow in the circuit and so a perfect
voltmeter has …………………… resistance to stop current passing through it and leaving the
main part of the circuit.
Ammeters are connected in …………………. with the component they component they are
measuring the current through.
This is because ammeters need to record the flow of charge through a component so need
to see how many electrons are passing through the wire leading to or from the component
they are measuring.
A perfect ammeter does not interfere with the energy flow in the circuit and so a perfect
ammeter has ………………… resistance to stop it reducing the energy of the electrons in the
circuit.
The Potential Divider
Although it is simple, the potential divider is a very useful circuit. In its simplest form it is
two resistors in series with an input voltage Vs across the ends. An output voltage Vout is
obtained from a junction between the two resistors.
R1
Vs
Vout
R2
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In a series circuit you must remember that for each of the two resistors
1. The current is ………………………………
2. The potential difference is ………………………………..
The total current is
I = Vs
R1 + R 2
Now Vout = IR2 = __Vs__ x R2
R1 + R 2
This formula is not on the
formula sheet and so you
must learn it.
 Vout = __R2___× Vs
R1 + R2
This result can be thought of as the output voltage being the same fraction of the input
voltage as R2 is the fraction of the total resistance. There is no need to work out the
current. Let us do an example putting some numbers in.
Example
What is the output voltage Vout of this potential divider, and the potential difference across
the 6300 resistor?
12 V
6300 
Vout
3700 
0V
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In the example on the previous page, we used two fixed value resistors. There is no reason
why one or both of the resistors should not be a variable resistor.
The following circuit consists of a potential divider made up from an LDR and a fixed resistor
R2.
LDR
Vs = 12V
R2
Vout
4. In the dark the resistance of the LDR
is ………………………….
1. In the light the resistance of the LDR
is ………………………….
5. The LDR will therefore receive a
……………… share of the voltage
2. The LDR will therefore receive a
……………… share of the voltage
6. The output voltage will therefore
be……………….
3. The output voltage will therefore
be……………….
If the output voltage was connected to a computer circuit it could be used to trigger a light.
When the voltage level rises above or drops below a certain value this could be used to turn
on or turn off a light. This creates a simple light sensor.
The same circuit could be set up with a thermistor instead of an LDR to act as a temperature
sensor
Example
Calculate the output voltage in the above circuit when i) the LDR is in the light and its
resistance is 200Ω and R2 = 1000Ω ii) the LDR is in the dark and its resistance is 2000Ω.
i)
LDR in the light
ii)
LDR in the dark
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The Potentiometer
So far we have used combinations of fixed and variable resistors to control the output of the
potential divider circuit. These can be replaced by a single variable resistor.
The fixed ends are connected to the supply Vs and the slider can be moved anywhere along
the resistance wire. The slider effectively seperates the single resistor into 2 separate parts
like the potential divider circuits above.
This allows us to control the output voltage at an unlimited number of values between zero
and the supply voltage. Such an arrangement is called a potentiometer, which is found in
the volume control of a radio or hifi.
Vs
Vout
In this kind of set up, if we have the slider half way along, we get half the voltage. If it is
three quarters of the way up, we get 0.75 of the voltage, and so on.
Example
5cm
12V
12cm
Vout
In the circuit above find the output voltage
In general for a potentiometer the output voltage can be found by………
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The following circuit is the one which is used to determine the characteristics ( I against V )
curves for different components.
It enables any voltage from zero up to the power supply voltage to be applied to the
component and to be measured by the voltmeter V and the corresponding current can be
measured using the ammeter A.
You must learn how to
draw this circuit off by
heart. It is fairly
common to have to
draw it in the exam.
A
component
V
EMF and Internal Resistance
Batteries (or more strictly speaking cells) convert chemical energy into electrical energy. In
doing so, they keep the negative terminal with an excess of electrons and the positive
terminal with a deficiency of electrons. A battery does a job of work in pumping the
electrons around the circuit.
A battery is said to produce Electromotive Force (Emf) which is defined as the
chemical energy converted into electrical energy when a unit charge passes
through the battery.
This is similar to the definition for potential difference that we saw before, except that it
describes the conversion to electrical energy, rather than the conversion from electrical
energy. It represents the total energy that can besupplied to a circuit. No circuit is 100 %
efficient. Some energy is disippated in the wires, or even in the battery itself. We can relate
the emf to the energy with a simple formula:

ε is the emf of a power supply measured in volts (V) or (JC-1)


E is the total energy transformed in the circuit measured in Joules (J)
Q is the total charge in the circuit measure in coulombs (C)
A more simple and practical way of remembering emf is to say that it is the terminal voltage
of a power supply in open circuit, i.e. when there is no external circuit connected to the
terminals of the supply. (only a voltmeter of infinte resistance to measure the potetial
difference between its terminals)
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Internal Resistance
We have already considered energy being transformed in resistors, bulbs and other
components in the circuit. However in a circuit energy is also transformed in the power
supply and the wires as well. The amount transformed in wires is generally so small that we
can consider it to be negligeable but the energy tranformed in the power supply itself may
need to be considered.
The key thing to remember is that the total chemical energy transformed in a battery is NOT
the same as the total energy transformed in the components in the circuit.
This is because all power supplies dissipate heat internally when giving out a current, due to
internal resistance.
A perfect battery has no internal resistance, but unfortunately there is no such thing as a
perfect battery. Nickel-Cadmium and Lead-Acid batteries have very low internal resistance,
and we can regard these as almost perfect. You may need to know where the internal
resistance arises from
1. In a battery the as charge carriers pass through the chemicals in the battery they
encounter resistance and so dissipate heat.
2. In a power pack like we use in the lab the electrons flowing through the wires,
resistors and capacitors in the power pack itself encounter resistance and so disipate
heat.
Suppose we connect a cell to a high resistance voltmeter as shown below. The voltmeter
will read the emf, the true chemical energy converted into electrical energy in the power
supply. For example lets say 12V
V
I
V
Suppose we now add a load as shown below. We will assume the wires have negligible
resistance.
V
I
V
R
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This time we find that the reading on the voltmeter drops, in our example to lower than 12V.
This tells us that not all of the chemical energy transformed in the battery is being
transferred to the outside circuit. Someof it has been lost due to the internal resistance of
the battery itself which will have lost energy due to heat.
Energy per unit
charge supplied by
the cell
=
Emf
Energy per unit
charge transformed in
the components of
the circuit
+
Energy per unit
charge lost to heat
due to internal
resistance
= Useful volts + Lost volts due to internal resistance
E= V+ v
So we represent a circuit with internal resistance as:
E
r
I
V
R
So our cell is now a cell in series with an internal resistor, r. You cannot open up the battery
to find the internal resistor; it is part and parcel of the battery.
We can now treat this as a simple series circuit and we know that the current, I, will be the
same throughout the circuit. We also know the voltages in a series circuit add up to the
battery voltage.
Emf = voltage across R + voltage across the internal resistance
Ε =
V
+
v
We also know that V = IR so we can write:
 = IR + Ir

