Particles and Waves
Particles and Waves
This section will last for 40 hours , covering 7 areas.
The Standard Model , Forces on charged particles , Nuclear Reactions , Wave Particle Duality , Interference
and Diffraction , Refraction of light and Spectra
The course is outlined in more detail later . Each area is divided into subsections . You can use this
information to check your understanding. The statements are broad therefore it is essential that
you read your summary sheets and keep all your work up to date throughout the course.
Assessment
A 40 minute NAB must be passed . This will cover knowledge and understanding and test your skills ;
Outcome 1
Demonstrate and apply knowledge and understanding of subatomic physics and waves
Performance Criteria
(a) Make accurate statements about subatomic physics and waves facts, concepts and relationships.
(b) Use relationships to solve subatomic physics and waves problems.
(c) Use knowledge of subatomic physics and waves to explain observations and phenomena.
Outcome 2
Demonstrate skills of scientific experimentation, investigation and analysis in the field of subatomic
physics and waves
Performance Criteria
(a) Use a range of data-handling skills in a scientific context.
(b) Use a range of skills related to experimental design.
(c) Use a range of skills related to the evaluation of scientific evidence.
For Outcome 2, PC(a), candidates are required to demonstrate that they can use a range of datahandling skills. These skills include selecting, processing and presenting information. Information can
be presented in a number of formats including: line graphs, scatter graphs, bar and pie charts,
tables, diagrams and text.
For Outcome 2, PC(b), candidates are required to demonstrate they can use a range of skills
associated with experimental design. These skills include planning, designing and evaluating
experimental procedures.
For Outcome 2, PC(c), candidates are required to demonstrate they can use a range of skills
associated with the evaluation of scientific evidence. These skills include drawing valid conclusions
and making predictions.
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Particles and Waves
The 7 key areas in which the skills and knowledge and understanding are developed are outlined
below. For each key area a broad outline of the key facts is given, this is what you will be examined
on.
1 The Standard Model
a) Orders of magnitude.
The range of orders of magnitude of length from the very small (sub-nuclear) to the very
large (distance to furthest known celestial objects).

b) The Standard Model of Fundamental Particles and Interactions.






The evidence for the sub-nuclear particles and the existence of antimatter.
Fermions, the matter particles, consist of Quarks (6 types) and Leptons (Electron, Muon and
Tau, together with their neutrinos).
Hadrons are composite particles made of Quarks.
Baryons are made of three Quarks and Mesons are made of two Quarks.
The force mediating particles are bosons (Photons, W and Z Bosons, and Gluons).
Description of beta decay as the first evidence for the neutrino.
2 Forces on charged particles
a) Electric fields around charged particles and between parallel plates.

Examples of electric field patterns include single point charges, systems of two point charges
and the field between parallel plates. No calculation of electric field strength required.
b) Movement of charge in an electric field, p.d. and work, electrical energy.


The relationship between potential difference, work and charge gives the definition of the
volt.
Calculating the speed of a charged particle accelerated in an electric field.
c) Charged particles in a magnetic field.


A moving charge produces a magnetic field.
The direction of the force on a charged particle moving in a magnetic field should be
described for negative and positive charges (right hand rule for negative charges). No
calculations required.
d) Particle accelerators

2
Basic operation of particle accelerators in terms of acceleration, deflection and collision of
charged particles.
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3 Nuclear Reactions
a) Fission and fusion.
 Nuclear equations to describe radioactive decay and fission and fusion reactions.
 Mass and energy equivalence, including calculations.
 Coolant and containment issues in nuclear fusion reactors.
4 Wave Particle Duality
a) The photoelectric effect and wave particle duality.





Photoelectric effect as evidence for the particulate nature of light.
Photons of sufficient energy can eject electrons from the surface of materials.
The threshold frequency is the minimum frequency of a photon required for photoemission.
The work function is the minimum energy required to cause photoemission.
The maximum kinetic energy of photoelectrons can be determined.
5 Interference and diffraction
a) Conditions for constructive and destructive interference.

Coherent waves have a constant phase relationship and have the same frequency, wavelength
and velocity.
b) Interference of waves using two coherent sources.




Constructive and destructive interference in terms of phase between two waves.
Maxima and minima are produced when the path difference between waves is a whole number
of wavelengths or an odd number of half wavelengths respectively.
Investigations which lead to the relationship between the wavelength,
distance between the sources, distance from the sources and the spacing between maxima or
minima.
c) Gratings



Monochromatic light can be used with a grating to investigate the relationship between the
grating spacing, wavelength and angle to the maxima.
A white light source may be used with a grating to produce spectra.
Compare the spectra produced by gratings and prisms.
6 Refraction of light
a) Refraction.
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Particles and Waves





Refractive index of a material as the ratio of the sine of angle of incidence in vacuum (air) to
the sine of angle of refraction in the material.
Refractive index of air treated as the same as that of a vacuum.
Investigations should include situations where light travels from a more dense to a less dense
substance.
Refractive index as the ratio of speed of light in vacuum (air) to the speed in the material.
Also as the ratio of the wavelengths.
Variation of refractive index with frequency.
b) Critical angle and total internal reflection
 Investigating total internal reflection, including critical angle and its relationship with
refractive index.
7 Spectra
a) Irradiance and the inverse square law.
 Investigating irradiance as a function of distance from a point light source.
 Irradiance as power per Unit area.
b)









4
Line and continuous emission spectra,
Absorption spectra and energy level transitions
The Bohr model of the atom.
Electrons can be excited to higher energy levels by an input of energy.
Ionisation level is the level at which an electron is free from the atom.
Zero potential energy is defined as equal to that of the ionisation
level, implying that other energy levels have negative values.
The lowest energy level is the ground state.
A photon is emitted when an electron moves to a lower energy level and its frequency depends
on the difference in energy levels.
Planck‘s constant is the constant of proportionality.
Absorption lines in the spectrum of sunlight as evidence for the composition of the Sun
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Particles and Waves
Waves
A wave allows energy to be transferred from one point to another without any particles of the
medium travelling that distance: e.g. Consider the water waves below:
A
B
Energy is transferred from points A to B where the boat feels the effect but the water does not
move this distance. The energy in Radio and TV Waves (and all other members of the
Electromagnetic Spectrum) are also transferred via this method though they do not require a
medium.
Transverse Waves
A transverse wave is one in which the particles vibrate at 90o to the direction of motion of the
energy.
Amplitude (m)
crest

