Fundementals Of Nuclear Physics

核能发电基本常识
认识科学做一个人聪明的外行人
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Atoms and Nuclei
Each topic is subdivided into a number of episodes.
An episode represents a coherent section of teaching – perhaps one or two lessons.
Each episode contains links to a number of activities.
Quantum physics
Episode 500: Preparation for quantum physics topic
Episode 501: Spectra and energy levels
Episode 502: The photoelectric effect
Lasers
Episode 503: Preparation for lasers topic
Episode 504: How lasers work
Wave particle duality
Episode 505: Preparation for wave-particle duality topic
Episode 506: Particles as waves
Episode 507: Standing waves

Radioactivity
Episode 508: Preparation for radioactivity topic
Episode 509: Radioactive background and detectors
Episode 510: Properties of radiations
Episode 511: Absorption experiments
Episode 512: Nuclear equations
Episode 513: Preparation for exponential decay topic
Episode 514: Patterns of decay
Episode 515: The radioactive decay formula
Episode 516: Exponential and logarithmic equations
Accelerators and detectors
Episode 517: Preparation for accelerators and detectors topic
Episode 518: Particle accelerators
Episode 519: Particle detectors
Rutherford’s experiment
Episode 520: Preparation for Rutherford scattering
Episode 521: Rutherford’s experiment
Episode 522: The Size of the Nucleus
Nuclear stability
Episode 523: Preparation for nuclear stability topic.
Episode 524: Stable nuclides
Episode 525: Binding energy

Nuclear fission
Episode 526: Preparation for nuclear fission topic
Episode 527: Nuclear transmutation
Episode 528: Controlling fission
X-ray and neutron diffraction
Episode 529: Preparation for X-ray and neutron diffraction topic
Episode 530: X-ray diffraction
Episode 531: Neutron diffraction
Particles and antiparticles
Episode 532: Preparation for particle physics topic
Episode 533: The particle zoo
Episode 534: Antiparticles and the lepton family
Episode 535: Particle reactions
Episode 536: Vector bosons and Feynman diagrams
Quarks
Episode 537: Preparation for deep scattering and quarks topic
Episode 538: Electron scattering
Episode 539: Deep inelastic scattering
Episode 540: Quarks and the standard model
资料来源：
http://www.iop.org/activity/education/Projects/Teaching%20Advanced%20Physics/Atomic%20and%20
Nuclei/index.html

1
Episode 500: Preparation for the quantum physics topic
It is most likely that this will be a topic that is completely unfamiliar to all students from pre-16 level
courses. It is also one where the impact on everyday life is apparently very limited and where
students think that they have no direct experience of its consequences. Nothing could be further
from the truth: e.g. all modern electronics relies on quantum physics.
However these very facts make it a most fascinating subject and one whose very novelty should
attract the interest of your students.
Main aims
Students will:
1. Know that atoms absorb and emit light as quanta (photons).
2. Explain how this is used to explain emission spectra.
3. Know how to calculate photon energies.
4. Describe the photoelectric effect, and explain it in terms of photons and electrons.
5. Describe an experiment to determine Planck’s constant using the photoelectric effect.
Prior knowledge
Students should be familiar with the nuclear model of the atom. They should know that metals
contain ‘free’ (conduction) electrons.
Where this leads
These episodes (and work on lasers) lead on to general ideas about wave-particle duality.
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Summary
Demonstration: Looking at emission spectra. (20 minutes)
Discussion: The meaning of quantisation. (20 minutes)
Demonstration: Illustrating quantisation. (10 minutes)
Discussion: Energy levels in a hydrogen atom. (10 minutes)
Worked example + Student Questions: Calculating frequencies. (20 minutes)
Discussion: Distinguishing quantisation and continuity. (5 minutes)
Worked example: Photon flux. (10 minutes)
Student calculations: Photon flux. (20 minutes)
Student experiment: Relating photon energy to frequency. (30 minutes)
Demonstration:
Looking at emission spectra
Show a white light and a set of standard discharge lamps: sodium, neon, hydrogen and helium.
Allow students to look at the spectrum of each gas. They can do this using a direct vision
spectroscope or a bench spectroscope, or simply by holding a diffraction grating up to their eye.
What is the difference? (The white light shows a continuous spectrum; the gas discharge lamps
show line spectra.)
Emission and absorption spectra
(Diagram: resourcefulphysics.org)
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The spectrum of a gas gives a kind of 'finger print' of an atom. You could relate this to the simple
flame tests that students will have used at pre-16 level. Astronomers examine the light of distant
stars and galaxies to discover their composition (and a lot else).
Discussion:
The meaning of quantisation
Relate the appearance of the spectra to the energy levels within the atoms of the gas. Students will
already have a picture of the atom with negatively charged electrons in orbit round a central
positively charged nucleus. Explain that, in the classical model, an orbiting electron would radiate
energy and spiral in towards the nucleus, resulting in the catastrophic collapse of the atom.
This must be replaced by the Bohr atomic structure – orbits are quantised. The electron’s energy
levels are discrete. An electron can only move directly between such levels, emitting or absorbing
individual photons as it does so. The ground state is the condition of lowest energy – most electrons
are in this state.
Think about a bookcase with adjustable shelves. The bookshelves are quantised – only certain
positions are allowed. Different arrangement of the shelves represents different energy level
structures for different atoms. The books represent the electrons, added to the lowest shelf first etc
Demonstration:
Illustrating quantisation
Throw a handful of polystyrene balls round the lab and see where they settle. The different levels
on which they end up – the floor, on a desk, on a shelf – gives a very simple idea of energy levels.
Some useful clipart can be found below
TAP 501-1: The emission of light from an atom
Resourceful Physics >Teachers>OHT>Emission of Light
An energy input raises the electrons to higher energy levels. This energy input can be by either
electrical, heat, radiation or particle collision.
When the electrons fall back to a lower level there is an energy output. This occurs by the emission
of a quantum of radiation.
Discussion:
Energy levels in a hydrogen atom
Show a scale diagram of energy levels. It is most important that this diagram is to scale to
emphasise the large energy drops between certain levels.
The students may well ask the question, “Why do the states have negative energy?” This is
because the zero of energy is considered to be that of a free electron 'just outside' the atom. All
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energy states 'below' this – i.e. within the atom are therefore negative. Energy must be put into the
atom to raise the electron to the 'surface' of the atom and allow it to escape.
Worked example + student questions:
Calculating frequencies
Calculate the frequency and wavelength of the quantum of radiation (photon) emitted due to a
transition between two energy levels. (Use two levels from the diagram for the hydrogen atom.)
E2 – E1 = hf
Point out that this equation links a particle property (energy) with a wave property (frequency).
Ask your students to calculate the photon energy and frequency for one or two other transitions.
Can they identify the colour or region of the spectrum of this light?
Emphasise the need to work in SI units. The wavelength is expressed in metres, the frequency in
hertz, and the energy difference in joules. You may wish to show how to convert between joules
and electronvolts.
Discussion:
Distinguishing quantisation and continuity
The difference between the quantum theory and the classical
theory is similar to the difference between using bottles of
water (quantum) or water from a tap (classical). The bottles
represent the quantum idea and the continuous flow from the
tap represents the classical theory.
The quantisation of energy is also rather like the kangaroo
motion of a car when you first learn to drive – it jumps from one
energy state to another, there is no smooth acceleration.
It is all a question of scale. We do not 'see' quantum effects
generally in everyday life because of the very small value of
Planck's constant. Think about a person and an ant walking across a gravelled path. The size of the
individual pieces of gravel may seem small to us but they are giant boulders to the ant.
We know that the photons emitted by a light bulb, for example, travel at the speed of light
(3 × 108
m s-1
) so why don’t we feel them as they hit us? (Although all energy is quantised we are
not aware of this in everyday life because of the very small value of Planck’s constant.)
Students may worry about the exact nature of photons. It may help if you give them this quotation
from Einstein:
‘All the fifty years of conscious brooding have brought me no closer to the answer to the question,
“What are light quanta?”. Of course, today every rascal thinks he knows the answer, but he is
deluding himself.’
Worked example:
Photon flux
Calculate the number of quanta of radiation being emitted by a light source.
(Illustrations: resourcefulphysics.org)
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Consider a green 100 W light. For green light the wavelength is about 6 × 10-7
m and so:
Energy of a photon = E = hf =hc / λ= 3.3 × 10-19
J
The number of quanta emitted per second by the light N = 100 × λ / hc = 3 × 1020
s-1
.
Student calculations:
Photon flux
TAP 501-2: Photons streaming from a lamp
TAP 501-3: Quanta
Student experiment:
Relating photon energy to frequency
TAP 501-4: Relating photon energy to frequency.
Students can use LEDs of different colours to investigate the relationship between frequency and
photon energy for light.
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TAP 501-1: The emission of light from an atom
Electron in orbit round a nucleus in an atom
Energy input. The electron is excited and
rises to a higher energy level (shell).
The electron falls back to its original energy
level and energy is emitted in the form of
radiation. The bigger the drop the greater the
energy emitted and the shorter wavelength
the radiation has (blue light).
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TAP 501-2: Photons streaming from a lamp
What to do
Complete the questions below on the sheet. Provide clear statements of what you are estimating;
show what calculations you are performing and how these give the answers you quote. Try to show
a clear line of thinking through each stage.
Steps in the calculation
1. Estimate the power of a reading lamp in watts.
2. Estimate the average wavelength of a visible photon.
3. Calculate the energy transferred by each photon.
4. Calculate the number of photons emitted by the lamp in each second.
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Practical advice
This question, or a substitute for it, needs to come early on in the discussion of photons to avert
questions concerning our inability to be aware of single photons. However, single photon detectors
are now used in astronomy etc.
Alternative approaches
This may be prefaced or supplemented by such a calculation performed in class. It is well done by
linking to other such questions that yield large numbers.
Social and human context
Every time we meet a pervasive quantity like power it is useful to compare it to our place in the
Universe (75 W or so as a useful power output over any length of time) and to compare developed
and developing countries in this respect.
Answers and worked solutions
1. P = 40 W
2. λ = 5 × 10–7
m
3. Calculate the frequency of the photons corresponding to this wavelength:
.Hz106
m105
sm103
14
7
18
×=
×
×
=
=
−
−
λ
c
f
Now calculate the energy of each photon:
J.104
Hz106sJ106
19
14134
−
−−
×=
×××=
= hfE
4. Energy per second = 40 J s–1
Energy per photon = 4 × 10–19
J.