E is the emf of a power supply measured in volts (V) or (JC-1)


I is the total current flowing in the circuit measured in amps (A)
R is the total resistance in the circuit outside of the power supply measured
in ohms ()
r is the internal resistance of the power supply measured in ohms()

AS/ unit 1 2011
27
Example
A high resistance voltmeter reads 1.5 V when it is connected to a battery in open circuit. It
reads 1.2 V when the battery is supplying a current of 0.30 A through a resistor of resistance
R.
E =1.5 V
r
0.30 A
V = 1.2 V
V
R
(a) What is the potential difference lost due to internal resistance
(b) What is the internal resistance, r?
(c) What is the value of the resistance of the resistor, R?
We can use the apparatus in the following circuit to determine the internal resistance of a
cell.
E
r
I
V
R
A



We adjust the variable resistor so we can record a range of voltages and currents.
We use the switch to avoid flattening the battery, and preventing the variable resistor
from getting too hot.
We plot the results on a graph of V against I
AS/ unit 1 2011
28
P.d. (V)
Current (A)
The graph is a straight line, of the form y = mx + c. We can make the equation for internal
resistance V = -rI + E. There are three features on the graph that are useful:
Activity: in the space underneath write one equation above the other and by comparing the
two equations determine

The intercept on the y-axis tells us the………………………………………………..

The intercept on the x- axis tells us the …………………………………………………………………

The negative gradient tells us the ………………………………………………..
In laboratory power supplies producing high volatages (HT supplies) and those producing
very high voltages (EHT supplies) very high resistances are connected internally in the
supplies in order to limit the current they can produce. This is to protect the user. E.g. If a
supply has an emf of 5000 V and an internal resistance of 1 MΩ the maximum current it can
produce( if it was short circuited or the user connected themselves across the terminals) is
5000 / 1 MΩ = 5 mA
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29
Alternating Currents
Direct current from a battery moves in one direction only, from positive to negative.
In alternating current the direction is changing all the time. The charge carriers are moving
forwards and backwards many times a second. In Europe it is 50 Hz (cycles per second), in
the USA 60 Hz.
AC and DC are equally good at heating, lighting, or running motors. DC is essential for
chemical processes such as electrolyis.
AC is much more easily distributed than DC due to the fact it can be used with transformers
which DC cannot.
The graph below shows the difference between AC and DC.
DC from a
battery
+V0
AC
waveform
Time (s)
-V0

One complete alternation is called a cycle (NOT wavelength).

The frequency is the number of cycles per second. Units are hertz (Hz).

The period is the time taken for one cycle. It is measured in seconds. f = 1/T.

This is a sinusoidal waveform, which is the simplest form of AC.

The current follows exactly the same wave form as voltage.
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30
The Cathode Ray Oscilloscope (CRO)
When studying AC current we cannot use an analgoue meter to display the current and
voltage as the needle would be constantly bouncing backwards and forwards as the current
changed direction. Instread we sometimes use a cathode ray oscilloscope. The CRO can be
used as an AC or DC voltmeter, measuring time intervals and frequencies and to display
waveforms.
The cathode ray oscilloscope (CRO) is a very useful instrument that we can use to look at AC
waveforms. It tells us the shape of these waveforms which can be very useful for an
electronic engineer. A voltmeter cannot do this for us. It only tell us the rms voltage of the
AC. (we will discuss this later in this booklet)
The CRO can tell us:
 The peak-to peak voltage
 The frequency
 The shape of the wave
 The phases of two separate waves.
 The time taken between two pulses.
The CRO has a few disadvantages:
 We don’t get a direct numerical read out. We have to work out the values ourselves.
 It takes practice to use it; it can be tricky at times!
 It is rather bulky and quite expensive.
The CRO is connected in exactly the same way as a voltmeter, i.e. in parallel with a
component.
The CRO can only display waveforms that are repeated regularly
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31
This is a typical display of a sinusoidal waveform on the CRO screen.
Voltage / V
Time / s
The screen can be thought of as a graph with the origin in the middle
We measure the voltage on the vertical axis, which is controlled by the y-plates. The scale
of the y-axis is known as the voltage sensitivity.
We measure the time of cycles using the horizontal axis which is controlled by the x-plates.
The scale of the x-axis is known as the time base.
The screen has a grid of 1 cm squares and the y-axis is marked in volt cm-1. The x-axis is
marked in ms cm-1 or μs cm-1.
Activity: on the CRO trace above mark on clearly the peak-to-peak voltage, the peak voltage
and the time period of the signal.
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32
Example
Using the diagram above if the y-gain and the time base are set on 2 V cm-1 and 0.5 ms cm-1
respectively, determine:
i)
The peak voltage..................................................................................
ii)
The peak to Peak voltage....................................................................
iii)
The time period of one cycle …………………………………………
iv)
The frequency of the signal.....................................................................................
...............................................................................................................
Example
A vertical line is displayed on the screen which is 4cm long. The y sensitivity is set at 5 Vcm-1.
Determine i) the peak to peak value of the voltage applied ii) the peak value
i)
Peak to peak......................................................................................
ii)
Peak value..............................................................................................
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33
Activity: on the following grids draw a picture to show what the trace would look like for the
type of current listed in the box underneath
AC current with the time base switched
on
AC current with the time base switched
off
DC current with the time base switched
on
DC current with the time base switched
off
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34
It is possible that in the exam you may also have to draw the trace of an AC current from
given information.
Example:
Using the the blank oscilloscope screen below draw an AC current with a frequency of 50Hz
and a peak voltage of 10 V. The oscilloscope is set with a time base of 5ms div-1 and a voltage
sensitivity of 4V div-1
Before you attempt any CRO drawing you need to first calculate
…………………… and ……………………….
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Root Mean Square Value
The values of voltage and current are constantly changing in AC, unlike in DC in which they
are steady. We can measure AC voltages in two ways:


Measure the peak to peak voltage, easily done on a cathode ray oscilloscope (CRO).
Measure the root mean square (rms) value, or the effective value.
We use the rms value because its use allows us to do electrical calculations as if they were
direct currents. It also allows us to make comparisions with the direct current. We define
the rms value as:
The rms value is the equivalent value to a steady direct current which converts
electrical energy into other forms of energy for a given resistance at the same rate
as the AC.
This is a bit of a mouthful, but let us look at the graph to show this:
Power
+V0
Time (s)
Current
-V0
Voltage
waveform