y
a
z
time (s)
x
a
trough
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Particles and Waves
The particles of the medium vibrate along the direction X to Y whereas the energy is transferred
along X - Z
The wavelength is the distance between similar points on adjacent waves eg. peak to peak (measured
in metres - m)
The frequency is the number of waves that pass a point in 1 second and is measured in Hertz - Hz.
The amplitude is the distance from the line of zero amplitude to a peak or trough (A), this gives an
indication of the amount of energy transferred.
The speed of a wave can be calculated via 2 equations:
v = d/t
and v = f.
The PERIOD of a wave motion is the time for 1 wavelength to pass a point. As the frequency is the
number of waves that pass a point in 1 sec then the period, T, must equal 1/frequency.
T = 1/f
Example
Light of wavelength 4.5 x 10-7 m is reflected off a mirror. Calculate:
(a)
the frequency of the light
(6.67 x 1014 Hz)
(b)
the Period of the wave motion and
(1.5 x 10-15 s)
(c)
the time it takes the light to travel 1.5m
(5 x 10-9 s)
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Wave Properties
Any wave motion can be REFLECTED e.g. light signals travelling down a Fibre Optic cable via total
internal reflection but particles can also be reflected eg. a ball bouncing on a road.
All wave motions can be REFRACTED eg. light waves being focused onto the retina of an eye by a
lens but particles can also be refracted e.g. a car travelling along the road shown below will change
speed and direction when the wheels enter the mud.
AIR
GLASS
TAR
MUD
MOTION
Diffraction in waves can be illustrated by radio signals ‘bending’ into a valley yet particles can also
exhibit diffraction.
When two or more COHERENT waves (same frequency, amplitude and phase difference remaining
constant) overlap the phenomenon of INTERFERENCE is observed. It is extremely difficult to get 2
Coherent waves from 2 sources therefore a single source is used to split the waves up as shown:
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Particles and Waves
We looked at two cases of interference: CONSTRUCTIVE and DESTRUCTIVE interference. For
constructive interference to take place the waves must be Coherent and in Phase i.e. If we consider
2 coherent sources A and B then a crest from A arrives at exactly the same time as a crest from B
and similarly 2 troughs arrive together:
CONSTRUCTIVE INTERFERENCE
Two waves of equal amplitude
arriving in phase at the same
point
in
space.
Result
is
constructive interference.
DESTRUCTIVE INTERFERENCE
Two waves of equal amplitude
A
arriving
completely
out
of
phase at the same point in
B
space. Result is destructive
interference.
For destructive interference the waves are 180o out of phase i.e. a crest from A arrives at the same
time as a trough from B and vice-versa. The two waves cancel each other out and the resultant is a
dark band (no light).
In all cases, the displacements from the equilibrium line of each wave is added to give the
displacement of the resultant wave, bearing in mind that displacement is a vector (so direction
is very important). Destructive interference is the ‘test for a wave motion’ .
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Particles and Waves
Young’s Slits
If light (or any other type of wave) from a single
source is split to produce two sources whose waves
meet again at a screen, then an interference pattern
Screen
will be seen. If the two paths are of exactly the
same length (i.e. at the centre-point of the screen)
then constructive interference will occur and a
Path 1
Path 2
bright spot will be seen. However, as we move away
from the centre-point of the screen the path lengths
become different. Generally,
path difference = m  for maxima (bright spots,
Double slit
constructive interference)
path difference = (m + ½)  for minima (dark spots,
Source
destructive interference)
where n is an integer.
This is the pattern that will appear on
the screen in the diagram above. The
maxima (bright region) in the centre
zeroth order
is called the zeroth order maximum,
first order
second order
third order
third order
second order
first order
and each one removed from this is the
first, second, third, etc. Dark regions
are called minima.
When we use light (or any other electromagnetic radiation) that is monochromatic, i.e. of one colour,
it has the same frequency and wavelength throughout.
No particles can exhibit DESTRUCTIVE interference and so this is the test for a wave motion.
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Particles and Waves
Applications
1)
Some cars are fitted with a microcomputer and speakers that emit sounds 180o
out of phase with the road/engine noise so canceling them out and making the inside
of the car extremely quiet.
2)
Holograms are basically interference patterns formed from a reference beam and
reflected beam.
Reference beam
Laser
3)
photo plate
Some birds’ feathers cause white light to be reflected and as some of the colours are out
of phase destructive interference occurs and the feathers appear to be coloured.
4)
A thin film gives reflection at both surfaces and
destructive interference occurs for some
wavelengths and so the remaining spectrum is seen.
This is commonly seen in soap bubbles and a layer of
petrol lying on a puddle.
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Particles and Waves
5)
Radio/T.V. Waves can be reflected off passing aircraft to a house antenna and thus
cause a flicker on the screen.
Radio/ TV transmitter
PATH DIFFERENCE
X
A
B
Consider the 2 coherent wave sources A and B, the waves meet at point X , obviously the waves from
B travel a greater distance than those from A i.e. BX > AX.
The difference between the two
BX - AX is called the path difference (p.d.)
For constructive interference the p.d. must be a whole number of wavelengths and for destructive
interference the p.d. = a half of no. of wavelengths:
for MAXIMA p.d. = m 
m = 0,1,2,3……
for MINIMA p.d. = (m + 0.5) 
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Particles and Waves
Example
The two loudspeakers A and B, 1 m apart are connected to an oscillator of frequency 1700 Hz. A
microphone is moved along the line RT and the first maxima is detected at T, 0.5 m from S. Calculate
the speed of sound. (340 m/s)
R
A
1.0m
1700 Hz
S
B
T
2.4m
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Diffraction Grating
A DIFFRACTION GRATING is a large number of close parallel equidistant slits ruled on glass or
metal. Typically the spacing, d, between each slit is of the order 1 x 10-6 m or of the same order as
the wavelength as visible light.
If monochromatic light is shone onto a diffraction grating then the pattern below is obtained:
ie. a Principal maximum is obtained with less intense maxima either side of it. As the number of slits
is increased the maxima become sharper. The maxima either side of the principal are called 1st
order, 2nd order, 3rd order maxima..........
(A C.D. acts as a diffraction grating when white light is shone onto it and it splits the light up into its
spectrum)
The maxima are caused by constructive interference and the minima result from destructive
interference.
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Particles and Waves
Directly opposite the grating there will be a bright central maximum since the path difference is the
same for all the waves ie. constructive interference .
At some angle  each wave is ahead of the next by 1 wavelength and so if these waves are brought
together constructive interference occurs and a bright maxima is formed.
For the 1st order maxima light from slit 1 travels 1 wavelength further than that from slit 2 and so
on for slits 3, 4, 5.........
X
bc = 
Y
de = 2 
fg = 3 
a
Angle bca = 900
Side ab = d ( slit
spacing )
Angle cab =
c
b
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Particles and Waves
At other angles destructive interference takes place and dark bands (minima) are formed
Suppose aX and bY represent 2 diffracted rays then we can see that the path difference (p.d)
between them is represented by bC.
Look at the right angled triangle acb and you can see that the length bc = d.sin 
(sin  = bc/d)
For constructive interference the p.d. = m
ie. m 
= d.sin
 = wavelength of light (m)
d = slit separation (m)
m = order of spectra
 = Angle of diffraction of light rays (degrees)
Example
Calculate the angle between the 1st order maxima on either side of the principal when violet light of
wavelength 410 nm is shone onto a grating with 1.0 x 104 slits per cm. ( = 48.4o)
Calculate the maximum order of interference pattern viewed. (2nd)
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Particles and Waves
Dispersion of White Light
White light is made up from a complete mixture of the various colours of the spectrum ie.
red
prism
screen
grating
white light
violet
red
violet
white light
O
Y
G
B
I
violet
red
Central maxima,
undeviated white
light.
This splitting of white light into its spectrum is called DISPERSION and takes place as the different
frequencies of light are refracted by different amounts at the air/glass and glass/air boundaries.
Colour of light
Red
Orange
Yellow
Green
Blue
Violet
Wavelength (nm) 1nm = 1 x 10-9m
660
610
580
550
470
410
If a diffraction grating is used to split the white light up the spectrum is still obtained but the
colours are ‘swapped’ around as shown above. We can see that the red end of the spectrum is
diffracted more than the blue end whereas the reverse is true of the prism, ie. the blue end is
refracted more than the red end.
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Particles and Waves
Refraction of Light
Another example of dispersion occurs in Rainbows, in which refraction by water droplets give rise to
colours. Rainbows are often seen when a storm is departing, if we look at the departing rain with the
sun at our backs. When white light enters a spherical raindrop as shown below, light of each colour is
refracted by different amounts. The light is reflected of the back surface of the drop and
refracted again as it passes into the air again. Although each water drop disperses the light into its
full spectrum we only see one colour from each drop since the one colour of light travels in the
correct direction for our eye to see it. Of course we see all the colours as there are millions of
drops of water at different elevations .
sunlight
Violet
Red
When a light ray leaves water and enters air it is REFRACTED. This makes the pond look shallower
than normal ie.
To eye
A
Light rays from the fish travel to the surface where refraction occurs and the light is bent away
from the normal. When these light rays enter the eye they appear to come from point A. ie. at a
point actually above the real position, this is called a VIRTUAL image.
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Particles and Waves
Expts. have shown that when light passes from one medium to another it is refracted ie.
it
changes speed
Light travels at 3 x 108 m s-1 in a vacuum and for our purposes we assume it travels at this speed in
air (note that nothing with mass can travel faster than this) and so when the light enters eg. glass it
slows up and bends towards the normal. On leaving the glass the light speeds up again and bends
away from the normal.
Our expts. have shown that:
sin i / sin r = a constant
This constant is called the ABSOLUTE REFRACTIVE INDEX
ie. sin i / sin r = n1
The subscript 1 refers to the material e.g. ng is the refractive index for light passing from
air/vacuum into glass.
ng can also be expressed as (speed of in air/speed in glass)
thus ng = sin i / sin r = vo/vg
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Particles and Waves
Frequency and Refraction
We know that different colours of light are refracted by different amounts and so we can see that
the refractive index of a material depends on the frequency of light used. We also know that
different colours of light have different frequencies and so we should really quote frequency when
talking about refractive indices.
Colour
Frequency (x 1014 Hz)
Refractive Index (Diamond)
Red
Orange
Yellow
Green
Blue
Violet
4.54
4.92
5.17
5.45
6.38
7.32
2.410
2.415
2.417
2.426
2.444
2.458
Air
Glass
glass
air
As can be seen the waves are refracted at the boundary. The frequency of the waves cannot change
(no of waves generated per second ) and so the wavelength does.
Example
A beam of infra-red radiation of wavelength 1.2 x 10-6m travelling through air enters glass at an
angle of 300 to the normal and is refracted such that angle r = 210. Calculate:
(a)
the wavelength of the radiation inside the glass (8.6 x 10-7m).
(b)
the speed of the radiation inside the glass (2.15 x 108m).
(c)
the refractive index for the material (1.4).
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Particles and Waves
More Refraction
We can show that the following relationship holds:
sin i v1 1