.101
J104
sJ40
photonperenergy
secondperenergy
secondperphotons
20
19
1-
×=
×
=
=
−
External reference
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This activity is taken from Advancing Physics chapter 7, question 20E
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TAP 501- 3: Quanta
Speed of electromagnetic radiation in free space (c) = 3.00 x 108
m s-1
Planck’s constant (h) = 6.63 x 10-34
J s
1. Write down the equation for the quantum energy of a photon in terms of its frequency.
2. Calculate the energies of a quantum of electromagnetic radiation of the following wavelengths:
(a) gamma rays wavelength 10-3
nm
(b) X rays wavelength 0.1 nm
(c) violet light wavelength 420 nm
(d) yellow light wavelength 600 nm
(e) red light wavelength 700 nm
(f) microwaves wavelength 2.00 cm
(g) radio waves wavelength 254 m
3. Calculate the wavelengths of quanta of electromagnetic radiation with the following energies:
(a) 6.63 x 10-19
J
(b) 9.47 x 10-25
J
(c) 1.33 x 10-18
J
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Practical advice
Pupils may need to be reminded that a wavelength of 10-3
nm is 1 x 10-12
m and that some students
could need help in using their calculators.
1 E = hf
2
(a) f = c/λ E = hf so E = h c/λ
E = (6.63 x 10-34
x 3 x 108) / (1 x 10-12
) = 1.99 x 10-13
J
(b) E = 1.99 x 10-15
J
(c) E = 4.74 x 10-19
J
(d) E = 3.01 x 10-19
J
(e) E = 2.84 x 10-19
J
(f) E = 9.95 x 10-24
J
(g) E = 7.83 x 10-19
J
3
(a) λ = hc/E λ = (6.63 x 10-34
x 3 x 108) / 6.63 x 10-19
= 3 x 10-7
m (300 nm)
(b) 0.21 m
(c) 1.5 x 10-7
m (150 nm)
(d) 5 x 10-6
m
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TAP 501- 4: Relating energy to frequency
Photons have a characteristic energy
Light of a particular colour is a stream of photons of a specific frequency. Light appears granular
when seen at the finest scale. A bright light delivers lots of energy every second. If light is granular
then the amount of energy must be related to the number of granules arriving each second. The
intensity of the light will also depend on the energy delivered by each granule. This activity relates
the energy of each photon to the frequency of that photon.
You will need
multiple LED array
peering tube
power supply, 5 V (smooth and regulated)
multimeter
five 4 mm leads
Measuring energy
The energy released by each electron as it travels through the LED is transferred to a photon. To
measure the energy released by each electron measure the potential difference across the LED
when it just glows. Then we multiply this figure by the charge on the electron (1.6 × 10–19
C). The
quantity that characterises the photon is the frequency so we then seek to find a connection
between this frequency and the energy.
1. Set up the circuit and check that each LED can be lit by altering the pd
2. Calculate the frequency of the LEDs.
V
0 V
+5 V
to 5 V power
supply
Knob on
pot
Alter pd so
that LED
just lights
select LEDs one at a time
by flying lead
select LED by flying lead
470 nm 502 nm 650 nm563 nm 585 nm 620 nm
to voltmeter
100 Ω
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3. Measure the pd just sufficient to strike each LED. At this pd the energy supplied by the
electrons is all transferred to photons. Use the peering tube to cut out room lighting.
4. Look for a pattern connecting energy to frequency (plot a graph!). You should be
prepared to re-measure any points that do not fit and to check your results with those
from other measurements.
5. See if you can quantify the relationship. By how much does the energy of the photon
change for each hertz?
Energy and frequency
1. The energy associated with a photon is related to its frequency.
2. This relationship introduces the important quantity, h, the Planck constant.
Practical advice
We suggest setting up several competing research groups, and actively encouraging students to
form a consensus about the relationship between frequency and energy. An appropriate degree of
collaboration gets the correct answer; inappropriate degrees yield a work of fiction or no consensus.
Thus can physics progress.
Students will know about the existence of an LED from previous work on electricity and will know
that it conducts in one direction only. Thus electrons, simply introduced as what moves when
electricity is conducted, can be presented as meeting an electrical barrier when the LED is reverse
biased and falling down that barrier when forward biased. This simple model of the action of an LED
is enough for this purpose. Connecting this electrical model to an energetic model requires the
notion of potential difference to be reviewed as being likely to be the sensible way of determining
the height of the barrier and the energy as being the potential difference times the charge on the
electron. Analogies with the energy released in falling down a hill can reinforce this idea. So as to
make sure that none of the electrical energy is dissipated we need to insist that we require the
smallest pd across the photodiode. This energy, plotted against the frequency of emitted light
(taken from the manufacturer's specifications), can then be used. Experience shows that the
measurements made by the students may not be so accurate, and that encouragement to settle on
a simple pattern, together with the consensual approach suggested above and the ability to make
several measurements before deciding on the accurate answer, will be necessary. A class using a
graph-plotting package may make this review and interaction more likely.
Students should easily establish E = h f. A consensus on the value of h should give a value that is
far from embarrassing.
Students who are red/green or other forms of colour blindness will get different results. Often
red/green colour blind students need a higher striking pd to see some light from the LED or may not
be able to see particular wavelengths of light.
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Sample results:
LED
colour
Wavelength
/ nm
Frequency
/ 1014
Hz
Striking pd
/ V
Energy
/ J
h
/ 10–34
J s
Blue 470 6.38 2.38 0.381 6.0
Green 563 5.33 1.69 0.270 5.1
Yellow 585 5.12 1.63 0.261 5.1
Orange 620 4.83 1.48 0.237 4.9
Red 650 4.62 1.47 0.235 5.1
Technician’s information
The array of LEDs is used to make the connection between the frequency at which a photon is
emitted and the energy carried by that photon. Measurements are made of the minimum pd
required to just turn an LED on and of the wavelength of light from it. The wavelength may be better
taken directly from the manufacturer's specification. Each LED emits photons of one characteristic
frequency, specified in many catalogues by the peak wavelength emitted by the LED. You need a
wide range of wavelengths, fairly evenly spaced, so as to get a reasonable graph of pd against
frequency or wavelength. You may find a wider range of LEDs available at lower cost than when
this design was first produced, if so then exceeding the range suggested is fine; reducing that range
does not yield a reliable graph. To measure the energy carried by each photon students will need to
be able to measure the pd applied across each LED in turn. Students then plot energy / frequency.
So it may be useful to mark the peak frequencies or wavelengths emitted by the LEDs on the
apparatus.
How to make it
The requirement is to be able to apply a variable pd, 0 - 3 V, across a series of LEDs, one at a time
in turn. 5 LEDs are sufficient. Increasing the range of frequencies is more important than adding
more LEDs. We suggest that the LEDs be mounted in plastic ducting, a 150 mm length of 40 mm by
25 mm proved sufficient to mount all the components neatly.
Here is a circuit diagram:
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Variations are, of course possible. You may choose not to have sockets (which enable the current
through the LEDs to be measured), or perhaps to have only one return wire so that the LEDs come
on one after another as the pd is increased.
A suitable protective resistor (roughly equal in value to the resistance of the shortest wavelength
LED) in series with the wiper arm of the potentiometer will prevent applying too much pd across the
LEDs.
Important features
• Use as wide a range of wavelengths for the LEDs as are currently available.
• The LEDs should all be mounted in clear plastic, not mounted in coloured plastic.
• The LEDs should all have approximately the same power output.
• Provide a narrow opaque tube, about the length of a pencil, through which to peer at each
LED, excluding extraneous light, so as to detect when it just comes on, and obtain a good
value for the pd needed. Black paper or card is usually sufficient for the tube.
• The arrangement of the potential divider together with the protective resistor to protect the
LEDs allows the apparatus to be driven from a 5 V supply whilst protecting the LEDs. Other
arrangements might also work.
To establish the connection between the energy associated with each click as a Geiger counter
detects a gamma ray photon we suggest measuring the energy required to release one photon of
light in a light-emitting diode. This has the advantage that we can cheaply try out several
frequencies and rapidly obtain a picture of how energy varies with frequency. It is, of course, not the
only technique for establishing a link between frequency and energy. You may substitute others.
The photoelectric effect has been used for this for many years, as has appeal to the evidence of
spectra.
V
0 V
+5 V
to 5 V power
supply
Knob on
pot
Alter pd so
that LED
just lights
select LEDs one at a time
by flying lead
select LED by flying lead
470 nm 502 nm 650 nm563 nm 585 nm 620 nm
to voltmeter
100 Ω
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Studying engineering barriers of different heights to release different amounts of energy takes us
into the structures of semiconductor materials and engineering band gaps, which, whilst fascinating,
does not contribute to the central understanding sought here. It is, however, central to quantum
engineering. This can be used to start a discussion linking the potential barrier to an energetic
understanding of the situation.
External reference
This activity is taken from Advancing Physics chapter 7, activity 10E
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This episode introduces an important phenomenon. Light releases electrons from metal surfaces.
Summary
Demonstration: The basic phenomenon. (15 minutes)
Discussion: Summarising the phenomenon. (10 minutes)
Discussion: An analogy. (5 minutes)
Student questions: Using the photoelectric equation. The Millikan experiment: to verify
Einstein’s photo-electric relationship (30 minutes)
Student experiment: Measuring Planck’s constant. (30 minutes)
Demonstration:
The basic phenomenon
Introduce the topic by demonstrating the electroscope and zinc plate experiment.
TAP 502-1: Simple photoelectric effect demonstration
Point out to the students that the photoelectric effect is apparently instantaneous. However, the
light must be energetic enough, which for zinc is in the ultraviolet region of the spectrum.
If light were waves, we would expect the free electrons to steadily absorb energy until they escape
from the surface. This would be the case in the
classical theory, in which light is considered as
waves. We could wait all day and still the red
light would not liberate electrons from the zinc
plate.
So what is going on? We picture the light as
quanta of radiation (photons). A single electron
captures the energy of a single photon. The
emission of an electron is instantaneous as long
as the energy of each incoming quantum is big
enough. If an individual photon has insufficient
energy, the electron will not be able to escape
from the metal.
Discussion:
Summarising the phenomenon
Summarise the important points about the
photoelectric effect.
Ultra violet
light
Negatively
charged zinc
plate
Gold leaf falls immediately the
zinc plate is illuminated with
ultra violet light
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Potential well
high energy violet quantum
Electron leaves metal
Quantum energy
Electron energy
Work function
There is a threshold frequency (i.e. energy), below which no electrons are released.
The electrons are released at a rate proportional to the intensity of the light (i.e. more photons per
second means more electrons released per second).
The energy of the emitted electrons is independent of the intensity of the incident radiation. They
have a maximum KE.
Discussion:
An analogy
Try this analogy, which involves ping-pong balls, a bullet and a coconut shy. A small boy tries to
dislodge a coconut by throwing a ping-pong ball at it – no luck, the ping-pong ball has too little
energy! He then tries a whole bowl of ping-pong balls but the coconut still stays put! Along comes a
physicist with a pistol (and an understanding of the photoelectric effect), who fires one bullet at the
coconut – it is instantaneously knocked off its support.