Notice that the current and voltage are always in step with each other. We say that they
are in phase.
The power is always positive. A negative voltage multiplied by a negative current will
give a positive power.
The maximum power = V0I0.
The minimum power = 0.
The average power = ½ V0I0 = ½ I02R
This is a rather awkward term and we need a value that gives us a heating value that is
identical to the equivalent DC. This is by definition Irms.
½ I02R = Irms2R


AS/ unit 1 2011
 Irms2 = ½ I02
Io is the peak current measured in amps (A)
Irms is the effective root mean square current flowing in the circuit
measured in amps (A)
36
By a similar method we can can take ½ V0I0 and instead substitute for Vo instead of Io to get
a second equation


Vo is the peak voltage measured in volts (V)
Vrms is the effective root mean square voltage in the circuit measured in
volts (V)
+Vo
+Vrms
Time (s)
-Vrms
-Vo
Whenever performing calculations using the formulas we have looked at in this book so far
we should always convert peak values from AC current into rms values.
Example
1. What is the maximum voltage of the mains 240 V rms supply?
2. What is the peak current when mains current flows through a 3kΩ resistor?
3. What is the charge flowing through the resistor in 25 seconds
4. What is the energy dissapated in the resistor during this time
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37
Particles, Radiation, and Quantum Phenomena
Simple Atomic Structure
Constituents of the Atom
The simplest model of the atom is shown in the diagram below:
Proton
Electron
Shells
Neutron
Electron
Nucleus
This is the layout of a lithium atom, with three protons, three electrons, and four neutrons.
The protons and neutrons are found in the nucleus. They are called nucleons. The
electrons are found in shells orbiting the nucleus.
It is important to understand:

The nucleus is very small compared to the atom, about 100, 000 times smaller. The
diameter of an atom is in the order of 10-10 m, whereas the diameter of the nucleus in
the order of 10-15 m.
Property
Charge in terms of an
electron
Actual charge in
Coulombs
Mass
Relative Mass
(comparing to mass
of proton)
Electron
Proton
+1 e
0
-1.6 x 10-19 C
+1.6 x 10-19 C
0C
9.11  10-31 kg
1/1836
1.67  10-27 kg
1.0000
1.67  10-27 kg
1.0004
These values are all on your data sheet.
AS/ unit 1 2011
Neutron
-1 e
38
Notice that:
The electron and the proton have the same value of charge, but the signs are different.
The neutron has a very slightly higher mass than the proton. In terms of calculations in AS
physics we treat their mass as the same, 1.67  10-27 kg
Different atoms are distinguished by their numbers of protons and neutrons. We write
the symbols using the following notation:
A
X
Z

A is called the nucleon number, or the mass number. It is the total number of nucleons.
This is always the bigger of the two numbers.

Z is the proton number or the atomic number, which is the number of protons. This is
always the smaller of the two numbers.

The number of protons in an atom determines the element.
We need to be able to determine the number of protons, neutrons and electrons in an
atom.
Example: neutral carbon atoms are represented as:
12
C
6

Protons = ………………….

Neutrons = ……………...

Electrons = …………………
In a neutral atom, there are always equal numbers of protons and electrons.
If the numbers are not equal, then the atom is charged. Charged atoms are called ions.
Positive ions have fewer electrons than protons. Negative ions have more electrons than
protons.
Example: Using the same element above write down the number of protons, neutrons and
electrons if the element is charged +2e
12
C
6
AS/ unit 1 2011
2+

Protons = ………………….

Neutrons = ……………...

Electrons = …………………
39
Carbon has another form:
14
C
6

Protons = ………………….

Neutrons = ……………...

Electrons = …………………
This is an isotope of carbon.
Isotopes have the same numbers of protons, but different numbers of neutrons.


Isotopes have the same physical and chemical properties.
If the proton number is altered, the element changes.
Some isotopes are radioactive, as the nuclei are unstable. We will look at this in more detail
later in this booklet and discover how unstable atoms return to being stable by radioactive
decay.
Specific charge
In the exam you may be asked to calculate the specific charge of a given atom.
Specific charge = charge to mass ratio = charge in C
mass in kg
The units for specific charge are therefore C kg-1
Example:
238
92𝑈
is an isotope of uranium.
Determine the specific charge of this nucleus
AS/ unit 1 2011
40
This is not on the formula
sheet you must learn this
before the exam
Stable and unstable nuclei
When an isotope is unstable, it is radioactive and is called a radioisotope. Isotopes can be
unstable for one of 4 reasons:
1. They have too many neutrons
2. They have too few neutrons
3. They contain too many particles and are too large to be held together by the strong
interaction (see later in the notes booklet)
4. They contain too much energy
Radioactive decay is the process by which an unstable parent nucleus becomes more stable
by decay into a daughter nucleus by emitting particles and/or energy. The basic form can
be summed up as:
Radioactive
parent
nucleus
Daughter
Nucleus
+
+
Energy
nergy
Particle
The decay can consist of several steps. The unstable nucleus can decay to another nucleus
of a different atom by a process called transmutation. If the new nucleus is unstable it will
decay again. This is known as a decay chain.
There are three kinds of radiation:
· Alpha – a helium nucleus
· Beta – a high speed electron or positron (see next few pages)
· Gamma – electromagnetic radiation
These kinds of radiation can be emitted individually or in any combination, depending on the
type of isotope that is emitting the radiation. Often when an alpha particle is emitted the
nucleus is excited and releases the excess energy in the form of a gamma ray or gamma
photon.
Gamma radiation is always emitted as a after product of either alpha or beta. The gamma
ray given off does not affect the nuclear structure in anyway
When specimens of radioactive isotopes decay they do so entirely randomly. There is no
pattern whatsoever, and the rate of decay is not affected by temperature or other physical
constraints, or chemical reactions.
Some useful properties to remember:
1. ……………….. is the most penetrating
2. ………………. Is the least penetrating
3. ……………….. is the most ionising
4. ……………….. is the least ionising
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41
Alpha (α) emission




This happens in mostly in very large nuclei.
The atoms are too big for the strong nuclear force to hold the nucleus together.
The particle looks to become lighter by emitting an alpha particle.
An α particle is identical to the nucleus of a Helium atom. It consists of a very stable
combination of 2 protons and 2 neutrons.
You need to be able to complete decay equations for alpha and beta decays. The key is
that the proton and nucleon numbers on both sides of equations must balance.
Example equation for alpha decay:
224
228
90
Th
88
He
4
Ra +
+
2
Q
The daughter nucleus in this case is Radium. The energy given out in the equation appears
mainly in the form of kinetic energy of the particles. After the decay the alpha and the
remaining daughter nucleus move away from each other (recoil)
In general for an alpha decay the daughter nucleus has a proton number of ……….. less than
the parent and has a nucleon number of ……. less than the parent.
Beta minus (β-) emission. (Usually just called beta )


This occurs when there are too many neutrons in the nucleus.
A neutron in the nucleus changes into a proton and an electron. The electron is
emitted as a beta particle.
The electron comes from the nucleus but once out of the nucleus it behaves like
other electrons.