sin r v2 2
for light travelling from medium 1 to medium 2. The relationships still holds even though the wave
motion is not travelling to/from air (vacuum).
1
2
normal
1
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2
Particles and Waves
Example
Light is refracted at a Perspex/water boundary. Calculate the angle of incidence in Perspex for a
ray of light giving an angle of refraction of 40o in water. (Remember that the absolute refractive
index is the ratio of the speed in air divided by the speed in the material. USE THIS IDEA TO
WORK OUT A REFRACTIVE INDEX GOING FROM PERSPEX TO WATER.)
np = 1.5
nw = 1.33
(34.7o)
Total Internal Reflection
In S.Grade we learnt how total internal reflection could be used to transmit digital laser signals down
a fibre optic cable. We learnt that the angle of incidence must be above some critical angle for this
to occur.
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Particles and Waves
When a light ray approaches the boundary between two media from the side with the higher
refractive index a number of things can happen at the boundary.

Firstly, if the incident ray approaches at an angle less than the critical angle it will be
refracted away from the normal line at the boundary, and there will be a weakly reflected ray.

With incidence at the critical angle the refracted angle is 90º, i.e. the refracted ray is
refracted along the boundary.

At incident angles greater than the critical angle all of the ray is totally internally reflected
and no light emerges from the right hand side of the block.
The Critical Angle C
boundary
From the relationship n =
sin  1
sin  2
=
sin90 0
sin c
n =
1
sin  c
c
medium
(n > 1)
air
At critical angle  the ray of light is refracted at 90o to the normal.
For light travelling from the medium to the air we can write:
sin i/ sin r = sin  / sin 90 = pa
but 1/ p = pa
therefore sin  / sin 90 = 1 / p and since sin 90 = 1
sin  = 1/ p
i.e. the inverse of the absolute refractive index = sin of the critical angle
this is normally written as
Example
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p = 1 / sin
Particles and Waves
The refractive index for diamond is 2.41. Calculate the critical angle.
(24.6o)
Applications
(1)
Prism Binoculars use total internal reflection as shown,
The angle of incidence = 45o which is greater
than the critical angle and so total
internal reflection occurs.
2)
The red rear reflectors on cars employ total internal reflection as shown
surface of rear reflector
light from car behind
bulb
total internal reflection of light
This shape of lens also ensures that the light from the rear bulb is refracted to the side
hence reducing the risk of dazzle to the driver behind.
Irradiance
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Particles and Waves
When an object is illuminated it is receiving LIGHT ENERGY. The IRRADIANCE at a surface on
which radiation is incident is defined as the power per unit area. Or in other words:
The amount of light energy per second falling on 1 square metre of the surface. Since energy
per second is POWER then the units of irradiance:
watts per square metre (Wm-2)
I
P
A
Irradiance 
Power
Area
The Inverse Square Law
The Irradiance on a surface obviously depends on the distance from the source (think of a spray can)
and the expt below was carried out to determine the relationship.
0 1
lamp
metre stick
photo-diode
When light shines on the reverse biased photo diode the current that flows is directly proportional
to the irradiance.
If a plot of I against d is plotted the relationship is not apparent.
Current (I)
0
Current (I)
d
0
1/d2
however a plot of I against 1/d2 gives a straight line through the origin.
ie. Current is inversely proportional to distance squared.
Remember that the Irradiance is directly proportional to the current and so we can write:
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Particles and Waves
Irradiance
I
k
d2