Ask how this is an analogy for the zinc plate experiment. (The analogy simulates the effect of
infrared and ultra violet radiation on a metal surface. The ping-pong balls represent low energy
infrared, while the bullet takes the place of high-energy ultra violet.)
Now you can define the work function. Use the potential well model to show an electron at the
bottom of the well. It has to absorb the energy in one go to escape from the well and be liberated
from the surface of the material.
Units
The electronvolt is introduced because it is a convenient small unit. You might need to point out that
it can be used for any (small) amount of energy, and is not confined to situations involving
electrically accelerated electrons.
Potential well
It is useful to compare the electron with a person in the bottom of a well with totally smooth sides.
The person can only get out of the well by one jump, they can't jump half way up and then jump
again. In the same way an electron at the bottom of a potential well must be given enough energy to
escape in one 'jump'. It is this energy that is the work function for the material.
Now you can present the equation for photoelectric emission:
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Energy of photon E = hf
Picture a photon being absorbed by one of the electrons which is least tightly bound in the metal.
The energy of the photon does two things.
Some of it is needed to overcome the work function φ.
The rest remains as KE of the electron.
hf = φ + (1/2) mv2
A voltage can be applied to bind the electrons more tightly to the metal. The stopping potential Vs is
just enough to prevent any from escaping:
hf = φ + eVs
Student questions:
Using the photoelectric equation
Set the students some problems using these equations.
TAP.502-2: Photoelectric effect questions
TAP 502-4: Student Question. The Millikan experiment
The Millikan experiment question may best come after
TAP 502-3: Student experiment: Measuring threshold frequency.
Student experiment:
Measuring Planck’s constant
TAP502-3: Measuring threshold frequency
Students can measure Planck’s constant using a photocell.
(Some useful clipart is given here below)
to
oscilloscope
coloured filter
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TAP 502-1: Simple photoelectric effect demonstration
Resources needed
Gold leaf electroscope or coulomb meter
Zinc plate attachment (sand-papered clean to remove oxidation)
Laser (class 2)
Mains lamp (a desk lamp is ideal)
Ultra violet lamp with clear quartz envelope
Safety
A class 2 laser requires a warning: Do not stare down the beam.
A short-wave UV lamp must be shielded so that the UV emerges through a hole. The hole is always
directed away from eyes. The presence of UV can be demonstrated by showing fluorescence of
paper.
Technique
Attach the zinc plate to the top of the electroscope. (A coulomb meter can be used instead of the
electroscope.)
Charge the plate negatively.
o
No effect No effect With U.V. leaf
falls
immediately
(Diagrams: resourcefulphysics.org)
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Shine red laser light onto the cleaned zinc plate – no effect.
Use a mains light bulb emitting white light – no effect.
Use an ultra violet lamp – the leaf falls immediately.
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TAP 502-2: Photoelectric effect questions
hf = φ + (1/2) mv2
and hf = φ + eVs
e = 1.60 x 10-19
C,
h = 6.63 x 10-34
J s,
mass of electron = 9.11 x 10-31
kg
1 The work function for lithium is 4.6 x 10-19
J.
(a) Calculate the lowest frequency of light that will cause photoelectric emission.
(b) What is the maximum energy of the electrons emitted when light of 7.3 x 1014
Hz is used?
2 Complete the table.
Metal
Work Function
/eV
Work Function
/J
Frequency
used /Hz
Maximum KE of
Ejected electrons /J
Sodium 2.28 6 x 1014
Potassium 3.68 x 10-19
0.32 x 10-19
Lithium 2.9 1 x 1015
Aluminium 4.1 0.35 x 10-19
Zinc 4.3 1.12 x 10-19
Copper 7.36 x 10-19
1 x 1015
3 The stopping potential when a frequency of 1.61 x 1015
Hz is shone on a metal is 3 V.
(a) What is energy transferred by each photon?
(b) Calculate the work function of the metal.
(c) What is the maximum speed of the ejected electrons?
4 Selenium has a work function of 5.11 eV. What frequency of light would just eject electrons?
(The threshold frequency is when the max KE of the ejected electrons is zero)
5 A frequency of 2.4 x 1015
Hz is used on magnesium with work function of 3.7 eV.
(a) What is energy transferred by each photon?
(b) Calculate the maximum KE of the ejected electrons.
(c) The maximum speed of the electrons.
(d) The stopping potential for the electrons.
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1(a) hf = φ
hf = 4.60 x 10-19
f = 4.60 x 10-19
/ 6.63 x 10-34
= 6.94 x 1014
Hz
(b) hf = φ + (1/2) mv2
. (6.63 x 10-34
x 7.30 x 1014
) = 4.60 x 10-19
+ (1/2) mv2
4.84 x 10-19
- 4.60 x 10-19
= (1/2) mv2
= 0.24 x 10-19
J
2
Metal
Work Function
/ eV
Work Function
/ J
Frequency
used / Hz
Maximum KE of
ejected electrons / J
Sodium 2.28 3.65 x 10-19
6 x 1014
0.35 x 10-19
Potassium 2.30 3.68 x 10-19
6 x 1014
0.32 x 10-19
Lithium 2.90 4.64 x 10-19
1. x 1015
1.99 x 10-19
Aluminium 4.10 6.56 x 10-19
1.04 x 1015
0.35 x 10-19
Zinc 4.30 6.88 x 10-19
1.2 x 1015
1.12 x 10-19
Copper 4.60 7.36 x 10-19
1 x 1015
0
For copper 1 x 1015
Hz is below the threshold frequency so no electrons are ejected.
3
(a) 1.07 x 10-18
J
(b) hf = φ + eVs, so φ = hf - eVs, so φ = 1.07 x 10-18
– (1.6 x 10-19
x 3) = 5.9 x 10-19
J
(c) eVs = (1/2) mv2
so (1.60 x 10-19
x 3) = 0.5 x 9.11 x 10-31
x v2
so v2
=1.04 x 1012
and v = 1.02 x 106
m s-1
4 1.2 x 1015
Hz
5
(a) 1.6 x 10-18
J
(b) (1/2) mv2
= 1.x 10-18
J
(c) v2
= 1.1 x 1012
so v = 1.1 x 106
m s-1
(d) eVs = (1/2) mv2
so eVs = 1.00 x 10-18
and Vs = 0.63 V
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TAP502- 3: Measuring threshold frequency
Use a white light source and a set of coloured filters to find the threshold frequency, and hence the
work function, of the photosensitive material in a photocell. This may well be a standard piece of kit
in your school or college. Use a spreadsheet to plot and analyse a graph of your results.
This experiment uses a photocell to investigate the photoelectric effect. Light of various frequencies
is incident on the cell and photoelectrons are emitted and then form an electric current. A white
light source is shone through various coloured filters to produce a series of different frequencies of
light falling on the photocell. The current of photoelectrons produced in the cell maybe amplified
internally and is measurable on the ammeter. Otherwise an amplifying picoammeter is needed.
The potential divider provides an adjustable voltage. The incident frequency, threshold frequency,
and stopping potential are related by the following equation:
hf =eV + hfo
Procedure
For each coloured filter, adjust the potential divider until the stopping potential has been reached.
Record the stopping potential and the wavelength of light transmitted by the filter. Select the middle
of the range as the transmitted frequency.
NB: the filter might have written on it the range of wavelengths it transmits measured in
Enter your results of frequency and stopping potential on a spreadsheet and plot a graph of
frequency f versus stopping potential V.
Use your graph to determine the value of the threshold frequency f and hence calculate the work
function φ. Express your result in J and in eV.
Estimate the uncertainties in your measurements of V and in the values of f that you have used.
Use these estimates to add error bars to your graph and hence estimate the uncertainty in your
values of f0 and φ.
Decide how you could use your graph to determine the value of Planck's constant if you knew only
the value of e and not h.
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Data
Planck constant h = 6.60 x 10-34
J s
electron charge e = 1.67 x 10-19
C
speed of light c = 3.00 x 108
m s-1
1eV = 1.67 x 10-19
J
Practical advice
This section revisits ideas about charge, energy and potential difference and introduces the idea of
a stopping potential in order to measure the kinetic energy of photoelectrons. Students need to
realise that, if a charged particle is accelerated by a pd, energy is transferred to it, whereas if it
moves the other way, it loses kinetic energy, and that the two situations are the exact reverse of
each other. Students should appreciate that the work function represents the minimum amount of
work that an electron must do in order to get free and that the expression for kinetic energy
represents the maximum possible kinetic energy of the photoelectron. This energy is only
attainable if the energy transfer from photon to electron is 100% efficient and there is no energy
dissipation, e.g. due to heating.
This is quite a demanding activity, as it involves a relatively complicated and unfamiliar set-up.
Make sure students appreciate the use of the potential divider, (as in Episode 118 The Potential
Divider).
In analysing their results, students need to plot a graph and determine the y-intercept. Students will
have met graphs of the type y = mx + c before but still might not be very confident in using them, this
might need some discussion. We recommend using a spreadsheet graphing package here.
Students should also take account of experimental uncertainties; the most significant is likely to be
in the frequency, as the filters available do not have a very definite cut-off wavelength. There might
also be some uncertainty in deciding exactly the pd at which the photocell current drops to zero.
Einstein's ideas
Albert Einstein explained the photoelectric effect in a paper published in 1905. It was the second of
five ground-breaking papers he wrote that year. In the first paper, Einstein explained the mysterious
Brownian motion of particles contained in pollen grains as due to the random impact of much
smaller particles. This work led to the acceptance of the molecular or atomic nature of matter, which
until then had been quite speculative. Einstein's third paper that year is now his most famous. Here
Einstein introduced his Special Theory of Relativity which, in a later paper, led to probably the most
famous equation in science: E=mc2
, which describes the equivalence of mass and energy. But it
was Einstein's second paper, that contained his work on the photoelectric effect, that at the time
was the most revolutionary of the three, and it was for this work that Einstein was eventually
awarded the Nobel Prize, in 1922. (The Nobel Committee works somewhat more slowly than the
speed of light!) In this paper Einstein broke away from the idea that light (electromagnetic radiation)
is continuous in nature and introduced us to the idea of the quantum (plural quanta) or photon as a
`packet' of light. (The term quantum is used for any packet of energy, while a photon is a quantum
associated with electromagnetic radiation.) The wave model of light had been fairly conclusively
established a century earlier, mainly due to the work of Thomas Young, who demonstrated and
explained interference patterns. But the wave model cannot explain the photoelectric effect;
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Einstein realised this and took the bold step of putting forward a completely different model in order
to explain the following experimental results:
• for any given metal, with radiation below a certain threshold frequency no electrons are
released even if the radiation is very intense;
• provided the frequency is above the threshold, some electrons are released
instantaneously, even if the radiation is very weak;
• the more intense the radiation, the more electrons are released;
• the kinetic energy of the individual photoelectrons depends only on the frequency of the
radiation and not on its intensity.