𝟎
−𝟏𝜷
is the symbol for the beta particle. It is sometimes written as −𝟏𝟎𝒆. The -1 indicates its
charge (same as proton but negative).
Example:
29
13
29
Al
14
0
Si +
e
-1
0
+ 0 e + Q
On an atomic level the equation for the decay of the neutron into a proton via β decay is:
1
0
1
n
1
0
p +
̅ in both equations is the electron antineutrino.
𝝂
AS/ unit 1 2011
42
-1
e
0
+ 0 e + Q
Neutrinos
Neutrinos are probably the most numerous particles in the universe. They outnumber the
protons and neutrons by a factor of about 109. Neutrinos created at the time of the Big Bang
still permeate the universe. They are also emitted by radioactive nuclei and from nuclear
reactions. The Earth is bathed in neutrinos from the Sun. Every second about 60 thousand
million neutrinos pass through every square cm of the Earth’s surface. Neutrinos and
antineutrinos are extremely difficult to detect. They are not charged and they interact with
other matter very weakly.
The neutrino is a fundamental particle with no charge. It has a very small or zero
mass. It interacts with other matter very weakly.
The neutrino is represented by the symbol νe and the antineutrino by the symbol 𝛎̅𝐞 (we
will look at anti particles in the next few pages)
The subscript ‘e’ stands for electron and these neutrinos should be called electron neutrinos
because other types of neutrino exist.
Although it appears, the neutrino doesn’t actually contribute to the balancing the equation
here. However, in a few pages you will see that it definitely does, so remember to always
include it in the beta decay equations! Don’t forget it!!!
Examples:
1. Thorium
228
90Th is
an alpha emitter which decays to Radium (Ra)
Complete the following equation for alpha decay adding all nucleon and atomic numbers.
228
90Th
= Ra
2. Potassium 39
19K is a beta emitter decaying to Calcium Ca. Write down the decay
equation including atomic and nucleon numbers.
3. In the decay of 238
92U to
emitted?
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206
82Pb
8 α particles are emitted. How many β particles are
43
Beta plus (β+) emission.


This occurs when there are too few neutrons in the nucleus.
A proton in the nucleus changes into a neutron and a positron. The positron is
emitted as a beta+ particle.
The positron comes from the nucleus but once out of the nucleus.
The Positron is the anti particle of the electron. We will be discussing what an
antiparticle is fully in the coming pages.


𝟎
+𝟏𝜷
is the symbol for the beta+ particle. It is sometimes written as +𝟏𝟎𝒆+ . The +1 indicates its
charge (same as proton).
Example:
22
11
22
Na
10
Ne +
0
e
+1
+ 0e
0
On an atomic level the equation for the decay of the proton to a neutron via β+ decay is:
1
1
1
p
0
0
n
+
e
+1
+ 0e
0
Note that the neutrino in these decays is a regular neutrino not an antineutrino.
Electron Capture
There is another way that a proton is turned into a neutron, and that is by electron capture.
An electron is captured from the electron cloud and combines with a proton to form a
neutron.
Example
19
9
F
On an atomic level the equation for the electron capture is:
1
1
p
Make sure you learn which decay equations contain a
neutrino and which decay equations contain an anti neutrino. Don’t get them mixed up!
AS/ unit 1 2011
44
Further examples
( The following elements may help you to write full answers: 90Th
24Cr 28Ni 23V 91Pa
Complete the following equation for an alpha decay
238
92
U
Complete the following equation for a beta+ decay
52
25
Mn
Complete the following equation for an electron capture
60
29
Cu
Complete the following equation for a beta- decay
49
22
Ti
Complete the following equation if 3 alphas and 4 beta- are given off in a decay chain
237
93
Np
Complete the decay below to show the number of alpha and beta decays present to
complete the decay chain
222
86
Rn
AS/ unit 1 2011
206
75
Re
45
)
Particles, antiparticles and Photons
British Physicist Paul Dirac predicted the existence of a particle with exactly the same mass
as the electron but with a positive charge, before the discovery of the positron. He predicted
that all particles have antiparticles. The first antiparticle, the positron, was discovered in
1932.
All particles have antiparticles.
An antiparticle is a mirror image of a particle, with identical mass and opposite
charge.
When a particle meets its antiparticle twin, the particles are drawn together by electrostatic
attraction until they annihilate each other.
Annihilation is the conversion of the mass of a particle and its antiparticle to a pair
of photons of electromagnetic radiation (energy).
+
Particle
Antiparticle
2 photons of energy
When a positron and an electron meet, they annihilate each other. Two identical gamma
rays are emitted in opposite directions.
It is possible for this process to be reversed. The opposite process, where matter is created
from energy is called pair production.
Pair production is the process in which a photon of electromagnetic radiation is
converted to a pair of particles.
Particle
+
Antiparticle
Photon of energy
For example a photon of radiation could be converted into a positron and an electron that
move off in opposite directions.
In pair production there are always 2 particles created; one is a conventional particle and the
other is its antimatter twin. This satisfies the conservation of charge, since before the event
there is only a photon of radiation which carries no charge.
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46
In 1955 the first antinucleon was discovered. Protons were accelerated to energies of 6 MeV
and were collided. By colliding the two protons an extra proton and antiproton were
created from the kinetic energy of the two original particles. A year later the antineutron
was produced by using antiprotons to collide with protons. A neutron and an antineutron
were produced.
In order for particles to be produced the photon must have a minimum energy. This is
because each unit of mass has an equivalent amount of energy. This comes from Einstein’s
famous equation E=mc2. So to create a specific amount of mass we must have at least the
equivalent amount of energy.
The table below shows the section of the formula sheet that gives you the equivalent energy
of some of the common particles.
You can see the unit used
here is the MeV. This is an
alternative to the Joule for
measuring energy and will
be discussed fully in the
sections for energy levels
and the photo electric effect
later in this booklet.
Example:
What is the minimum energy of a photon that is transformed into an electron and positron.
What would happen if the energy of the photon was slightly higher than this value?
If the energy of the photon is higher than the combined rest
energies of the two particles being created then the remaining
energy is transformed into …………………………… of the produced
particles as they move apart from one another.
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47
Fundamental forces
What holds particles together in atoms or nuclei? Positive charges repel each other and at
such short distances, the electrostatic forces pushing the nucleus apart are very large. So
why does the nucleus of an atom stay together?
Current theories suggest there are only 4 types of interactions between particles.
Gravity.