1 / distance
2
where k is a constant
This is an example of the Inverse square law and only applies to POINT SOURCES (for our
purposes the lamp was a point source)
Example
The Irradiance falling on a plate 2m from a point source is 10 W m-2. Calculate the irradiance of the
radiation falling on a plate 4 m from the source. (2.5 W m-2)
Ex 2
The Irradiance from the sun is c.a. 0.2 kW m-2 in Scotland (on a good day!). Calculate how much
energy is absorbed by a solar panel of cross sectional area 100 m2 over a period of 10 minutes. What
is the Power output of the cell if it is 10% efficient (12000 kJ, 2 kW)
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Particles and Waves
The Bohr Atom
We shall use a simple model of the atom in which the nucleus contains the protons and neutrons and
the electrons are outside the nucleus. The electrons occupy discrete energy levels i.e. the
energy levels are quantised. (this is for free atoms only).
Structure of a free atom
electron orbits
ionisation - free electron 0 J
- 1.36 x 10-19 J
- 2.42 x 10-19 J
nucleus
- 5.45 x 10 -19 J
- 21.8 x 10-19 J
electron orbit diagram
Ground
state
energy level diagram
Remember that the electrons have discrete energies only and they do not have in between values.
The ionization energy is defined as the energy needed to free the electron from the electrostatic
attraction of the nucleus. The electron has zero electrical potential energy at this point hence the
‘other electron energy levels’ are taken to be negative.
We shall now use this model to explain emission and absorption spectroscopy.
Emission Spectra
When light is given off from a light source it is split into its different colours by a prism or
diffraction grating and forms a spectrum called an emission spectrum.
Emission spectra can either be continuous or a line spectra. Line spectra are formed when low
pressure gases are excited eg. gas discharge lamps. Continuous spectrum are formed when high
pressure gases are excited or when objects are heated up eg. the SUN.
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Line Spectra
The electrons in an atom are normally in the ground state but if eg. an electric current is passed
through the sample then the electrons are excited to higher energy levels. The electrons fall back
down to the ground state emitting this excess energy in the form of electromagnetic radiation.
E3
E2+
+ energy
E1
Ground state
This energy is emitted as a photon of electromagnetic radiation. The energy of one photon of
electromagnetic radiation is given by :
E = h.f
Where h = Plank’s constant , 6.63 x10-34 Js
f = frequency of light emitted and
E = energy gap between excited and lower energy level.
For the above case 1 photon was emitted when the electron fell from E3 to E1. If however the
electron fell from level E3 to E2 then from E2 to E1 2 different photons of light would have been
emitted as the energy gaps are different N.B. not all the possible transition are ‘allowed’ and the
laws of Quantum Physics explain which are forbidden.
As the electrons occupy discrete energy levels then the frequencies of the light emitted will also be
discrete ie. the spectrum will consist of a series of lines of different frequencies. The line spectrum
of Mercury is shown below:
violet
blue
green
yellow
438 nm
490 nm
545 nm
575 + 580 nm
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Particles and Waves
Not all the lines have the same intensity indicating that some transitions are more favourable than
others but the spectrum is unique to Mercury and is such can be used as a finger print for the
element.
Example
Calculate the energy gap responsible for the violet line in the mercury spectrum.
E = hf
f = v/
3x10 8
f 
 6.85 x1014 Hz
9
438 x10
E  hf  6.63x10 34 x6.85x1014  4.54 x10 19 J
Try another one yourself your answer should be in the order of 10-19 J.
Continuous spectra
In a solid, liquid or high pressure gas, the atoms are much closer together than in a low pressure gas.
( Think back to the band theory of solids )Therefore the electrons experience forces from various
atoms and so some of the energy bands get smeared out and so the spectrum does not consist of
discrete lines but a continuous band of colour.
28 Physics/DS/BMN
Particles and Waves
Absorption Spectra
White light emitted by a hot source produces a continuous spectrum when viewed through a
spectroscope. If the white light is passed through a gas before entering the spectroscope then dark
lines are observed on the spectrum. These dark lines correspond to the same frequency as the
emission spectrum of the gas.
The white light is made up of all the different frequencies of light and when it passes through the
gas photons of a specific energy can excite the electrons to a higher energy level. If these photons
are used to excite the electrons then they must be missing from the spectrum after it has passed
through the gas and so dark lines are observed.
Once the electrons are excited to the higher, less stable state they fall back to the ground state
and emit light of specific frequency. This light is radiated in all directions so the amount of light
reaching the spectroscope (the re-radiated light) is very small and the dark bands are visible i.e.
E3
E2
E1
grating
collimator
source
sodium
flame
Physics/DS/BMN
spectrum
29
Particles and Waves
The sun is like a giant nuclear reactor in which fusion reactions take place i.e. 2 small atoms join
together to form a larger atom. One of the reactions taking place is:
2
H
1
2
+
3
1
He + n
2
0
H
1
Deuterium
Helium
+
energy
neutron
ie. helium is produced in the sun.
If we look at the spectrum of sunlight we can see dark lines corresponding to the line spectrum of
helium. (called Fraunhofer Lines). Astrophysicists use this technique to estimate the age of stars as
different nuclear reactions take place at different stages during a star’s life and so the age of the
star can be estimated.
30 Physics/DS/BMN
Particles and Waves
Photoelectric Emission
We have previously said that light was a WAVE MOTION citing YOUNG’S double slit experiment as
evidence. However there is a lot of evidence that cannot be explained by regarding light as a wave
motion notably the photoelectric effect.
UV lamp
visible lamp
Hol
es
mo
ve
metal plate, e.g. zinc
insulator
acr
oss
to p
gold leaf
typ
electroscope
e- (negatively
and
charged)
elec
electrons
tron
s
mo
ve
acr
oss
The electroscope measure the potential
to n difference between the plate and earth, the bigger the
deflection the bigger the p.d.
typ
e
When ultra violet radiation is shone onto the negatively charged zinc plate the leaf of the
electroscope falls indicating that the plate has discharged. The same expt but with a positively
charged plate reveals that the electroscope does not fall thus precluding the obvious explanation
that the air around the electroscope has been ionised. Similar expts with electromagnetic radiation
of lower frequency fail to discharge the plate no matter the irradiance and if a higher irradiance
source of ultra violet is used the electroscope discharges even faster!
This evidence suggests that the ultra violet radiation can eject electrons from the zinc plate making
it positive. The electrons from the electroscope flow up to the zinc plate discharging it. These
ejected electrons are called photoelectric electrons and a flow of them a photoelectric current.
Physics/DS/BMN
31
Particles and Waves
The fact that low frequency radiations did not eject electrons suggests that there is a threshold
frequency below which no photoelectrons will be emitted. Different metals have different threshold
frequencies:
Photoelectric current(mA )
kinetic energy of photoelectron (J )
Caesium
Potassium
Beryllium
I (Wm-2)
0
0
f(Hz)
Wave Particle Duality
In 1902 it was discovered that the kinetic energy of the ejected photoelectrons was independent of
the Irradiance of the radiation but it did vary with the frequency.
If we assume light to be a wave motion then the greater the Irradiance then the greater the energy
per second reaches the metal plate and so more electrons will be ejected but this theory cannot
explain why there is a minimum threshold frequency for the various metals.
However Max Plank showed that electromagnetic radiation could be explained on the basis that
energy is emitted in ‘discrete quantities’ called Quanta and that the energy of 1 quantum of radiation
is
Energy = plank’s constant x frequency
E = h.f.
E = energy (J)
f = Frequency
h = plank’s constant
= 6.63 x 10-34 Js
Einstein then suggested that the photoelectric effect could be explained by applying this Quantum
theory. He assumed that light (electromagnetic radiation) of frequency, f, contains quanta of
energy = h.f.
ie. light can be considered to have particle behaviour and these particles are called photons.
The energy of these photons is proportional to the frequency of the radiation and the number of
photons is proportional to the Irradiance ie.
I = N.h.f
Irradiance = no of photons x plank’s constant x frequency
32 Physics/DS/BMN
Particles and Waves
1 photon can eject 1 electron from the metal and to do so must have a minimum amount of energy
hence the threshold frequency. 2 photons would eject 2 electrons and so on. If the photon has
insufficient energy then no matter how many are fired at the metal then no electrons will be ejected.
Interest only
Photons of light have zero rest mass . This means that a photon of light does not exist unless it is
moving.
Electrons also exhibit wave particle duality e.g. electron diffraction patterns can be obtained as well
as the use of electrons in electron microscopes. In fact all particles exhibit wave properties but it is
only significant for small fast moving particles.
Photoemission of electrons
The photoelectrons are ejected with a maximum kinetic energy, Ek, given by
Ek = h.f. - h.fo f = frequency of radiation
fo = threshold frequency
h.fo = Work Function
This is applying the conservation of energy principle.
Example
Sodium metal has a threshold frequency of 4.8 x 1014 Hz.
Calculate the maximum kinetic energy of the ejected photoelectron and its velocity when the incident
radiation has a wavelength of 150 nm.
(1.0 x 10-18 J, 1.5 x 106 m s-1) mass of electron = 9.1 x 10-31kg.
Orders of magnitude
Physics/DS/BMN
33
Particles and Waves
What are the extremes of scale from the size of the universe to the smallest particles we
have found so far? We have to use scientific notation to describe these extremes. Powers of
10 are referred to as orders of magnitude, i.e. something a thousand times larger is three
orders of magnitude bigger. ( 10 3 ) Numbers alone, however, can make it difficult to get a
sense of how scale changes.
Follow what happens when we start from 1 metre and progress through seven orders of
magnitude:
10 0
m
10 1
m
10 2
m
10 3
m
10 4
m
10 5
m
10 6
m
10 7
m
Human scale – the average British person is
1.69 m
The height of a house
The diameter of a city square, like George
Square, Glasgow
The length of an average street
The diameter of a small city like Perth
Distance between Aberdeen and Aviemore or
Stirling and Ayr
Length of Great Britain
Diameter of Earth
This id for info only
34 Physics/DS/BMN
Particles and Waves
If we now look to the very small and very big :
Size
Powers of 10
10 –18 m
1 fm (femto)
1 pm (pico)
1Å (Angstrom)
1 nm (nano)
10 –15 m
10 –14 m
10 –12 m
10 –10 m
10 –9 m
10 –8 m
10 –7 m
1 μm (micro)
10 –6 m
10 –5 m
10 –4 m
1 mm (milli)
1 cm (centi)
1m
1 km (kilo)
10 –3 m
10 –2 m
10 –1 m
10 0 m
10 3 m
10 4 m
1 Mm (mega)
10 5 m
10 6 m
1 Gm (giga)
10 9 m
1 Tm (tera)
10 12 m
10 21 m
10 23 m
10 29 m
Physics/DS/BMN
Examples
Size of an electron
Size of a quark
Size of a proton
Atomic nucleus
Atom
Glucose
DNA
Antibody
Haemoglobin
Wavelength of visible light
Virus
Lyosome
Red blood cell
Width of a human hair
Grain of salt
Width of a credit card
Diameter of a shirt button
Diameter of a DVD
Height of door handle
Central span of the Forth Road Bridge
Typical altitude of an airliner,
diameter of Large Hadron Collider,
CERN
Height of the atmosphere
Length of Great Britain
Moon’s orbit around the Earth,
The farthest any person has travelled.
Diameter of the Sun.
Orbit of Jupiter around the Sun
Diameter of our galaxy
Distance to the Andromeda galaxy
Distance to the edge of the observable
universe
35
Particles and Waves
Fundamental Particles
The ancient Greeks believed that everything was made from a few basic ‘elements’ : Earth, air, fire
and water. A little later this was refined to everything is made from atoms ( meaning indivisible ), we
now know that atoms are made from protons , neutrons and electrons. Electrons are fundamental
particles but protons and neutrons are made from quarks. The big question : Are electrons and
quarks fundamental particles or as we get more advanced will we find that they are made from
smaller particles ?
Remember most of the atom is made up of empty space, 99%.
Structure
Atom
Nucleus
Scale ( m )
10-10
10-14
36 Physics/DS/BMN
Proton/ electron/
neutron
10-15
Quark
10-18
Particles and Waves
Rutherford Scattering Expt
Up until 1909 the atom was viewed as being like a plum pudding with electrons and protons
distributed throughout it. Rutherford carried out the first experiment in which an alpha particle was
fired at gold leaf. Well it was actually his assistants Geiger and Marsden who did the donkey work.
This was carried in a vacuum so that the alpha particles were not absorbed by air. Geiger and
Marsden had the tedious job of counting scintillations of light each time an alpha particle was
detected.
The main results of this experiment were:


Most of the alpha particles passed straight through the foil, with little or no
deflection, being detected between positions A and B.
A few particles were deflected through large angles, e.g. to position C, and a very
small number were even deflected backwards, e.g. to position D.
Rutherford was so surprised by this second result in particular that he described it as being
like firing a cannonball at tissue paper and having it bounce back. It was known that the
alpha particles were relatively heavy and fast moving, and if they were encountering the
spread-out charge and matter of the Thomson model there would be nothing solid enough for
them to bounce off. Thus the expectation was that all of the particles would be detected
between A and B.
Rutherford interpreted his results as follows:
 The fact that most of the particles passed straight through the foil, which was at least
100 atoms thick, suggested that the atom must be mostly empty space.
 In order to produce the large deflections at C and D, the alpha particles must be
encountering something of very large mass and a positive charge.
Physics/DS/BMN
37
Particles and Waves
A Small
deflection
No deflection
Alpha
particles
B Small
deflection
Atom and nucleus (not
to scale)
D Deflected
right back
C Large
deflection
Rutherford suggested that the atom has a small positive nucleus, which contains most of the
mass of the atom and is small compared to the size of the atom. The remaining space is
taken up by the electrons (negative particles) orbiting the nucleus. By analysing the data he
was able to estimate the diameter of the atom to be about 10,000 times the diameter of the
nucleus.
Standard Model
Physicists have a rather bold theory to explain what the world is and what holds it together : The
Standard Model. We can explain it in terms of 6 quarks, 6 leptons and force carrier particles. All
known matter particles are composites (made from) of quarks and leptons, they interact by
exchanging force carrier particles.
Antimatter and Matter
Every matter particle has a corresponding antiparticle. The particles
have the same mass but opposite charge except for antineutrons and
neutrons which don’t have any charge( the anti neutron is made from
antiquarks). When a matter particle and its antiparticle equivalent
come together they annihilate each other and energy is released.
Anti particles are denoted by a bar above them :
Proton , p , matter particle
p+
and antiproton, , anti particle
annihilation,
During the Big Bang equal amounts of matter and antimatter were produced, why we live in a
universe dominated by matter is not yet understood.
38 Physics/DS/BMN
Particles and Waves
Positron emission tomography ( interest : a use for antimatter)
Positron emission tomography (PET) uses antimatter annihilation to obtain detailed 3 -D scans
of body function. CT and MRI scans can give detailed pictures of the bone and tissue within
the body but PET scans give a much clearer picture of how body processes are a ctually
working.
A β + tracer with a short half-life is introduced into the body attached to compounds
normally used by the body, such as glucose, water or oxygen. When this tracer emits a
positron it will annihilate nearly instantaneously with an electron. This produces a pair of
gamma-ray photons of specific frequency moving in approximately opposite directions to
each other. (The reason it is only an approximately opposite direction is that the positron
and electron are moving before the annihilation event takes place.) T he gamma rays are
detected in a ring of scintillations, each producing a burst of light that can be detected by
photomultiplier tubes or photodiodes. Complex computer analysis traces tens of thousands
of possible events each second and the positions of the original emissions are calculated. A
3-D image can then be constructed, often along with a CT or MRI scan to obtain a more
accurate picture of the anatomy alongside the body function being investigated.
Tracing the use of glucose in the body can be used in oncology (the treatment of cancer)
since cancer cells take up more glucose than healthy ones. This means that tumours appear
bright on the PET image. Glucose is also extremely important in brain cells, which makes PET
scans very useful for investigation into Alzheimer’s and other neurological disorders. If
oxygen is used as the tracking molecule, PET scans can be used to look at blood flow in the
heart to detect coronary heart disease and other heart problems.
© Jens Langner
The detecting equipment in PET scanners has much in common with particle detectors and
the latest developments in particle accelerators can be used to improve this field of medical
physics
Physics/DS/BMN
39
Fundamental particles
Particles and Waves
These cannot be broken down into smaller constituents
Quarks
: Again there are 6 types of quarks ( along with
their anti particles ) divided into 3 families. Family 1 the up /
down quarks are the constituents of everyday matter whilst
families 2 and 3 , the charm / strange and top / bottom
quarks make up exotic matter. Quarks have fractional charge
of the electron.
Particles made up of quarks are called Hadrons. Hadrons are
subject to the weak and strong force. Particles made up of an
anti quark and a quark are called Mesons, these particles are
unstable. Particles made up of 3 quarks are called Baryons.
Protons are made up of A proton is made from 2 up and 1 down quarks
(u u d ) total
2 2
1 charge ( = 1 )
3