Einstein was the first to use the equation E = hf to explain the photoelectric effect. It is known as the
Planck equation, and h is called Planck's constant, because Max Planck had already proposed that
when electromagnetic radiation was absorbed or emitted, energy was transferred in packets. That
work earned Planck the 1918 Nobel Prize.
External references
This activity is taken from Salters Horners Advanced Physics, section DIG, activity 30
and the Einstein notes above from Salters Horners Advanced Physics, section DIG additional sheet
11
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TAP 502- 4: The Millikan experiment to verify Einstein’s
photo-electric relationship.
The photoelectric effect was – well known by the end of the 19th century. Its explanation was one of
Einstein’s first applications of his photon model for light. He devised an equation relating the energy
of the photoelectrons to the frequency of the light and the work function of the metal used. In 1916,
American physicist Robert Millikan completed some experiments that tested Einstein's equation.
Though Millikan had been firmly against quantum theory, the results convinced him that Einstein
was right.
In Millikan's photoelectric apparatus, monochromatic light was incident on each of the
newly-cleaned metal plates in turn. The resulting photoelectrons were collected by electrode C and
flowed, via the variable resistor and microammeter, back to the plate assembly. By adjusting the
potentiometer, Millikan found the potential difference that was just large enough to stop the
electrons moving round the circuit. For each metal, he used radiation of several different
frequencies, noting the `stopping voltage' for each. This graph shows some of his results for
sodium.
(a) Use the graph to find the threshold frequency for sodium.
(b) Calculate the work function for sodium using your answer to (a). h = 6.63 x 10-34
J s.
(c) Use your answer to (b) to find the maximum kinetic energy of photoelectrons emitted from
sodium when the frequency of the incident light is 10 x 1015
Hz. Give your answer in joules
and in electronvolts. e = 1.6 x 10-19
C
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External reference
This activity is taken from Salters Horners Advanced Physics, section DIG, additional sheet 13
External reference
Answers and worked solutions are taken from Salters Horners Advanced Physics, section DIG,
additional sheet 14
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Episode 503: Preparation for lasers topic
It is likely that all pupils will have experienced laser technology in their homes or at school but may
well not familiar with the range of uses of lasers, their operation and safety.
Section TAP 504-2 gives details of the safety measures required.
Lasers form rather more of a 'tool' and so demonstration experiments are relatively few. However
some ideas and an explanation of the workings and other details of a laser are given.
Main aims
As regards post-16 examinations, the formal requirements laid down are modest, or non-existent,
so that the level of treatment here is not detailed.
Students will:
1. Outline the principles of operation of a laser.
2. State some uses of high and low energy lasers.
Prior knowledge
Students should know about the wave nature of light, including interference. They should also know
how light is emitted by electron transitions within atoms.
ruby rod
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This episode considers uses of lasers, and the underlying theory of how they work.
Safety:
Ensure that you are familiar with safety regulations and advice before embarking on any
demonstrations (see TAP 504-2).
Summary
Demonstration: Seeing a laser beam. (10 minutes)
Discussion: Uses of lasers. (15 minutes)
Discussion: Safety with lasers. (10 minutes)
Discussion: How lasers work. (20 minutes)
Worked examples: Power density. (10 minutes)
Student calculations: (10 minutes)
Demonstration:
Seeing a laser beam
A laser beam can be made visible by blowing smoke or making dust in its path. Its path through a
tank of water can be shown by adding a little milk.
Show laser light passing through a smoke filled box or across the lab and compare this with a
projector beam or a focussed beam of light from a tungsten filament light bulb.
Show the principle of optical fibre communication by directing a laser beam down a flexible plastic
tube containing water to which a little milk has been added.
Show a comparison between the interference pattern produced by a tungsten filament lamp (with a
'monochromatic' filter) and that produced by a laser.
Discussion:
Uses of lasers
Talk about where lasers are used – ask for suggestions from the class. As far as possible this
should be an illustrated discussion with a CD player, a laser pointer, a set of bar codes, a bar code
reader and the school’s laser with a hologram available for demonstration.
TAP 504-1: Uses of lasers
Show the list of uses. Invite students to consider the uses shown in the list. Can they say why lasers
are good for these? The reasons might be:
• A laser beam can be intense.
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• A laser beam is almost monochromatic.
• A laser beam diverges very little.
• Laser light is coherent.
Discussion:
Safety with lasers
Lasers must be used with care. Use the text as the basis of a discussion of the precautions which
must be taken.
TAP 504-2: Lasers and safety
Discussion:
How lasers work
If students are familiar with energy level diagrams for atoms, and of the mechanisms of absorption
and emission of photons, you can present the science behind laser action. Point out the difference
between:
(a) excitation – an input of energy raises an electron to a higher energy level
(b) emission - the electron falls back to a lower energy level emitting radiation and
(c) stimulated emission – the electron is stimulated to fall back to a lower energy level by the
interaction of a photon of the same energy
Define population inversion: Usually the lower energy
levels contain more electrons than the higher ones (a).
In order for lasing action to take place there must be a
population inversion. This means that more electrons
exist in higher energy levels than is normal (b).
For the lasing action to work the electrons must stay in
the excited (metastable) state for a reasonable length of
time. If they 'fell' to lower levels too soon there would
not be time for the stimulating photon to cause
stimulated emission to take place.
‘Laser’ stands for Light Amplification by Stimulated Emission of Radiation. The diagrams in
TAP 503 shows the ruby laser and the snowball effect of photons passing down a laser tube, and
the diagram above shows the three level laser action. The electrons are first ‘pumped’ up to the
higher energy level using photons. They then drop down and accumulate in a relatively stable
energy level, where they are stimulated to all drop back together to the ground state by a photon
whose energy is exactly the energy difference to the ground state.
(a) (b)
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Discuss coherent and non-coherent light. Coherent light is light in which the photons are all in 'step'
– in other words the change of phase within the beam occurs for all the photons at the same time.
There are no abrupt phase changes within the beam. Light produced by lasers is both coherent and
monochromatic (of one 'colour').
Incoherent sources emit light with frequent and random changes of phase between the photons.
(Tungsten filament lamps and 'ordinary' fluorescent tubes emit incoherent light)
Worked examples:
Power density
The laser beam also shows very little divergence and so the power density (power per unit area)
diminishes only slowly with distance. It can be very high.
For example consider a light bulb capable of emitting a 100 W of actual light energy.
At a distance of 2 m the power density is 100 / 4πr2
= 2 W m-2
. The beam from a helium-neon gas
laser diverges very little. The beam is about 2 mm in diameter 'close' to the laser spreading out to a
diameter of about 1.6 km when shone from the Earth onto the Moon!
At a distance of 2 m from a 1 mW laser the power density in the beam would be
0.001 / (π × 0.0012
) = 320 W m-2
! This is why you must never look directly at a laser beam or its
specular reflection.
Student calculations
Ask the class to calculate the power densities for a 100 W lamp and a 1 mW laser at the Moon.
(Distance to Moon = 400 000 km; diameter of laser beam at Moon = 1.6 km)
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TAP 504-1: Uses of lasers
• repairing damaged retinas
• bar code reader
• communication via modulated laser light in optical fibres
• neurosurgery - cutting and sealing nerves sterilization – key hole surgery (microsurgery)
• laser video and audio discs (CD and DVD)
• cutting metal and cloth
• laser pointer
• laser printer
• holography - three-dimensional images
• surveying - checking ground levels
• production of very high temperatures in fusion reactors
• laser light shows
• making holes in the teats of babies' bottles
• cutting microelectronic circuits
• physiotherapy - using laser energy to raise the temperature of localised areas of tissue e.g.
removing tonsure tumours
• laser lances for unblocking heart valves; removal of tattoos or birth marks
• laser guidance systems for weapons
• laser defence systems ('Star Wars')
• a modification of the Michelson-Morley experiment to check the existence of the ether
• distance measurement
• laser altimeters
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TAP 504-2: Lasers and safety
The following is an extract from the CLEAPSS Science Publications Handbook Section 12.12:
12.12 Lasers
A low-power, continuous-wave, helium-neon laser is useful for teaching wave optics because it
produces a beam of light that is:
• highly monochromatic (very narrow spread of wavelengths) and coherent (the same phase)
both across the beam and with time;
• of high intensity;
• of small divergence (typically 1 mm in diameter when it leaves the laser, 5 mm in diameter
4 m away).
Because of its intensity, care must be taken to prevent a beam from a laser falling on the eye
directly or by reflection, as it could damage the retina. In fact, it is now known that eyes could be
damaged by the beam from the low power Class II lasers used in schools only if a deliberate
attempt were made to stare at the laser along the beam or to concentrate the beam from a IIIa laser
with an instrument; the normal avoidance mechanism of the body would prevent damage in other
cases. Nevertheless, it is good practice to take precautions to avoid a beam falling on the eye.
Lasers should be positioned so that beams cannot fall on the eyes of those present, i.e., are
directed away from spectators. Ancillary optical equipment must be arranged so that reflected
beams cannot reach eyes.
Ten years ago, the lasers affordable by schools would work for only a few years and then only if run
periodically. Those currently available have longer lives and do not require this.
DES Administrative memorandum 7/70
This advises on the use of lasers in schools and FE colleges. It confines use at school level to
teacher demonstration. Safety rules include the avoidance of direct viewing; screening pupils who
should be at least 1 m away; keeping background illumination as high as possible (so that eye
pupils are as small as possible); displaying warning notices; keeping lasers secure from
unauthorised use or theft; use of goggles by the demonstrator. Because of the more recent
realisation that the lasers used in schools and colleges will not harm an eye by a beam accidentally
falling on it, these rules are not strictly necessary but following them is good training. However,
goggles are expensive, impractical and do not reduce hazard as they make it harder for the
demonstrator to see the beam, stray reflections etc.
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Episode 505: Preparation for wave-particle duality topic
In the first quarter of the twentieth century physicists began to realise that particles did not always
behave like particles – they could behave like waves. They called this wave-particle duality.
This theory suggests that there is no basic distinction between a particle and a wave. The
differences that we observe arise simply from the particular experiment that we are doing at the
time.
As with quantum theory, this is a section of the course that candidates will find completely new.
They are unlikely to have already met the wave nature of particles or the wave nature of electrons
bound within atoms.
Episode 507: Standing waves
Main aims
Students will:
1. Understand that electron diffraction is evidence for wave-like behaviour.
2. Use the de Broglie equation.
3. Identify situations in which a wave model is appropriate, and in which a particle model is
appropriate, for explaining phenomena involving light and electrons.
4. Use a standing wave model for electrons in an atom.
Prior knowledge
Students should have an understanding of wave phenomena, including diffraction and interference.
They should know how to calculate momentum.