Gravitational force has an infinite range.
On the scale of the universe it is the most important of all the interactions but
on an atomic scale it has very little influence.
It is the weakest of all the fundamental forces.
It acts on any particles with mass
Electromagnetic Force
 This only acts between all charged particles.
 It holds atoms and molecules together and so is responsible for almost
everything that happens to us.
 Forces such as friction and all contact forces are electromagnetic in origin.
 It has an infinite range
Strong interaction
 The strong interaction or strong nuclear force holds the nucleus together.
 It acts between the neutrons and protons and keeps the nucleus stable.
 It is a short range force, acting over the nuclear distance scale of around 10-15m.
 At very short distances of up to about 0.5fm it is a repulsive force, which
prevents the nucleus collapsing to a point.
 It then becomes an attractive force up to about 3fm, which pulls the nucleus
together and is strong enough to overcome the repulsive force between the
protons.
 It acts on hadrons only (hadrons will be discussed in the next few pages)
Weak interaction
 This acts between all particles
 It has a very short range, about 10-18m.
 The weak force is responsible for radioactive decay. (See later)
For each of the 4 forces you need to know 3 things
1. What it is responsible for (what it does)
2. What its range is
3. What particles it acts upon
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48
Particle Interactions
Exchange Particles
The Japanese physicist Hideki Yukawa suggested that when two particles A and B exert a
force on each other a ‘virtual particle’ is created. This virtual particle can travel between
particles A and B and affect their motion.
An exchange particle is a virtual particle, which may exist for only a short time, and
carries force between two particles.
If one person on skates throws a ball to another person on skates, the motion of both
skaters will be affected as they will move apart. Each fundamental force has an exchange
particle or particles which are called gauge bosons.
Fundamental force
Gravity
Electrostatic
Weak
Strong
Gauge Boson
Graviton – G
Photon - γ
W and Z bosons – W+, W -, Zo
Gluon - g
Classification of Particles
Up until now you may have thought the universe only existed of protons, neutrons and
electrons plus the particles we have added to this list over the last few pages the neutrino,
anti neutrino and positron. Well there are many many more……..
Current theories suggest there are only three families of fundamental particles. These are
leptons, quarks, and gauge bosons.
Fundamental means they have no internal structure and cannot be broken down further
into other smaller particles.
Leptons








Leptons and their antiparticles, antileptons, are believed to be fundamental
particles.
There are three charged leptons: the electron, the muon and the tau particle.
The muon is 207 heavier than the electron and the Tau particle is 3500 heavier than
the electron
The muon and tau are similar to the electron but more massive.
Each of the charged leptons has an associated neutrino and antineutrino.
Leptons are not affected by the strong interaction.
Leptons are subject to the weak interaction.
All these particles have an antiparticle of opposite charge, making 12 leptons in
total.
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49
Hadrons








Hadrons are made of quarks.
There are two main groups within the Hadron family: baryons and mesons.
Baryons are made of 3 quarks and mesons are made of 2 quarks.
All hadrons are unstable apart from the proton.
All Baryons eventually decay into a proton.
The proton is a very stable particle. It is the only stable hadron.
The Baryons include the proton and the neutron and their antiparticles.
The mesons were originally discovered in cosmic rays, but are now commonly
created in particle accelerators.
Hadrons are made up of quarks, which are fundamental particles. The quarks are held
together by gluons.
Quarks cannot exist on their own; they are confined in pairs or triplets. They are regarded
as the fundamental particles of matter. We do not have as yet the means to probe deeply
their nature or their structure.
There are three main quarks, up, down, and strange. The names have no real significance
beyond the imagination of the physicist that dubbed them such. They have corresponding
antiquarks.
There are three others with even odder names, top (sometimes called "truth"), bottom
("beauty"[!]), and charm, which we will not be dealing with at this stage.
Like many of the particles we have considered, quarks and antiquarks have the property
strangeness. The table shows some of the properties of quarks:
Quark
Down (d)
Up (u)
Strange (s)
Antidown (đ)
Antiup (ū)
Antistrange (s)
Charge (Q)
-1/3
+2/3
-1/3
+1/3
-2/3
+1/3
Baryon Number (B)
+1/3
+1/3
+1/3
-1/3
-1/3
-1/3
Strangeness (S)
0
0
-1
0
0
+1
On the formula sheet you get the details of the numbers for the
down, up and strange quarks but as you can see the numbers for
the anti quarks are the same but with opposite sign.
AS/ unit 1 2011
50
Let us look at some points about quarks and antiquarks:




Baryons are made of three quarks.
Antibaryons are made of three antiquarks.
Mesons are made up of one quark and one antiquark.
Gluons bind quarks together; they are subject to the strong interaction.
Let us look at how quarks are assembled to make a proton. A proton is made of two up
quarks and one down.
Activity: using the information on the previous page or on the formula sheet see if you can
derive the quark structure for the proton and neutron
Proton =
Neutron =
The table shows the combinations of quarks for some different particles
Activity: In the exam you need to be able to know or be able to derive the quark structures
of the common baryons and mesons. Using a sheet of scrap paper derive the quark
combinations needed to fill the table below (there are some helpful starters under the table)
particle
structure
antiparticle
structure
p
n
π+
πo
k+
ko
All π mesons
have a
strangeness of
zero
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The k+ meson has
a strangeness of
+1
51
The ko meson has
strangeness of +1
The pi meson or pion has 3 different forms, positively charged π+, negatively charged π-, and
uncharged π0. Many other mesons have since been discovered. K mesons or Kaons appear
as the decay products of some neutral particles and always turn up in pairs.
You may also be given the properties of a particle in the exam but not its name and be
expected to state its quark structure.
Example:
State the quark structure of a meson with a strangeness of zero and a charge of 1
State the quark structure of a baryon with strangeness of 1 and a charge of zero
State the structure of a meson with a strangeness of -1 and a charge of -1
If a particle is made of ssd quarks then write down all the properties and names you can
deduce for this particle
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Non - Fundamental
Fundamental
Particle summary sheet: fill in all the particles in each category
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Particle interactions
Whenever particles combine, decay, annihilate or are produced from a photon the following
things must be conserved on top of the usual conservation of energy.