3

3
( an anti proton is made up of two anti up and one anti down quarks )
whilst a neutron is made up of one up and two down quarks. ( d d u )
1
1 2
   0
3
3 3
Quarks and leptons belong to a family of particles
called Fermions. Fermions are subject to the
Pauli Exclusion Principle which basically says that
no two fermions can have the same quantum state
at the same time and place. Particles which do not
obey the Pauli Exclusion principle are called
Bosons
total charge = (0)
Name
Fraction of electron
charge
up
down
charm
strange
top
bottom
⅔
–⅓
⅔
–⅓
⅔
–⅓
Only a small part of the mass of a Hadron is due to the quarks , this is where the Higgs Boson comes
in.
40 Physics/DS/BMN
Particles and Waves
Leptons
There are 6 types in total, 3 with and 3
without charge. Leptons are solitary particles
and are not subject to the strong force.
Each of these particles also has an anti
particle. The electron and electron neutrino
are constituents of ‘ordinary matter’ and the
muon and tau along with their neutrinos are
found in cosmic rays and particle accelerators.
The uncharged leptons are electron neutrino,
tau neutrino and muon neutrino. These all have
a tiny mass and are very difficult to detect, millions are passing through as you read this
Beta decay led to the existence of neutrinos being hypothesised ; A neutron inside a nucleus can
decay into a proton and an electron :
u
d
d
n
p
+
e-
u
u
d
+
e-
Studies showed that the proton and electron were
ejected in the direction shown by the dashed arrow.
If momentum was to be conserved then a particle
must be ejected horizontally to the right. This was
initially called a neutrino by Fermi , meaning small
neutral one. In Beta decay it is actually an antineutrino
that is produced.
What holds this together ?
Fundamental particles interact by exchanging force
carrier particles. There are 4 fundamental forces ;
Gravity, Electromagnetic , Weak and the Strong Force.
The holy grail of Physics is to unite all the forces
together to create a theory of everything.
To get a handle on the force carrier particles think
about two people standing on ice. If they throw a
basketball ball back and forwards to each other they
will both accelerate i.e. a force must be acting on the
people. If no basketball is thrown then there is no
force.
Physics/DS/BMN
41
Particles and Waves
Electromagnetism : This is the force that causes like charges to repel and unlike to attract, Photons
are the force carrier particles. This is the force that holds atoms together. The electrons from one
atom attract the protons of another.
Strong Force :There is a huge problem inside the nucleus, the protons should repel each other
splitting the nucleus up. However there is a strong force of attraction between the quarks that
make up neutrons and protons. This force acts over distances less than 10-14 m. The greater the
distance between quarks the stronger the force becomes. The nucleus is held together by the strong
force that acts between a quark in one proton and a quark in another inside the nucleus.
Weak Force : All the stable matter appears to be made up of the two least massive quarks, u and d (
up and down ), and the least massive leptons , e- and 
( electrons and neutrinos ). Weak
interactions cause the decay of massive quarks / leptons into the above. The force carrier particles
are called W+ + W- boson and the Z boson . The weak force is also responsible for Beta decay. The
weak force acts on leptons and hadrons and acts over distances less than 10-17 m. The weak force is
also responsible for controlling the rate of a nuclear reaction inside the sun that effectively
controls the rate of ‘burning of the fuel ‘ (Hydrogen ions.)
Gravity : This is not explained in the Standard model but it is hypothesised that gravitons are the
force carrier particles.
Force
Intensity Distance(m) Carrier
Strong
1
Electromagnetic 10-2
10-15 m
infinite
Weak
10-5
10-18m
Gravity
10-42
infinite
42 Physics/DS/BMN
Example Approximate
decay time
(s)
Gluons
Holds
Nucleus
together
Photons
Holds
atoms
together
W and Z Beta
Bosons
Decay
Gravitons Holds
galaxies
together
10 –23
10 –10
10 –20 –10 –16
Undiscovered
Particles and Waves
Remember that matter is made up from particles in the first generation , the 2nd and 3rd generation
are generated in particle accelerators and are unstable.
Physics/DS/BMN
43
Particles and Waves
Particle Accelerators
Fermilab : the most
powerful accelrator
in the USA
http://www.fnal.gov/
To find out what something is made of you might a) look at it, b) heat it up and see what happens or
c) smash it up by brute force. The latter method is what particle Physicists used to do: They fired
high energy electrons or protons at nuclei and observed the resulting new particles spawned.
Heating atoms up allows for example electrons to be ionised leaving a nucleus behind. The best way
however is to look at it.
We use visible light, wavelength typically 500nm ( 5.0 x10-7m) to look at objects. Atoms however have
a diameter of c.a. 10-10 m and so light of a smaller wavelength than visible is needed, we can use XRays. The nucleus has a diameter of typically 10-15 m and quarks are c.a. 10-18m, we have a problem if
we want to probe inside the atom.
Particles also exhibit wave behaviour and waves can exhibit particle behaviour, we can use this idea
to probe into the atom.
Remember that the energy of one photon of light is given by
E=hxf
where h = Planck’s constant and f = frequency of the radiation.
The frequency of light , f, = c / λ, therefore we can say that
E = h x c/ λ.
Energy in particle Physics is normally measured in electron volts, eV. 1 eV is the energy gained by an
electron when accelerated across a pd of 1V. i.e.
E gained = charge on electron x voltage
W=QxV
W = 1.6x10-19 x 1 = 1.6 x10-19J = 1eV
Getting back to the previous bit if we multiply the two constants h and c together we get (3.0 x108 x
6.63 x 10-34 =1.989x10-25 J or approx 10-6eV ( work this out to convince yourself).Energy and
wavelength are related then 1eV corresponds to 10-6m. To probe the nucleus we need GeV energy
particles.
44 Physics/DS/BMN
Energy
1eV
1keV
1Mev
1Gev
1Tev
Particles and Waves
Wavelength(m)
10-6
10-9
10-12
10-15
10-18
Cyclotrons
( copyright LTS )
Exploration of the atom began with beams of alpha and beta particles from radioactive atoms. These
had small energies. When a charged particle is placed inside an electric field it experiences a force
and accelerates. The electrical potential energy is turned into kinetic energy of the particle.
A cyclotron consists of two hollow semi circular cavities or Ds, which face one another, there is a
small gap between them. If this is placed inside a magnetic field then the electrons or protons can be
made to follow a curved path. An electric field applied across the gap accelerates the charged
particles each time they travel across the gap. The electric field must alternate at the same
frequency as the particles rotating but as the speed of the particles increase their mass increases
and they take longer to complete a circuit and so they get out of step with the changing electric
field. The solution was to accelerate ‘bunches of particles’ ; the synchrocyclotron.
The first cyclotron was only 20cm in diameter , the Large Hadron Collider (LHC) at CCERN is 27km
long and collides two proton beams of 7Tev together. When charged particles rotate in a circle they
radiate energy ( snychtrotron radiation) hence energy needs to be pumped in to replace this loss.
The next generation of particle colliders will be linear to overcome this problem.
Linear Accelerators
The Stanford Linear Accelerator is the longest in the world . It can accelerate electrons to 50GeV in
just 3km whereas at CERN the LEP circular accelerator can reach 100GeV but has a circumference
of 27km.
Regardless of whether the particle accelerator is linear or circular, the basic parts are the
same:
Physics/DS/BMN
45
Particles and Waves