This work follows on from a study of the photoelectric effect.
Where this leads
These episodes merely skim the surface of quantum physics. For students who wish to learn a little
more, here is some suggested reading:
The new quantum universe; Tony Hey and Patrick Walters; CUP
Quantum physics: An introduction; J Manners; IoPP
You can extend the idea of electrons-as-waves further, to the realm of the atom.
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This episode introduces an important phenomenon: wave - particle duality.
In studying the photoelectric effect, students have learned that light, which we think of as waves,
can sometimes behave as particles. Here they learn that electrons, which we think of as particles,
can sometimes behave as waves.
Summary
Demonstration: Diffraction of electrons. (30 minutes)
Discussion: de Broglie equation. (15 minutes)
Worked examples: Using the equation. (15 minutes)
Student questions: Using the equation. (30 minutes)
Discussion: Summing up. (10 minutes)
Student questions: Practice calculations. (30 minutes)
Demonstration:
Diffraction of electrons
The diffraction of electrons was first shown by Davisson and Germer in the USA and G P Thomson
in the UK, in 1927 and it can now be observed easily in schools with the correct apparatus.
Show electron diffraction. It will help if students have previously seen an electron-beam tube in use
(e.g. the fine beam tube, or e/m tube).
TAP 506-1: Diffraction of electrons
………
Electrons show
particle properties
Electrons show wave
properties
Thin graphite screen
Electron gun
Evacuated tube
Diffraction rings
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Before giving an explanation, ask them to contemplate what they are seeing. It is not obvious that
this is diffraction/interference, since students may not have seen diffraction through a
polycrystalline material. (Note that the rigorous theory of crystal diffraction is not trivial - waves
scattered off successive planes of atoms in the graphite give constructive interference if the path
difference is a multiple of a wavelength, according to the Bragg equation. The scattered waves then
appear to form a wave that appears to “reflect” off the planes of atoms, with the angle of incidence
being equal to the angle of reflection. In the following we adopt a simplification to a 2D case - see
TAP 506-1)
Qualitatively it can help to show a laser beam diffracted by two ‘crossed’ diffraction gratings. Rotate
the grating, and the pattern rotates. If you could rotate it fast enough, so that all orientations are
present, you would see the array of spots trace out rings.
TAP506-2: Diffraction of light
From their knowledge of diffraction, what can they say about the wavelength of the electrons? (It
must be comparable to the separation of the carbon atoms in the graphite.) How does wavelength
change as the accelerating voltage is increased? (The rings get bigger; wavelength must be getting
smaller as the electrons move faster.)
Discussion:
de Broglie equation
In 1923 Louis de Broglie proposed that a particle of momentum p would have a wavelength λ given
by the equation:
wavelength of particle λ = h/p
where h is the Planck constant,
or λ = h/mv for a particle of momentum mv.
The formula allows us to calculate the wavelength associated with a moving particle.
Worked examples:
Using the equation
1. Find the wavelength of an electron of mass 9.00 × 10-31
kg moving at 3.00 × 107
m s-1
.
λ = h/p = [6.63 × 10-34
] / [9.00 × 10-31
× 3.00 × 107
] = 6.63 × 10-34
/ 2.70×10-23
= 2.46×10-11
m = 0.025 nm
This is comparable to atomic spacing, and explains why electrons can be diffracted by graphite.
2. Find the wavelength of a cricket ball of mass 0.15 kg moving at 30 m s-1
.
λ = h/p = [6.63 × 10-34
] / [0.15 × 30] = 1.47×10-34
m = 1.5 10-34
J s (to 2 s.f.)
This is a very small number, and explains why a cricket ball is not diffracted as it passes near to the
stumps.
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3. It is also desirable to be able to calculate the wavelength associated with an electron when
the accelerating voltage is known. There are 3 steps in the calculation.
Calculate the wavelength of an electron accelerated through a potential difference of 10 kV.
Step 1: Kinetic energy Ek = eV = 1.6 × 10-19
× 10000 = 1.6 × 10-15
J
Step 2: EK = ½ mv2
= ½m (mv) 2
= p2
/ 2m, so momentum
p = √2mEk = √2 × 9.1 × 10-31
× 1.6 × 10-15
= 5.4 × 10-23
kg m s-1
Step 3: Wavelength λ = h / p = 6.63 × 10-34
/ 5.4 × 10-23
= 1.2 × 10-11
m = 0.012 nm.
Student questions:
Using the equations
A useful set of questions can be found at Resourceful Physics on the web
This can also be accessed from
http://resourcefulphysics.org/download/361/waves_and_particles.doc
and is available to subscribers.
Discussion:
Summing up
You may come across a number of ways of trying to resolve the wave-particle dilemma. For
example, some authors talk of ‘wavicles’. This is not very helpful.
Summarise by saying that particles and waves are phenomena that we observe in our macroscopic
world. We cannot assume that they are appropriate at other scales.
Sometimes light behaves as waves (diffraction, interference effects), sometimes as particles
(absorption and emission by atoms, photoelectric effect).
Sometimes electrons (and other matter) behave as particles (beta radiation etc), and sometimes as
waves (electron diffraction).
It’s a matter of learning which description gives the right answer in a given situation.
The two situations are mutually exclusive. The wave model is use for ‘radiation’ (i.e. anything
transporting energy and momentum, e.g. a beam of light, a beam of electrons) getting from
emission to absorption. The particle (or quantum) model is used to describe the actual processes
of emission or absorption.
Student question:
Interpreting electron diffraction patterns
TAP 506-3: Interpreting electron diffraction patterns
TAP 506-4: Electron diffraction question
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42
TAP 506- 1: Diffraction of electrons
Start by setting up the electron diffraction demonstration tube according to the manufacturer’s
instructions. Check the connections before switching on as it is easy to burn out the graphite grid
unless manufacturer’s instructions are correctly followed.
Wire carefully, no bare conductor
above 40 V
School EHT supplied are limited to a maximum
output current of less than 5 mA so they are
safe, but can still make the user jump. The lead
connecting the supply to the anode should have
a female connector so that no metal is exposed.
You will need two supply voltages:
a low-voltage supply to provide the current to heat the cathode;
a high-voltage supply to provide the potential difference between the cathode and the
anode, to accelerate the electrons.
These are both usually supplied by the EHT unit.
Qualitative experiments
Check that you can identify the following:
• the electron gun, which includes the cathode and the anode;
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43
• the graphite target;
• the fluorescent screen, which will glow when the electrons strike it.
When the cathode has heated up (you will see it glowing), increase the accelerating voltage V.
An invisible beam of electrons emerges from the electron gun and passes through the graphite film.
To show that there is an electron beam present, bring up a bar magnet close to the tube and
observe the pattern shifting. Magnetic fields deflect moving electrons. So this qualitative demo
shows both the wave aspects (the diffraction pattern) and the particle aspects (deflection by a
magnetic field) in the same equipment.
Look for a diffraction pattern on the screen at the end of the tube. What shape is the pattern? Where
can you see constructive interference? And destructive interference?
Now predict: If you increase the accelerating voltage, how will the energy and speed of the
electrons change? How will this affect the diffraction pattern?
Test your ideas.
Quantitative experiments
Choose a feature of the diffraction pattern that is easy to measure.
It might be the diameter of the first bright ring, or of the first dark ring. We will call this chosen
quantity d.
Investigate how d depends on V. Make several measurements.
Determine the mathematical relationship between d and V.
If the relationship is of the form d proportional to Vn
, you can find the value of n by plotting
a log-log graph. The gradient of the graph is equal to the value of n.
What other information would you need if you were to use this experiment to determine the atomic
spacing in graphite?
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Practical advice
It is difficult to present a convincing discussion of wave–particle duality in a few lines. We have
adopted the approach that it is an observed phenomenon, witness the diffraction of electrons.
The de Broglie equation wavelength = h/p simply allows us to translate between the wave and
particle pictures.
Increasing the accelerating voltage increase the electrons’ energy and momentum; greater
momentum means shorter wavelength, which in turn means that the electrons are diffracted
through a smaller angle. Hence the diameters of the diffraction rings get smaller. Students could
make measurements of the rings and relate these to the accelerating voltage. A log-l graph will
reveal the relationship between them. It is reasonable to say that ring diameter is proportional to
wavelength; a log-log graph of diameter against voltage will thus be a straight line with
gradient (-1/2).
Apparatus
electron diffraction tube
power supply (6.3 V) for cathode
e.h.t. supply (0 – 5000 V dc) with voltmeter
connecting leads
Great care must be taken to set the tube up correctly. The graphite can be damaged by incorrect
connections. Notice that the positive e.h.t supply terminal is used without the protective resistor in
some set ups. Take care.
As the discussion in this section is almost entirely in terms of electron diffraction, students might get
the idea that only electrons exhibit wave–particle duality whereas in fact it applies to all particles.
You might like to mention that neutron diffraction is also used as a tool for probing material structure.
Large bio-molecules have now been diffracted.
The chosen method is to introduce wave particle duality via the experiment however a little
mathematics may be of use. This mathematics is given so an experimental or theoretical route can
be chosen or the mathematics later used to back up the experiment.
E=hf and since fλ = c then E =hc/λ
Taking E = mc2
then mc2
= hc/λ and so mc = h/λ
momentum = mass x velocity = p =mc
And this gives the de Broglie relation p = h/λ
Do notice that the switch from mc to mv has not been justified other than it works. (Note, this
derivation really only refers to photons and not to electrons).
For the diffraction tube where V is the anode cathode pd and v the electron speed then
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45
½ mv2
= eV so v = (2eV/m) 1/2
giving mv = m (2eV/m) 1/2
= (2meV) 1/2
p = h/λ = (2meV) 1/2
Simplifying the Bragg formula into a two dimensional treatment for a transmission grating,
for diffraction θ = λ/b (approximately) where b is the separation between the planes of
carbon atoms. D, if required, can be obtained from manufacturers details.
θ = d/D from geometry so d/D = λ/b or λ proportional to d as diffracting gap size b and
target screen distance D are constants.
So using the momentum and accelerating pd equation above then
p = h/λ = (2meV) 1/2
or
1/λ is proportional to V1/2
or
λ is proportional to V-1/2
External references
This activity is taken from Salters Horners Advanced Physics, section PRO, activity 18, with extra
material added in the last two sections, adapted from Revised Nuffield Advanced Science Physics
teachers guide, book 2, section L2.
θ
Tube screen
Graphite Target
d
D
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TAP 506-2: Diffraction of light
Apparatus
torch bulb in holder with power supply
diffraction gratings, 2 each of various spacing, e.g. 100 lines mm-1
, 300 lines mm-1
red, blue and green filters (one of each colour)
2 glass slides (e.g. microscope slides)
lycopodium dust
Safety
Lycopodium is dried pollen. Some people are allergic to pollen so, before use, it is wise to check for
hay-fever sufferer. (See Safeguards in the School Lab 4.4). Lycopodium powder in air will explode
so extinguish all flames before using it.