Charge must be conserved
Baryon numbers must be conserved
Lepton number must be conserved
Strangeness must be conserved
Only baryons
have baryon
number
Only leptons
have lepton
number
The baryon number
of a proton and
neutron is ………..
In some reactions strangeness is not conserved but these reactions take place via the weak
interaction.
Examples:
1. A neutron decays by the weak interaction into a proton an electron and antineutrino are
also emitted.
Write the general equation for this:
Write here the equation for the change in quark structure taking place:
Now use the space below to show the whether the decay is allowed using conservation laws
2. An electron anti neutrino combines with a proton to form a neutron. Write out the
equation for this interaction.
Is this interaction valid? If not what is the missing particle?
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More examples:
1. What class of particle is represented by the combination of three antiquarks
2. Name a hadron that has an antiparticle identical to itself.
3. The Kaon K+ has a strangeness of +1. Give its quark composition.
The K+ may decay by the process
K+ = π + + π 0
State the interaction responsible for this decay.
Why is this the case?
4. The K+ may also decay by the process
K+ = μ+ + νμ
Change each particle of this equation to its corresponding antiparticle in order to
complete an allowed decay process for the negative kaon KK- =
5. To what class of particles do μ+ and νμ belong?
6. State one difference between a positive muon and a positron.
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Feynman diagrams
We use what are called Feynman diagrams to represent what happens when particles
experience the effect of one of these exchange particles.
A Feynman diagram is effectively a pictorial diagram laid on top of a set of axis.
time
The axis are not
usually drawn you
have to imagine they
are there!
Position

Particles are represented by labelled straight lines moving up the page

The gauge bosons representing the fundamental forces are represented using wavy
lines.

Lines moving towards each other represent particles moving closer together in space

Lines moving away from each other represent particles moving away from each
other in space
There are different conventions for Feynman diagrams
but for this exam board lines on a Feynman diagram can
never be seen to be moving downwards on the page. This
would mean
…………………………………………………………………………………………
………………………………………………………………………………………..
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The electromagnetic force
The electromagnetic force is carried between charged particles by the virtual photon γ.
The photon is a massless, chargeless particle. It is its own antiparticle.
This is the Feynman diagram showing two electrons feeling the electromagnetic force as a
result of exchange of a virtual photon. In this case because the electrons have the same
charge the force is repulsive.
Complete the
diagram labelling the
particles involved
and the interaction
The Weak Interaction
The weak interaction has a very short range and has three gauge bosons, known as
W +, W- and Z. These particles have a rest mass and the W bosons are charged. They have a
very short range (0.001fm).These bosons were discovered in 1983 at CERN in Geneva.
The weak interaction acts on leptons and hadrons. It is the only force, other than gravity,
which acts on neutrinos. This explains why neutrinos are reluctant to interact with anything.
All the following are due to the weak interaction and are mediated by a W boson.
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Positron decay (beta plus decay): to help you write the beta plus decay for a proton
from earlier in this booklet if you can remember it
Complete the
diagram labelling the
particles involved
and the interaction
with direction
………… boson takes …………………… charge from the proton and effectively gives ………………
charge to the positron.
beta decay (beta minus): first write out the equation for beta minus decay from a
neutron
Complete the
diagram labelling the
particles involved
and the interaction
with direction
………… boson takes ………………… charge from the neutron and effectively gives ………………
charge to the electron.
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Electron capture and electron collision:
first write out the equation for electron
capture for a proton. The equation is identical for electron collision.
In the electron capture a proton in the nucleus captures an electron from the cloud
In electron collision an electron from outside of the atom can collide with a proton in the
nucleus.
Complete the two diagrams underneath and note the subtle difference
Electron capture
Electron – proton collision
Note the difference in direction of the arrow. In the electron capture the proton is pulling in
the electron from the cloud so the arrow goes from the proton to the electron.
In the electron proton collision the electron is the particle moving and smashing into the
proton. Therefore the arrow goes from the moving electron to the stationary proton.
Example:
1. Complete the following Feynman diagram in terms of quarks so that it represents β+
decay.
.....
.....
You must learn how to draw
all these diagrams and
remember the relevant
equations for the exam
.....
U
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The Strong Force
As an extension, you may need to be able to draw the Feynman diagram for the strong
force.
Hopefully you can recall the following
 The strong force has a gauge boson called the ……………………………….
 The symbol for the gauge boson is ………………………………..
 From the centre of the nucleus to 0.5fm the strong force is ……………………………………
 From 0.5fm to 3.0fm the strong force is ……………………………………………
 Beyond 3.0fm the strong force has ……………………………………………………..
In the space below draw a Feynman diagram showing how to protons interact at a
separation of 0.25fm
The line to represent the exchange particle is drawn
as a wavy line for weak and electromagnetic like
this
and as a loopy line for the exchange particle of the
strong force.
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The Particle Model of Light
We know that light shows wave properties such as:
 Reflection
 Refraction
 Diffraction
 Polarisation
However it can also be shown to have particle properties as well.
The Photoelectric Effect – Evidence for the particle nature of light
We can show the photoelectric effect with apparatus like this:
Sheet of
reactive
metal ( zinc)
Gold leaf
Gold leaf
electroscope
1.
2.
3.
4.
5.
We charge the electroscope with a negative charge.
We expose the reactive metal to light of a long wavelength, e.g. red.
We observe that there is no effect, however bright the light.
We then expose the metal to short wavelength light, e.g. UV.
This time we see that the gold leaf drops down, showing that the electroscope is
losing charge.
6. It does not matter how bright or dim the UV light is.
7. No effect was observed when the electroscope was positively charged.
8. The experiment was repeated with different metals replacing the zinc.
This leads to the conclusion that:





Electrons were being emitted from the metal surface.
Red light would not show this effect however bright it was. So the amplitude of the light
wave was not important.
This is because red light has too low a frequency.
A threshold frequency (minimum frequency) was needed
For any frequency below this the effect did not occur no matter how bright (intense) the
light.
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