a source of particles (this may be another accelerator)
beam pipes (a guide along which the particles will travel whilst being accelerated)
accelerating structures (a method of accelerating the particles)
a system of magnets (either electromagnets or superconducting magnets as in the LHC)
a target (in the LHC the target is a packet of particles travelling in the opposite
direction).
Electric Fields
Just like masses accelerate inside a gravitational field so do charged particles when inside an
Electric Field .A gravitational field always attracts masses whereas an electric field can attract or
repel a charged particle . An electric field therefore is an area around a charged object, if another
charged object is placed inside this field it experiences a force.
As the charged particle experiences a force it will be accelerated and gain kinetic energy i.e. work is
done on the charged particle by the field.
Work done equals kinetic energy gained by charged particle;
W = Q x V = ½mv2
Where Q = charge on particle and V equals potential difference through which the particle is
accelerated.
Example
Calculate a) the kinetic energy gained by an electron as it is accelerated by the electric field shown
and b) the velocity of the electron at the +vely charged plate if it was initially at rest.
- 100 V
+ 200 V
Stationary electron
a)4.8x10-17 J, b) 1.03x107 ms-1
46 Physics/DS/BMN
Particles and Waves
Electric Field Patterns
The arrows indicate the direction a free positive charge would be accelerated in , the closer the lines
are the stronger the field.
http://www.physicsclassroom.com/class/estatics/u8l4c2.gif
The field around an isolated +ve charge is radially outwards. If the charge was –ve the arrows
would point towards the charge.
http://physicscatalyst.com/elec/chr_fig6.gif For a +ve and –ve charge of
equal magnitude the field pattern is as shown ( similar to the
magnetic field around a bar magnet )
Physics/DS/BMN
47
Particles and Waves
http://www.physicsclassroom.com/class/estatics/u8l4c16.gif
For parallel plates the electric field is taken to be uniform inside the plate area
https://upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Field_lines_parallel_plates.svg/
524px-Field_lines_parallel_plates.svg.png
Equal charges , there is a null point
between the charges
http://upload.wikimedia.org/wikimedia/en-labs/a/ab/Fhsst_electrost18.png
48 Physics/DS/BMN
Particles and Waves
Magnetic Fields
Magnetic fields are used to guide the charged particles inside a particle accelerator. A moving
charge has a magnetic field about it which interacts with the magnetic fields of the deflectors.
It is possible to remember the
direction of the magnetic field
round a current-carrying wire
for electron flow using the
left-hand grip rule. The thumb
direction of
points in the direction of the
electron flow
north pole and the fingers curl
around in the direction of the
North Pole.
© Douglas Morrison
When the moving charged particle interacts with a magnetic field we can predict what will happen
using the Right Hand Motor Rule
Physics/DS/BMN
49
Particles and Waves
The magnetic field does no net work on the moving charge this means that its direction only changes
and its speed remains constant.
Charged particles inside Electric Fields
http://knol.google.com/k/-//3m2gdefbt6ovt/nd458g/1.jpg
Inside the field the electron is accelerated towards the +ve plate. The electron has a uniform
horizontal velocity and so the motion is similar to projectile motion i.e. two components one of which
is uniform and the other being uniform acceleration. If a +vely charged particle was now fired into
the field it would accelerate downwards. When the charged particles exit the field they continue in
motion at a constant velocity.
50 Physics/DS/BMN
Particles and Waves
Nuclear Reactions
In 1905, a series of four papers by Albert Einstein was published in the journal Annalen der Physik.
One of these ‘Does the inertia of a body depend upon its energy content’ led us to one of the bestknown relationships in the world:
E = mc2
E is energy measured in joules (J)
E = mc2
m is mass measured in kilograms (kg)
c is the speed of light in a vacuum (m s–1)
This means that a 1kg has an energy equivalent of 9 x1016 J. This conversion of mass into energy and
vice versa actually happens. During the big bang energy was turned into mass and during nuclear
reactions the mass of the products is always les than the mass of starting materials. This mass
difference is turned into kinetic energy.
The atom
http://www.atomicarchive.com/Physics/Physics1.shtml
Physics/DS/BMN
51
Particles and Waves
In a simple model of the atom the nucleus consists of
protons, with mass number 1 and charge +1, and neutrons,
with mass number 1 and charge 0. Protons and neutrons
are collectively known as nucleons.
The total number of protons and neutrons in the
nucleus is called the mass number, A.
The number of protons in the nucleus is called the
atomic number, Z.
In a neutral atom the number of protons equals the
number of electrons.
Particle
Proton
Mass number
1
Charge
Symbol
+1
Neutron
1
0
Electron
0*
-1
1
1
p
1
0
n
0
1
e
*The mass of an electron is = 1/1840 of the mass of a proton.
Each element in the periodic table has a different atomic number and is identified by that number.
It is possible to have different versions of the same element, called isotopes. An isotope of an atom
has the same number of protons but a different number of neutrons, i.e. the same atomic number
but a different mass number.
An isotope is identified by specifying its chemical symbol along with its atomic and mass numbers. For
example:
52 Physics/DS/BMN
Particles and Waves
0
1
e
0
1
e
Nuclear isotopes
http://www.atomicarchive.com/Physics/Physics1.shtml
Radioactive decay
Radioactive decay is the breakdown of a nucleus to release energy and matter from the nucleus. This
is the basis of the word ‘nuclear’. The release of energy and/or matter allows unstable nuclei to
achieve stability. Unstable nuclei are called radioisotopes or radionuclides.
The following is a summary of the nature and symbols for the three types of nuclear radiation.
Notice that gamma radiation has zero mass and zero charge. It is an electromagnetic wave.
Radiation
Alpha particle
Nature
Helium nucleus
Symbol
Beta particle
Fast electron
0
1
Gamma ray
High frequency electromagnetic
wave
4
2
He
e