Technique
Observe what happens when light is diffracted by:
• a grating of parallel lines;
• a regular grid of crossed lines;
• a random array of fine dust particles.
Explore the effects of changing the separation of the lines and the wavelength of the light.
Set up a small (6 V) lamp. You are going to observe how light from the lamp is diffracted in different
situations.
Write down or sketch what you observe.
Hold a diffraction grating and a colour filter close to your eye.
Look through it at the lamp. Rotate the grating.
(A diffraction grating consists of many parallel, equally spaced lines, as much as several thousands
in each centimetre.)
Repeat with a finer or a coarser grating (using the same colour filter as before).
Now use two diffraction gratings. Place one on top of the other, so that their lines are at
90 degrees to each other. You have made a grid of lines through which the light is diffracted. Look
through the grid at the lamp.
Try holding the gratings so that their lines cross at a different angle – say, 60° or 45°. Try combining
gratings with different line spacing.
Finally, sprinkle fine dust (e.g. lycopodium powder) on to a glass slide. Blow off any excess dust.
Look through the slide at the lamp.
(Now you are looking at light diffracted by a random array of tiny particles.)
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47
Repeat the above, using a different colour filter.
Sum up your observations by saying how the diffraction patterns depend on:
• the separation of the diffracting objects
• the geometry of the diffracting objects
• the wavelength of the light.
Practical advice
This activity is intended to remind students of diffraction effects they may have previously observed.
Points to bring out are:
• the size of the pattern increases with increasing wavelength (red light is diffracted more
than blue)
• the size of the pattern depends inversely on the spacing of the diffracting objects (the finer
the grating, the more widely spaced the diffraction images)
• the geometry of the diffraction pattern depends on the geometry of the diffracting objects
• a random arrangement of small obstacles gives rise to a diffraction pattern that is a set of
concentric rings.
External reference
This activity is taken from Salters Horners Advanced Physics, section PRO, activity 17
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48
TAP 506-3: Interpreting electron diffraction patterns
For this question to make sense, students need to be aware that an obstacle (e.g. a nucleus) is
equivalent to a ‘hole’ of the same size. So far they have only met diffraction by ‘gaps’.
Use the electron diffraction patterns shown in Figures (a) and (b) to determine the diameters of
carbon and oxygen nuclei.
The diffraction patterns represented by the two graphs in Figures (a) and (b) were obtained using
electrons accelerated to 420 MV.
By following the steps below, you will get a flavour of how such diffraction data are interpreted.
You will also see some of the equations that must be used when electrons are moving at relativistic
speeds (that is, close to the speed of light).
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49
Calculate the kinetic energy Ek of an electron accelerated through 420 MV.
To calculate the momentum of the electron, you cannot use p=mv and EK = ½ mv2
, because these
equations don’t apply to relativistic particles.
Instead, it turns out that the electron’s momentum p is related to its kinetic energy by
Ek ~ pc
where c is the speed of light.
Calculate the momentum of the electron.
The de Broglie relationship
p = hλ
applies to relativistic and non-relativistic electrons because Relativity Theory is used in its
derivation.
Calculate the electron’s de Broglie wavelength.
The angle of the first minimum θmin on the graph is a clearly identifiable point, and this is used to
calculate the diameter of the nuclei.
From the graphs in Figure (a) and (b), determine the angle of the first minimum for carbon nuclei,
and for oxygen nuclei.
The smaller the nucleus, the more it diffracts the electrons.
From the angles you found, which are smaller, carbon nuclei or oxygen nuclei? Is this what you
would expect from their atomic numbers?
The diameter d of the nucleus is related to the electron wavelength and the diffraction angle θmin by
Use this relationship to obtain estimates of the diameters of carbon and oxygen nuclei.
Explain why your answers are only estimates.
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50
External references
This activity is taken from Salters Horners Advanced Physics, section PHM, activity 19 which was
an adaptation of Revised Nuffield Advanced Physics section L question 37(L).
Ek = 420 x 106
x 1.60 x 10-19
= 6.72 x 10-11
J
Ek ~ pc
so p = 6.72 x 10-11
/ 3 x 108
= 2.24 x 10-19
N s
λ = h/p = 6.63 X 10 -34
/ 2.24 x 10-19
. = 2.96 x 10-15
m
(a) carbon nuclei, 50°
(b) oxygen nuclei. 42°
d = 1.22λ
θ min
where d is the diameter of the nucleus
Remember, the angle should be in radians or use sin θ.
(a) carbon d = (1.22 x 2.96 x 10-15
) / 0.766 = 4.7 x 10-15
m
(b) oxygen d = (1.22 x 2.96 x 10-15
) / 0.669 = 5.3 x 10-15
m
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51
TAP 506- 4: Electron diffraction questions
1 In an electron diffraction experiment using graphite the larger ring formed by rows of
carbon atoms 1.23 x 10-10
m apart was formed at an angle of 0.167 radian.
(a) What is the wavelength? [θ in radians = λ / b where b is the diffracting object size]
(b) Write an expression for the kinetic energy of an electron (½ mv2
) in terms of its charge, and
accelerating voltage V
(c) Obtain an expression for momentum, p, in terms of e, V and m.
The accelerating voltage was 5000 V
(d) Work out h in mv = h/ λ
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52
Answers
(a) 0.205 x 10-10
m
(b) KE = 0.5mv2
= Ve
(c) p = mv = (2meV) 1/2
(d) h = 7.78 x 10-34
J s (the accepted value is 6.6 x 10-34
J s)
External reference
This activity is taken from Revised Nuffield Advanced Physics Unit L question 32.
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53
Episode 507: Electron standing waves
You could extend the idea of electrons-as-waves further, to the realm of the atom.
Summary
Demonstration: Melde’s experiment. (20 minutes)
Discussion: Electron waves in atoms. (10 minutes)
Demonstration: Standing waves on a loop. (10 minutes)
Student Question Electron standing waves (10 mins)
Demonstration:
Melde’s experiment
TAP 507-1: Standing waves – for electrons?
In this section we are going to introduce the idea of
standing waves within an atom. It is therefore useful
first to demonstrate standing waves on a stretched
elastic cord. This is known as Melde’s experiment.
(A very simple alternative to the vibration generator
is an electric toothbrush.)
Show that there are only certain frequencies at which standing wave loops occur.
Discussion:
Electron waves in atoms
The waves on the string are 'trapped' between the two fixed points at the ends of the string and
cannot escape.
If the electron has wave properties and it is also confined within an atom we could imagine a sort of
standing wave pattern for these waves rather like the standing waves on a stretched string. The
electrons are 'trapped' within the atom rather like the waves being 'trapped' on a stretched string.
The boundaries of these electron waves would be the potential well formed 'within' the atom.
This idea was introduced because the simple Rutherford
model of the atom had one serious disadvantage
concerning the stability of the orbits. Bohr showed that in
such a model the electrons would spiral into the nucleus in
about 10-10
s, due to electrostatic attraction. He therefore
proposed that the electrons could only exist in certain
states, equivalent to the loops on the vibrating string.
electron
nucleus
L
M
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54
If your students have met the idea of angular momentum, you could tell them that Bohr proposed
that the angular momentum of the electrons in an atom is quantised, in line with Planck's quantum
theory of radiation. He stated that the allowed values of the angular momentum of an electron
would be integral multiples of h/2π. This implied a series of discrete orbits for the electron. We can
imagine the electron as existing as a wave that fits round a given orbit an integral number of times.
Demonstration:
Standing waves on a loop
The wire loop is a two dimensional analogy of electron waves in an atom. As it vibrates at the
correct frequency, an integral number of waves fit round the orbit. These waves represent the
electron waves in an atom.
Student question:
Electron standing waves
de Broglie waves can be imagined as forming standing waves which fit into an atom
TAP 507-2: Electron standing waves
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55
TAP 507-1: Standing waves - for electrons?
Electrons have a frequency too
Electrons can be modelled as having a frequency. In another context you have seen how
superposition of waves in the laboratory produces standing waves. Here it is useful to put these two
together, describing electrons with standing waves, with their wavelength described by de Broglie’s
relationship:
./ mvh=λ
Here you look at some consequences of this step.
You will need:
vibration generator
signal generator
rubber cord
G-clamp
wooden blocks
Vibrating a rubber cord
1
2
3
5
7
8
9
Frequency Adjust
1
10
100
1000
10
100
1000
Frequency range
Outputs
A
power
10Hz 100kHz
1kHz 10kHz100Hz
Frequency
10 Hz
Wave
Make sure that you can get clear patterns with this apparatus. Note that only whole numbers of half
wavelengths fit onto the cord.
Electrons trapped in an atom are also constrained. Describing them as waves, where the amplitude
tells you the chance of find them in any one place, constrains you to draw the waves in a similar
way.
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56
Making links
Putting relationships together with these results allows you to predict that electrons will have certain
allowed energy levels only.
simplest pattern next simplest pattern
L
λ
2
L
λ
2
from kinetic energy Ek =
1
2
mv2
p = mv
Ek =
p2
2m
Ek =
h2
8mL2
from diagrams λ = 2L
from de Broglie λ =
h
mv
mv =
h
λ
mv =
h
2L
λ = L
mv =
h
L
h2
2mL2
2 ? λ and 4 ? Ek
Ek =
See if you can continue the series for the next two standing wave patterns that will fit onto the cord.
You have
1. Reminded yourself about standing waves.
2. Seen some of the consequences of using standing waves to model electrons in atoms.
External reference
This activity is taken from Advancing Physics chapter 17, 140E
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57
TAP 507-2: Electron standing waves
If an electron is confined in a definite space, the de Broglie waves can be imagined as forming
standing waves that fit into that space.
h = 6.6 x 10-34
J s, charge on electron = 1.6 x 10-19
C, mass of electron is 9.1 x 10-31
kg
r = 1.0 × 10–10 m
de Broglie standing wave
diameter 0.2 × 10–10 m
r = 0.1 × 10–10 m
diameter 2.0 × 10–10 m
Suppose the standing wave fits with one half-wavelength across the diameter of the atom.
1. Write down the wavelength of the standing wave if the atom is imagined to have radius
r = 1.0 × 10–10
m.
2. Write down the wavelength of the standing wave if the atom is imagined ten times
smaller, with radius r = 0.1 × 10–10
m.
3. Other standing waves could fit inside the same diameter. Would their wavelengths be
longer or shorter than the waves shown here?
Electron momentum
The momentum of an electron with de Broglie waves of wavelength λ is m v = h / λ. If the
wavelength is the largest possible, the momentum must be the smallest possible.
4. Calculate the smallest possible momentum of the electron, if the atom is imagined to
have radius r = 1.0 × 10–10
m.