The more reactive the metal, the lower was the threshold frequency because reactive
metals have outer electrons that can be easily removed
The effect was instantaneous. There was no time delay. The electrons did not have to
wait to receive sufficient energy to escape. On the wave theory the electrons would not
have been emitted instantly.
This effect showed light behaving as ‘particles.’
These findings led to the particle like nature of light, where light was considered to be tiny
little packets of wave energy called photons.
Activity:
A common question in the exam is for you to explain why the fact that red light never
releases electrons from the metal and blue/UV does for a particular metal supports the
particle theory of light. Use the space here to try and put together the ideas above into a
coherent written answer as if it was a 6 mark essay question.
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
Work by Max Planck in 1900 produced the Photon Model of Electromagnetic Radiation. We
can sum this up in the following points:
 Light and other electromagnetic radiation is emitted in bursts of energy. We say that it
is quantised.
 The packets of energy, photons, travel in straight lines.
 The frequency of the light and the energy are related by a simple equation:



E is the energy of the individual photons in joules
h is Planck’s constant this can be found on the formula sheet
f is the frequency of the radiation in hertz
The constant h is Planck’s Constant with the value 6.63  10–34 Js (joule seconds, NOT joules
per second).
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Activity: We can combine the equation above with the wave equation:
E = hf
c=fλ
and
Example
What is the photon energy of light wavelength 350 nm?
What is the corresponding frequency of the light?
The answer to this example is expressed in joules, which is, of course, the SI unit for energy.
The energy as you can see is extremely small.
When working at the atomic scale the joule is too large a unit. So we use a unit called the
electron volt (eV).
The electron volt is the amount of energy transformed when an electron passes through a
potential difference of 1 volt.
W=QV
The charge on an electron is 1.6 × 10-19 C, so
Hint: Your answer in eV will
always be a significantly larger
number than the answer in
joules.
1 eV = 1.6 × 10-19 J.
You will need to remember this!
To convert Joules to eV divide by e – the charge on the electron (1.6 x 10-19)
To convert eV to Joules multiply by 1.6 x 10-19
Electron volts are almost always used in atomic and nuclear physics, but before using
equations like E = hf, the energies MUST be converted to the standard unit of joules.
Express the energy of the photon in the example above in eV
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Waves as Particles
Max Planck was the first to demonstrate the notion of the particle behaviour of light.
Albert Einstein developed the theory further to study how atoms interacted with photons.
He produced the notion of quantum physics, in which electromagnetic radiation has a
particulate nature and he explained the Photoelectric effect using this theory.
Einstein’s Photoelectric Equation

Energy is required to remove electrons from the surface of a metal.

Some electrons require more energy to remove them than others depending on
where they are in the metal and how much energy they have already.

The minimum energy required to remove an electron from a particular metal is
called the work function.
The work function is the minimum energy needed to remove an electron from
the surface of a metal.

One photon of energy E = hf can give its energy to one electron.

If that energy is greater than the energy the electron needs to escape from the
metal, it will escape and any energy left is given to the electron as kinetic energy.

The electrons requiring the least energy to escape will have the greatest kinetic
energy
From conservation of energy:
Energy of incoming Photon = work done to remove electron + kinetic energy of the electron
  is the work function of the metal measured in joules
 Ek(max) is the maximum kinetic energy with which an
electron can leave the material in joules
 The product hf is the energy of the incoming photon in
joules
We must note the following:
·
·
·
Ek is the maximum kinetic energy, i.e. the kinetic energy of the fastest electrons.
Many electrons are slower than these. The fastest electrons come from the top layers.
A minimum photon energy corresponds to a minimum frequency of incident radiation.
This minimum frequency is called the threshold frequency f0.
The threshold frequency f0 is the minimum frequency of incident radiation which
can produce electrons.
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Example:
A metal plate is illuminated with radiation of wavelength 5.1x10-7m. The work function of
the metal is 3.58x10-19J
Calculate the frequency of the radiation being used
Calculate the maximum kinetic energy of an emitted electron
Calculate the threshold frequency
Which of the following metals would emit photoelectrons if the same incident radiation
were shone upon it
………………………………………………………………………….
Another common question is to say what happens if the intensity of the light shining on the
metal or the frequency of the light is altered.
Activity: complete the following statements to explain what the effect on the emitted
electrons from the metals surface is
If the frequency of the incident light is increased then …………………………………………………………
……………………………………………………………………………………………………………………………………………..
……………………………………………………………………………………………………………………………………………..
……………………………………………………………………………………………………………………………………………..
……………………………………………………………………………………………………………………………………………..
if the intensity of the incident light is increased then …………………………………………………………..
……………………………………………………………………………………………………………………………………………..
……………………………………………………………………………………………………………………………………………..
……………………………………………………………………………………………………………………………………………..
……………………………………………………………………………………………………………………………………………..
Note: The emitted electrons are often called photoelectrons but they are the same as any
other electrons
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We can summarise these findings in three rules, the laws of photoelectric emission –
1. The number of electrons emitted per second depends on the intensity of the radiation.
2. The photoelectrons have a range of energy, from zero to a maximum value. The
maximum value is determined by the frequency of the incident radiation, not the
intensity.
3. A minimum value for the frequency of the incident radiation is needed, the threshold
frequency.
The graph below shows how the energy of the photoelectrons depends on the frequency
(colour) of the light:
Energy × 10-19 J
Threshold
Frequency f0
Frequency × 1014 Hz
We find that the gradient of this graph is constant, regardless of the metal. The equation of
the graph is:
Ek = hf - 
If you compare this equation with y = mx + c
 You can see the gradient is Planck’s constant, h.
 The intercept on the Y axis is - 
 The x axis intercept is the threshold frequency.
Exercise: (h = 6.6  10–34 Js)
1. Draw on the same axes another graph corresponding to a metal with a greater
work function.
2. 3.0 x 10-10Js-1 of light energy is incident on the 1mm2 surface of a metal. If the
frequency of the light is 1.5 x1015 Hz. Find:
1. The energy of each photon
b) The number of photons s-1 incident on the surface
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Example 2
A metal surface has a work function of 3.0 eV and is illuminated with radiation of
wavelength 350 nm. Work out:
(a) The threshold frequency
(b) The maximum wavelength that causes photoelectric emission
(c) The maximum kinetic energy of the photoelectrons
(d) The maximum speed of the photoelectrons.
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Energy Levels in Atoms
When photons of radiation are incident on a metal if they don’t have enough energy to
remove electrons from the metal they can still interact with atoms to give them extra
energy, which makes them excited. Atoms can also become excited by collisions with
electrons or by being heated from an external source. This results in a 4 step process
0 eV
Highest energy
level
-0.22 eV
2
1
3
4
-3.41 eV
1.
An incoming photon/heat source/electric current transfers energy to the atom
2.
This increase in the atoms energy causes an electron in a low energy level to move to
a higher energy level. Here it has a higher potential energy.
3.
The higher level is not a stable position and the electron cannot remain in this excited
state. It falls back down to a more stable, lower energy level.
4.
In order to do this it must emit energy to lower its potential energy. It does this by
emitting one or more photons of radiation.
The electron loses potential energy in releasing a photon. Therefore we start at the highest
level which we give a value of zero. This is where the electron is just freed.
If it falls from this level to a lower energy level, the lower level must have a negative value.
The highest energy level is where ionisation occurs.
The lowest level is the ground state.
Electrons can make transitions from any energy level to any other:
Ionisation is when an electron gains so much energy that it becomes free
of the atom.
Excitation occurs when an electron gains energy and moves to a higher
energy level
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Example:
The diagram below shows part of the energy level diagram for hydrogen
n = 5 _________________ 0.00 eV
n = 4 _________________–0.85 eV
n = 3_________________–1.50 eV
n = 2 _________________–3.40 eV
Energy
transferred
to the atom
Energy
transferred
away from
the atom
n = 1 _________________–13.60 eV