In the following equations both mass number and atomic number are conserved, ie the totals are the
same before and after the decay.
The original radionuclide is called the parent and the new radionuclide produced after decay is called
the daughter product (Which sometimes may go on to decay further).
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Alpha decay
http://www.atomicarchive.com/Physics/Physics1.shtml
In alpha decay, a positively charged particle, identical to the nucleus of helium 4, is emitted
spontaneously. This particle, also known as an alpha particle, consists of two protons and two
neutrons. It was discovered and named by Sir Ernest Rutherford in 1899.
Alpha decay
Alpha decay usually occurs in heavy nuclei such as
uranium or plutonium, and therefore is a major part of
the radioactive fallout from a nuclear explosion. Since
an alpha particle is relatively more massive than other
forms of radioactive decay, it can be stopped by a
sheet of paper and cannot penetrate human skin. A 4
MeV alpha particle can only travel a few centimetres
through the air.
Although the range of an alpha particle is short, if an
alpha decaying element is ingested, the alpha particle
can do considerable damage to the surrounding tissue.
This is why plutonium, with a long half-life, is
extremely hazardous if ingested.
Beta decay
http://www.atomicarchive.com/Physics/Physics7.shtml
Atoms emit beta particles through a process known as beta decay. Beta decay occurs when
an atom has either too many protons or too many
neutrons in its nucleus. Two types of beta decay can
occur. One type (positive beta decay) releases a
positively charged beta particle, called a positron,
and a neutrino; the other type (negative beta decay)
releases a negatively charged beta particle, called an
electron, and an antineutrino. The neutrino and the
antineutrino are high-energy elementary particles
with little mass and are released in order to conserve
energy and momentum during the decay process.
Negative beta decay is far more common than
positive beta decay.
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This form of radioactive decay was discovered by Sir Ernest Rutherford in 1899,although
the neutrino was not observed until the 1960s. Beta particles have all the characteristics of
electrons. At the time of their emission, they travel at nearly the speed of light. A typical
0.5 MeV particle will travel about 3 m through the air, and c an be stopped by 4-6 cm of wood
or thin metal.
Gamma decay
http://www.atomicarchive.com/Physics/Physics8.shtml
Gamma rays are a type of electromagnetic radiation that results from a redistribution of
electric charge within a nucleus. Gamma rays are essential ly very energetic X - rays; the
distinction between the two is not based on their intrinsic nature but rather on their
origins. X rays are emitted during atomic processes involving energetic electrons. Gamma
radiation is emitted by excited nuclei or other processes involving subatomic particles; it
often accompanies alpha or beta radiation, as a nucleus emitting those particles may be left
in an excited (higher-energy) state. When only gamma rays are emitted there is no change to
the mass or atomic no.
Gamma rays are more penetrating than either alpha or beta radiation, but less ionising.
Gamma rays from nuclear fallout would probably cause the largest number of casualties in
the event of the use of nuclear weapons in a nuclear war . They produce damage similar to
that caused by X-rays, such as burns, cancer and genetic mutations.
Fission: spontaneous decay and nuclear bombardment
http://www.atomicarchive.com/Physics/Physics9.shtml
Fission occurs when a heavy nucleus disintegrates, forming two nuclei of smaller mass number. This
radioactive decay is spontaneous fission. In this decay process, the nucleus will split into two nearly
equal fragments and several free neutrons. A large amount of energy is also released. Most elements
do not decay in this manner unless their mass number is greater than 230.
Spontaneous and Induced Fission
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The stray neutrons released by a spontaneous fission can
prematurely initiate a chain reaction. This means that the
assembly time to reach a critical mass has to be less than the rate
of spontaneous fission. Scientists have to consider the
spontaneous fission rate of each material when designing nuclear
weapons or for nuclear power.
For example, the spontaneous fission rate of plutonium 239 is
about 300 times larger than that of uranium 235.
Fission can also be induced, ie persuaded, to happen by neutron
bombardment:
http://www.atomicarchive.com/Fission/Fission1.shtml
And in equation form
235
92
U + 01 n 
92
36
Kr +
141
56
Ba + 3 01 n + energy
Nuclear fission and E = mc2
235
92
U + 01 n 
92
36
Kr +
141
56
Ba + 3 01 n + energy
Mass number and atomic number are both conserved during this fission reaction. Even though the
mass number is conserved, when the masses before and after the fission are compared accurately,
there is a mass difference . The total mass before fission is greater than the total mass of the
products. This brings us back to Einstein’s work, proposing a relationship between mass and energy:
2
E = mc
In fission reactions, the energy released is carried away as the kinetic energy of the fission
products.
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Example
Calculate the energy released during this fission reaction.
235
92
97
1
U + 01n  137
56 Ba + 42 Mo + 2 0 n + energy
Mass before fission (kg)
U
390.2 × 10–27
n
1.675 × 10–27
___________________
391.875 × 10–27
Mass after fission (kg)
Ba 227.3 × 10–27
Mo 160.9 × 10–27
2n 3.350 × 10–27
___________________________
391.550 × 10–27
Decrease in mass = (391.875 – 391.550) × 10–27 = 0.325 × 10–27 kg
Energy released during this fission reaction, using E = mc2
E = 3.25 × 10–28 × (3 × 108)2 = 2.9 × 10–11 J
This is the energy released by fission of a single nucleus. There are c.a. 2.56x1024 Uranium nuclei in
1kg therefore if all the Uranium nuclei underwent fission then 7.42 x1013 J of energy would be
released.
Note the need to work with six significant figures for mass due to the small difference.
Nuclear fusion: energy of the future?
For some time, governments have sought to become less reliant on nuclear fission. However, as we
face a future in which oil and other fossil fuel resources become increasingly scarce, it may become
necessary for society to either re-examine approaches to reducing our demand on these resources or
seek alternatives. Fuelling the world’s ever-increasing population in the future may require another
nuclear solution.
Nuclear energy can also be released by the fusion of two
light elements (elements with low atomic numbers).
In a hydrogen bomb, two isotopes of hydrogen, deuterium
and tritium are fused to form a nucleus of helium and a
neutron. This fusion releases 17.6 MeV of energy. Unlike
nuclear fission, there is no limit on the amount of the
fusion that can occur. Deuterium is an isotope of
hydrogen with two protons in its nucleus (heavy
hydrogen). Tritium is another hydrogen isotope (super
heavy hydrogen) with three protons in its nucleus.
Deuterium is naturally occurring in seawater and tritium
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can be made from lithium, which is readily available on Earth.
The immense energy produced by our Sun is as a result of nuclear fusion. Very high temperatures in
the Sun (2.3 × 107 K according to NASA; see
http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/981216a.html) supply sufficient energy for
nuclei to overcome repulsive forces and fuse together.
When nuclei fuse, the final mass is less than the initial mass, ie there is a mass difference or mass
defect. The energy produced can be calculated using Einstein’s famous equation.
Fusion has been successfully achieved with the hydrogen bomb. However, this was an uncontrolled
fusion reaction and the key to using fusion as an energy source is control.
The Joint European Torus (JET), in Oxfordshire, is Europe’s largest fusion device. In this device,
deuterium–tritium fusion reactions occur at over 100 million Kelvin. Even higher temperatures are
required for deuterium–deuterium and deuterium–helium 3 reactions (see http://www.jet.efda.org/).
To sustain fusion there are three conditions, which must be met simultaneously:
1. plasma temperature (T): 100–200 million Kelvin
2. energy confinement time (t): 4–6 seconds
3. central density in plasma (n): 1–2 × 1020 particles m–3 (approx. 1/1000 gram m–3, ie one
millionth of the density of air).
In a Tokamak the plasma is heated in a ring-shaped vessel
(or torus) and kept away from the vessel walls by applied
magnetic fields. The basic components of the Tokamak’s
magnetic confinement system are:
 The toroidal field – which produces a field around the
torus. This is maintained by magnetic field coils
surrounding the vacuum vessel (see figure). The toroidal
field provides the primary mechanism of confinement of
the plasma particles.
 The poloidal field – which produces a field around the
plasma cross-section. It pinches the plasma away from the walls and maintains the plasma’s shape
and stability. The poloidal field is induced both internally, by the current driven in the plasma (one
of the plasma heating mechanisms), and externally, by coils that are positioned around the
perimeter of the vessel.
The main plasma current is induced in the plasma by the action of a large transformer. A changing
current in the primary winding or solenoid (a multi-turn coil wound onto a large iron core in JET)
induces a powerful current (up to 5 million amperes on JET) in the plasma, which acts as the
transformer secondary circuit.
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One of the main requirements for fusion is to heat the plasma particles to very high temperatures or
energies.
Ohmic heating and current drive
Currents up to 5 million amperes are induced in the JET plasma – typically via the
transformer or solenoid. As well as providing a natural pinching of the plasma column away
from the walls, the current inherently heats the plasma – by energising plasma electrons and
ions in a particular toroidal direction. A few megawatts of heating power are provided in this
way.
Neutral beam heating
Beams of high energy, neutral deuterium or tritium atoms are injected into the plasma,
transferring their energy to the plasma via collisions with the plasma ions. The neutral
beams are produced in two distinct phases. Firstly, a beam of energetic ions is produced by
applying an accelerating voltage of up to 140,000 V. However, a beam of charged ions will not
be able to penetrate the confining magnetic field in the Tokamak. Thus, the second stage
ensures the accelerated beams are neutralised (ie the ions turned into neutra l atoms)
before injection into the plasma. In JET, up to 21 MW of additional power is available from
the neutral beam injection heating systems.
Radio-frequency heating
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As the plasma ions and electrons are confined to rotating around the magnetic field li nes in
the Tokamak, electromagnetic waves of a frequency matched to the ions or electrons are
able to resonate – or damp its wave power into the plasma particles. As energy is
transferred to the plasma at the precise location where the radio waves resonate with the
ion/electron rotation, such wave heating schemes have the advantage of being localised at a
particular location in the plasma.
In JET, a number of antennae in the vacuum vessel propagate waves in the frequency range
of 25–55 MHz into the core of the plasma. These waves are tuned to resonate with
particular ions in the plasma – thus heating them up. This method can inject up to 20 MW of
heating power.
Waves can also be used to drive current in the plasma – by providing a ‘push’ to electrons
travelling in one particular direction. In JET, 10 MW of these so -called lower hybrid microwaves
(at 3.7 GHz) accelerate the plasma electrons to generate a plasma current of up to 3 MW.
Self-heating of plasma
The helium ions (or so-called alpha-particles) produced when deuterium and tritium fuse
remain within the plasma’s magnetic trap for a time, before they are pumped away through
the diverter. The neutrons (being neutral) escape the magnetic field and their capture in a
future fusion power plant will be the source of fusion power to produce electricity.
When fusion power out just equals the power required to heat and sustain plasma then
breakeven is achieved. However, only the fusion energy contained within the helium ions
heats the deuterium and tritium fuel ions (by collisions) to keep the fusion reaction going.
When this self-heating mechanism is sufficient to maintain the plasma temperature required
for fusion the reaction becomes self-sustaining (ie no external plasma heating is required).
This condition is referred to as ignition. In magnetic plasma confinement of the D –T fusion
reaction, the condition for ignition is approximately six times more demanding (in
confinement time or in plasma density) than the condition for breakeven.’
Extracts and images © EFDA-JET
http://www.jet.efda.org/
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