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58
5. Calculate, or write down directly from the answer to question 4, the smallest possible
momentum of the electron if the atom is imagined to have radius r = 0.1 × 10–10
m.
6. Write a few lines explaining why an electron confined in a smaller space has a larger
minimum momentum.
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59
1. The waves have half a wavelength fitting into the diameter, so λ = 4.0 × 10–10
m.
2. The radius is 10 times smaller so the wavelength is 10 times shorter: λ = 0.4 × 10–10
m.
3. More half-wavelength loops have to be fitted into the same length, so the wavelengths
will all be smaller.
4.
.smkg1065.1
m104.0
sJ106.6
124
10
34
−−
−
−
×=
×
×
=
=
λ
h
mv
5. As for question 4 with the wavelength 10 times smaller, so the momentum is 10 times
larger: mv = 16.5 × 10–24
kg m s–1
.
6. The smaller the space the shorter the wavelength. But the shorter the wavelength the
greater the momentum, since mv = h / λ.
External reference
This activity is taken from Advancing Physics chapter 17, and uses part of question 160s.
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Episode 508 See Episode 513
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61
Episode 509: Radioactive background and detectors
This episode introduces the ubiquitous nature of radioactivity, and considers its detection. It draws on students’ previous
knowledge, and emphasises the importance of technical terminology.
Summary
Demonstration: Detecting background radiation (10 minutes)
Discussion: Sources of background radiation (15 minutes)
Demonstration: Radioactive dust (10 minutes)
Discussion + survey: Sources of radiation – should we worry? (15 minutes)
Demonstration + discussion: Am-241 source, plus use of correct vocabulary. (10 minutes)
Demonstration: Spark detector (10 minutes)
Demonstration:
Detecting background radiation
Use a Geiger counter to reveal the background radiation in the
laboratory. What is the ‘signal’ like? (It is discrete, erratic / random.)
Does it vary from place to place in the room? (No; it may appear to;
this is an opportunity to discuss the need to make multiple or
longer-term measurements.) Does it vary from time to time? (No, it’s
roughly constant.)
Count for 30 s to get a total count N; repeat several times to show
random variation. Calculate the average value of N.
(Note: a good rule of thumb is that the standard deviation is √Nave,
so roughly two-thirds of values of N will be within ± √Nave.)
Which is better: 10 counts of 30 s, averaged to get the activity, or one count of 300 s? (They amount to the same thing.
The statistics of this is probably beyond most A-level students.)
Calculate the background count rate from the data (typical value is 0.5 counts per second or 30 counts per minute, but
this varies a lot geographically.)
Discussion
Sources of background radiation
Look at charts showing sources of background radiation. Consider how these might vary geographically, with time,
occupation etc.
to scaler/ratemeter
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62
Pie chart for background radiations
Note that pie charts in text books etc showing relative contributions are often calibrated in units of equivalent dose of
radiation called sieverts (symbol Sv); sievert is a unit which takes account of the effects of different types of radiation on
the human body.
1 Sv = 1 J kg-1
= 1 m2
s-2
TAP 509-1: Doses
TAP 509-2: Whole body dose equivalents
Demonstration:
Radioactive dust
Airborne radioactive substances are attracted to traditional computer and TV screens that use a high voltage. Similarly a
‘charged’ balloon will also accumulate radioactive dust and have an activity larger than the average background. The
fresh dust in vacuum cleaner bags has a noticeably higher activity too.
Set up a Geiger counter to measure the activity of vacuum cleaner dust; don’t forget to measure background rate also.
TAP 509-3: Radiation in dust
0.4% fallout
10%
cosmic rays
12% internal
such as food
etc.
12% medical,
X rays etc.
14% gamma rays
from the ground
50% radioactive gases in the home
0.4% air travel
<0.1%
nuclear waste
0.2%
occupational
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Discussion + survey:
Sources of radiation – should we worry?
So “radiation is all around us”. Indeed, most substances, and things, are radioactive. Students are radioactive! Typically
7000 Bq. So “it’s dangerous to sleep with somebody”! However, most of the resulting radiation is absorbed within the
‘owners’ body.
Introduce activity of a sample as a quantity, measured in becquerels (Bq). Mass of typical student = 70 kg, so specific
activity = 7000/70 = 100 Bq kg-1
. The Radiation Protection Division of the Health Protection Agency (formerly the
National Radiological Protection Board, NRPB) defines a radioactive substance as having specific activity ≥ 400 Bq kg-1
.
Should we worry about this? Ask students to complete this survey, and then re-visit at the end of the topic. For each
statement, indicate whether they think it is true or false, or they don’t know.
S1 Radioactive substances make everything near to them radioactive.
S2 Once something has become radioactive, there is nothing you can do about it.
S3 Some radioactive substances are more dangerous than others.
S4 Radioactive means giving off radio-waves.
S5 Saying that a radioactive substance has a half life of three days means any produced now will all be gone
in six days.
Demonstration + discussion:
Am-241 source, plus use of correct vocabulary
Radioactive sources
Follow the local rules for using radioactive sources, in particular do
not handle radioactive sources without a tool or place them in close
proximity to your body.
Place an Am-241 source close to the GM tube and measure the count rate, which will be impressive, compared to
background. (Some end window GM tubes will not detect alpha emission from AM-241 but only weak gamma).
Geiger Muller tube
Radioactive source
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64
From here on, start to use appropriate technical vocabulary, drawing on students’ earlier experience. For example:
Substances are radioactive, they emit ‘radiation’ when they decay. Why are some substances radioactive? (They
contain unstable nuclei inside their respective atoms.) The unstable nucleus is called the mother and when it (she?)
decays a daughter nucleus is produced (it’s not quite like human procreation!).
Eventually the activity of a radioactive substance must cease. However, point out that the decay of the americium
doesn’t seem to be getting any less. There are a very large number of nuclei in there!
Am-241 is used in smoke alarms, so it won’t ‘run out’. They are supplied with 33.3 kBq sources. The half-life is 458 years.
What particular property does nuclear radiation have – what does it do to the matter through which it passes? (It is
ionizing radiation. It creates ions when it interacts with atoms.) What is an ion? (A neutral atom which has lost or gained
(at least one) electron.)
Simplified diagram of a smoke alarm
To knock an electron from an atom, the ionizing radiation transfers energy to the atom – this is how nuclear radiation is
detected. It is not difficult to detect the presence of a single ion – electron pair, so it’s easy to detect the decay of single
radioactive nucleus. Chemists can detect microgrammes or nanogrammes of chemical substances, physicists can
detect individual atomic events.
Demonstration:
Spark detector
Show a spark detector responding to the proximity of an alpha source. (NB At first, do not refer to the source as an alpha
source.) Move the source away a few centimetres; you do not need much distance in air to absorb this radiation. Ask
students to recall which type of radiation is easily absorbed by air. (Alpha.)
Alpha source
Current due to ionisation flows from + to - Current flow stopped by smoke
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65
TAP 509-4: Rays make ions
Comment that a GM tube is not dissimilar to a spark counter, but rolled up to have cylindrical symmetry. At this point, you
could discuss the sophisticated design of a GM tube and associated counter. The end window is usually made of mica
and has a plastic cover, with holes, to protect the mica.
+450 V
0 V
low pressure neon or argon gas
thin end window
anode
radioactive particle
anode
Radioactive source or flame
0 V
+ 5000 V
sparking here
thin wire
gauze
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66
TAP 509-1: Doses
Radiation dose measurements and units
activity in becquerel =
disintegrations per second
Radiation quality factors
alpha
beta
gamma
x-rays
neutrons
20
1
1
1
10
20 Sv
1 Sv
1 Sv
1 Sv
10 Sv
radiation factor dose equivalent
of 1 gray
dose in gray = energy deposited per kg
dose equivalent in sievert = dose in gray × quality factor
energy in different types
of radiation
radiation
source
dose in
gray
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67
Practical advice
This gives a simple view of the connection between gray and sievert as units of radiation dose measurements.
It may be best to change the size of the diagram and use it as an OHT.
External reference
This activity is taken from Advancing Physics chapter 18, display material 20O
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68
TAP 509-2: Whole body dose equivalents
Typicalwholebodydoseequivalentperyearfromvarioussources(Europe)
Artificialsources
530µSv
22%oftotal
Naturalsources
1860µSv
78%oftotalwork9µSv
airtravel8µSv
nuclearpower3µSv
nuclearweaponsfallout10µSv
cosmicandsolarradiation
310µSv
gammaradiationfrom
groundandbuildings
380µSv
radongasfromground
andbuildings800µSvfoodanddrink370µSv
medicalprocedures
500µSv
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69
Practical advice
This shows the breakdown of whole body doses, from different sources.
It may be best to change the size of the diagram and use it as an OHT.
External reference
This activity is taken from Advancing Physics chapter 18, display material 30O.
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70
TAP 509-3: Radiation in dust
Ionisation in the home
Radon gas is present in the atmosphere of our homes; its daughter products can contribute to the background count as
constituents of household dust. In this activity you are asked to collect dust and assess its level of radioactivity.
You will need
two sheets of kitchen paper towel
radiation sensor, alpha sensitive (NB not a standard GM tube)
stop watch
rubber band
What to do
1. Collect some household dust on a sheet of kitchen paper towel. One way to do this is to cover your finger
with the paper and then to wipe your finger over the surface of a dusty television or computer monitor screen. Do this
for the whole screen, more than one screen if possible – you need a substantial layer of dust. Put the paper carefully
to one side. Do not dislodge the dirt. (Incidentally, one reason for suggesting the dust from a television screen is
because it is charged. It therefore attracts the ionised daughter products from, amongst other things, radon decays.)
2. Take a new clean piece of identical kitchen paper. Fix it around the thin window end of the sensor using a
rubber band. Take a background measurement for a substantial time, several thousand seconds or even overnight
if possible. Automating the capture of the data will prove useful.
3. Without changing any other conditions replace the clean paper with the dusty paper. Wrap it around the
GM tube with the dust fingerprint side next to the window so that alpha particles are not absorbed by the paper. Take
care not to get the dust onto the sensor.
4. Measure the radioactive count from the dust for the same length of time as before.
5. Look critically at the results. Are they significantly different? Remember that variation in a radiation experiment
is equal to the square root of the measurement itself. Do the two results differ by substantially more than this?
You have
Measured some of the ambient radiation from a household.
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Practical advice
This experiment needs care but it does yield interesting results. It requires long timings and not a little luck. Household
dust has radioactive products from a number of decays.
In trials a count for 600 s produced the following results: background count (no paper): about 230 counts; background
count (with paper): about 240 counts; dust count: about 295 counts. There was a substantial amount of dust on the paper
from three computer monitors.
The use of TASTRAK plastic is a possible substitute here.