Note:
The lowest level n =1 (-13.6 eV) is the ground state. This is the normal configuration
of the atom. Energy must be put in to raise the electron to other levels.
The highest level, E = 0 is the ionisation energy.
Energy levels are not evenly spaced.
If an electron is at an excited level (E1) and makes a transition to a lower level (E2), then the
energy of the photon given out can be worked out with the equation:
E = E1 – E2 (this is the difference in energy between the two levels)
Since E = hf, we can rewrite this as:
hf = E1 – E2
Using the diagram above for hydrogen
a) What is the ionisation energy of the atom in eV?
b) When an electron of energy 12.1eV collides with the atom, photons of 3 different
energies are emitted. Show on the diagram using arrows, the transitions responsible
for these photons. (h = 6.6  10–34 Js)
c) Label the 3 transitions and calculate the frequencies of each emitted photon.
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d) Calculate the wavelength of the photon emitted with the highest energy.
When we heat a gas or pass an electric current through it we can make it glow. We have
ionised the gas. If we look at the glowing gas through a spectrometer, we see the spectrum
of the gas which is distinctive for that gas. Unlike the spectrum of the Sun, in which we see
all the colours of the rainbow, we only see certain colours, while others are absent. We call
this kind of spectrum a line emission spectrum. The colours are discrete wavelengths. Each
gas has its own line emission spectrum which can be used to identify the gas.
Red
Green
Blue
Violet
When we consider energy levels in atoms, we will tend to look at hydrogen which fits this
model well. (Hydrogen has one electron.) More complex atoms with several electrons do
not.
If we look at a spectrum of hydrogen, we find lines at the wavelengths in the table:
Wavelength (nm)
656
486
434
410
397
389
365
Photon Energy ( 10-19 J)
3.03
4.09
4.56
4.85
5.01
5.11
5.45
Photon Energy (eV)
1.90
2.56
2.86
3.03
3.13
3.19
3.41
Which wavelength would correspond to red light?..........................................
Which wavelength would correspond to violet light?.......................................
Each energy represents the energy of a photon emitted as an electron makes a transition
from a higher energy level to a lower.
Activity: explain why an excited atom emits a line spectrum and not a continuous spectrum
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
……………………………………………………………………………………………………………………………………………….
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The Fluorescent Lamp





When an electric current is passed through a fluorescent lamp, electrons collide
with atoms of mercury vapour.
If the electron has sufficient energy, the collision will excite electrons in the mercury
atoms of the gas to a higher energy level.
As the excited electrons return to the original state they emit photons of ultraviolet
light.
The fluorescent coating absorbs the UV photons and excites the atoms in the
coating
When the phosphor atoms de-excite they emit photons of visible light
Evidence for the Wave Behaviour of Particles
The Belgian physicist de Broglie (pronounced ‘de Broy’) reasoned that if waves have particle
properties, it was reasonable to suppose that particles had wave properties. He devised the
relationship, which states that particles have wave properties. It is the logical extension of
the particulate nature of electromagnetic wave phenomena.
He combined the following equations:
 Energy of photons:
E = hc/
 Einstein’s mass equivalence:
E = mc2
Now substitute and rearrange to make  the subject
The term mc is mass  speed, which is momentum. We give momentum the symbol
P = mv
We can rewrite the equation as
or
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 h is Planck’s constant measured in Js
 m is the mass of the object in kg
 v is the velocity of the object in ms-1
  is the de Broglie wavelength of the object
Therefore every particle with a momentum has an associated de Broglie wavelength, even
something as absurd as a car travelling at 20 ms-1.
Electrons can be shown to have wave properties by the simple use of an electron
diffraction tube. A slice of carbon is placed in a beam of electrons so that the electrons
diffract.
We know diffraction is a property of waves. The electron diffraction tube is evidence of
electrons behaving as waves.
Filament
Anode
Carbon disc
Phosphor
screen
6.3 V ac
supply to
the
filament
Diffraction
rings
0V
Electron
beam
5000 V
Cathode
We need to note a couple of points:
  is the de Broglie wavelength
 Strictly speaking we should count the mass and speed as relativistic. As the speed of
particles approaches the speed of light, the mass increases as kinetic energy is turned
into mass. We will not worry about this at this stage.
The wave properties of electrons have led to the development of the electron microscope,
which allows magnifications much bigger than was ever possible with the light microscope.
A good light microscope can magnify up to 1000 times. The electron microscope can
magnify up to about 1 million times, and can reveal the existence of individual atoms. The
electron beams are focused by magnets just like the lenses on a microscope.
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Examples: (h = 6.6 x 10-34Js)
1. Calculate the De Broglie wavelength of
a) An electron (mass = 9.1 x10-31kg) moving at 3.05x107ms-1
b)
A proton ( mass = 1.7 x 10-27kg) moving at the same speed
2. Calculate the momentum and speed of an electron that has a de Broglie wavelength
of 600nm
3. Calculate the De Broglie wavelength of a car of mass 1000kg moving at 20 ms-1
In the exam you may be asked to give example of how waves and particles exhibit both wave
and particle behaviour.
Using what we have discussed in this booklet try and fill in the table below with examples of
each.
Waves
Particles
Wave
behaviour
Particle
behaviour
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What Scientists Do








Scientists try to explain how and why things happen.
They suggest an answer by producing a theory or a model to try to explain the
observations.
They make a prediction or hypothesis based on the theory which suggests what will
happen in particular circumstances.
Tests must be carried out to provide evidence to support the theory or disprove it.
Other scientists will also test the theory to validate it.
If the evidence backs up the theory it is accepted until further evidence may
disprove it.
Evidence is often gained through controlled experiments from which meaningful
conclusions can be drawn.
A theory will only be accepted if it can be tested or validated.
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