The plastic known as CR-39 was developed in 1933 and in 1978 it was found to be an excellent detector of charged
particles, which could be revealed by etching the plastic. TASTRAK is a version of CR-39 developed specifically to
detect alpha particle tracks. It can be used to demonstrate the detection of radon.
The suppliers, TASL, offer kits of TASTRAK plastic for class use which may then be returned to the Track Analysis
Group for processing free of charge. This arrangement is STRICTLY for UK schools, colleges and universities only.
Track Analysis Systems operate a free etching service. It is not recommended that you attempt the etching process
yourself. When returning the exposed slides, remember to declare whether you require them to be in microscope or slide
projector form.
Be safe
Students should wash their hands before eating after collecting the dust.
External references
This activity is taken from Advancing Physics chapter 18, activity 20H.
You can find more information about TASTRAK from http://www.tasl.co.uk/schools.htm or Track
Analysis Systems Ltd, H H Wills Physics Laboratory, Tyndall Avenue, Bristol. BS8 1TL, U.K.
Tel: +44 (0)117 926 0353, Fax: +44 (0)117 925 172
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72
TAP 509- 4: Rays make ions
The particles and rays that come from radioactive (unstable) nuclei are known generically as ionising radiation. Ionising
radiations do just what their name says – they ionise atoms by removing one or more of the electrons outside the nucleus.
It is this property that helps us to detect the radiations in many of the instruments that may already be familiar to you.
In this activity you will learn to use a simple detector of ionising radiation – the spark detector.
You will need
spark counter
EHT power supply, 0 – 5 kV, dc
leads
almost pure alpha source (The only ‘pure’ alpha source available in schools is Pu-239. Am-241 emits gammas
too. However, since the spark counter only responds to the alphas, any alpha-emitting source will do here)
forceps or tweezers for handling the radioactive source (or source holder)
Ionisation and its effects
First, some ideas about ionisation and its effects.
Ionisation is the name given to the process in which an atom or molecule gains or loses one or more electrons. In the
detection of radioactivity we are normally concerned with the loss of an electron. The mechanism is that radiation is
emitted from an unstable nucleus; the particle or ray carries energy away with it. It is this loss of energy that allows the
radioactive atom to become more stable. As the particle moves away through the air or a more dense substance it
comes close to atoms, sometimes sufficiently close to interact. The particle can simply bounce off the atom – an elastic
collision – or it can interact inelastically and transfer some its energy to the atom. This gain of energy by the atom leads
to the removal of one of its electrons. You can think of the particle or ray as having knocked the electron free of its atom.
Energy taken from the incoming particle or ray is needed for this to occur.
Can you think of examples in which ionisation is used to detect radiation?
Getting going
1. Now, before setting it up, look closely at the spark detector. You should be able to see a grid or array of very fine
wires running parallel and close to the surface of a metal plate or above a wire. There may also be an
arrangement for holding a radioactive source a fixed distance from the wire array. Your power supply will
maintain a high potential difference between the plate and the wires. There will be a large electric field in the
space between the wires and the plate.
Radioactive sources
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73
Wire carefully, EHT supply I use
Although school EHT supplies are
current-limited and safe, using the extra limiting
resister (50 MΩ) reduces the shock current to a
trivial level.
2. Now connect up the detector to the power supply. Ask for help if you are not certain how to do this. To be safe
the wires (the part you are most likely to touch) should be at earth (0 V) potential. Adjust the EHT until sparks
just pass, then reduce it slightly.
3. Insert a source of alpha particles into the holder and ensure that the source is pointing towards the wire
array and about 10 mm from it. Take the usual handling precautions with the source.
+
e.h.t.
–
+ 5 kV0 V
5 kV
0 V
4. Does an increase in the potential difference make a significant change in the sparking rate?
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74
The alpha particles ionise the air molecules as they travel from the source. The sparking is a result of what happens
when the ionisation occurs in the strong electric field produced by the spark detector. Look at the diagram.
The field is directed between the wire and the gauze, or between the wires and the plate. So, once the electron and its
ion (the original atom) are separated, the electron moves towards the wire and the ion moves towards the plate. The ion
has a large mass and so gains speed slowly. The electron, however, has a low mass so its acceleration is large. (You
might want to estimate how large it is: to do this use the distance from wire to plate and the voltage setting to make a
reasonable estimate of the electric field strength, hence the force and the acceleration.)
If an electron can gain enough energy from the field it will be able to collide with another gas atom and cause a further
ionisation. So one electron has now produced two: the original one plus the one from this second ionisation. Both of
these can go on to accelerate and ionise again. The number of electrons in the space builds up rapidly and eventually the
air contains enough electrons in one region to allow a spark to jump from wire to plate. This is known as a cascade
process.
You have seen that
1. Radioactive particles are often detected using ionisation. Examples include the spark detector, the
Geiger–Müller tube, the cloud and bubble chambers, and photographic detection methods.
2. Such methods show us where the particles have caused ionisation. They are not direct detections of the
particles themselves.
3. Some methods rely on a cascade process in which ions are multiplied by successive ionisations in a
strong electric field.
Also try
TAP 519: Particle Detectors
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75
Practical advice
Students may need close supervision in using this apparatus. They will also need guidance in the correct earth setting to
avoid electric shock. The instructions provided in the activity may need to be altered to suit the style of spark detector you
have.
Radioactive sources
Wire carefully, EHT supply in use
Every time your teeth are x-rayed, ionisation processes are used to expose the film. The ubiquitous Geiger–Müller tube
involves a controlled cascade between the central wire and the outer cylinder inside the tube. We rely heavily on the
ionising effects of radiation for its detection.
External reference
This activity is taken from Advancing Physics chapter 18 activity 50E
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76
Episode 510: Properties of radiations
The focus of this episode is the properties of ionizing radiations. It is a good idea to introduce these
through a consideration of safety.
Summary
Discussion: Ionising radiation and health. (10 minutes)
Demonstration: Deflection of beta radiation. (10 minutes)
Student activity: Completing a summary table. (10 minutes)
Student experiment: Inverse square law for gamma radiation. (30 minutes)
Discussion: Safety revisited. (5 minutes)
Discussion:
Ionising radiation and health
Why are radioactive substances hazardous? It is the ionising property of the radiation that makes it
dangerous to living things. Creating ions can stimulate unwanted chemical reactions. If the
radiation has enough energy it can split molecules. Disrupting the function of cells may give rise to
cancer. Absorption of radiation exposes us to the risk of developing cancer.
Thus it is prudent to avoid all unnecessary exposure to ionising radiation. All deliberate exposure
must have a benefit that outweighs the risk.
Radioactive contamination is when you get a radioactive substance on, or inside, your body (by
swallowing it or breathing it in or via a flesh wound). The contaminating material then irradiates you.
How can you handle sources safely in the lab? Point out that you will be safe if you follow your local
rules which will incorporate the following:
• always handle sources with tongs
• point the sources away from your body (and not at any
anybody else)
• fix the source in a holder which is not adjacent to where your
body will be when you take measurements
• replace sources in lead-lined containers as soon as possible
• wash hands when finished
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Radioactive sources
Follow the local rules for using radioactive sources, in particular do not handle radioactive
sources without a tool or place them in close proximity to your body.
Demonstration:
Deflection of beta radiation
Show the deflection of β 
by a magnetic field.
(Make sure you have a small compass to
determine which are the N and S poles of
the magnet.) Is the deflection consistent
with the LH rule? (Yes; need to recall that
electron flow is the opposite of conventional
current.) Why is this demo is no good with
the α source? (α particles are absorbed too
quickly by the air.)
NB The diagram above is common in
textbooks, but is ONLY illustrative. For the
curvature shown of beta particles, the
curvature of the alpha tracks would be
immeasurably small.
Student activity:
Completing a summary table
Display the table, with only the headings and first column completed. Ask for contributions, or set as
a task; compile results.
TAP 510-1: α, β and γ radiation
alpha gamma
betamagnetic field
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78
Can you see any patterns in the table? (Most ionising - the largest electrical charge - is the least
penetrating.) Can you explain this? (The most ionising lose energy the quickest.) How can the
electrical charge determined? Deflection in a magnetic field.)
* NB Gamma radiation is never completely absorbed (unlike alpha and beta) it just gets weaker and
weaker until it cannot be distinguished form the background.
Student experiment:
Inverse square law for gamma radiation
Note: since you are unlikely to have sufficient gamma sources for several groups to work
simultaneously, this experiment can be part of a circus with others in the next episode. Alternatively,
it could be a demonstration.
Gamma radiation obeys an inverse square law in air since absorption is negligible. (Radiation
spreads out over an increasing sphere. Area of a sphere = 4 π r2
, so as r gets larger, intensity will
decrease as 1/r2
. The effect of absorption by the air will be relatively small.
TAP 5102: Range of gamma radiation
(Some students could do an analogue experiment with light, with an LDR or solar cell as a
detector.)
When detecting γ radiation with a Geiger tube
you may like to aim the source into the side of
the tube rather than the window at the end. The
metal wall gives rise to greater ‘secondary
electron emission’ than the window and this
increase the detection efficiency.
Correct readings for background.
How can we get a straight line graph? We
expect I ∝ r-2
, so a plot of I versus r–2
should be
direct proportion (i.e. a straight line through the
origin). It is much easier to see if a graph is a
straight line, rather than a particular curve. Lift
the graph and look along the line – it’s easy to
spot a trend away from linear. However, two points are worth noting: (i) Sealed γ sources do not
radiate in all directions, so do not expect perfect 1/r2
behaviour, and (ii) you do not know exactly
name symbol nature
elec
charge
"stopped by"
ionising
"power"
what is it?
alpha α particle +2
mm air;
paper
very good He nucleus
beta β particle -1 mm Al medium
very fast
electron
gamma γ wave 0 cm Pb * relatively poor
electromagnetic
radiation
to scaler/ratemeter
Radioactive source
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79
where in the Geiger tube the detection is taking place, so plotting I-1/2
against r gives an intercept,
the systematic error in the measurement.
Discussion:
Safety revisited
Return briefly to the subject of safe working. Background radiation is, say, 30 counts per minute.
How far from a gamma source do you have to be for the radiation level to be twice this? Would this
be a safe working distance? (Probably.) How much has your lifetime dose of radiation been
increased by an experiment like the above? (Perhaps one hour at double the background radiation
level – a tiny increase. It will be safe enough to carry out a few more experiments.)
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TAP 510-1: α, β and γ radiation
Using your knowledge from pre-16 level work, or using information from textbooks, draw up a table
to summarise the properties of α, β and γ radiation.
The table below provides a framework for your summary. Write items from the following list into
appropriate cells of the table. Note that some of the items are not needed and some may be used
more than once.
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81
Practical Advice
Some text books may be needed.
External reference
This activity is taken from Salters Horners Advanced Physics, section DIG, activity 25
INDEX

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