Particles, Radiation and
Quantum Phenomena
Contents
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Particles
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Rutherford Scattering
Constituents of the Atom
“Four Force” Model
Quarks and Antiquarks
Particles and Antiparticles
Particle Families
Particle Exchange
Beta Decay
Detecting Particles
Electromagnetic Radiation and
Quantum Phenomena
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Refraction
The Photoelectric Effect
Wave Particle Duality
Spectra and Energy Levels
Rutherford Scattering
Rutherford proposed a model of the atom to consist of:
A heavy, positively charged Nucleus at the centre, with a
much lighter, negatively charged electron field in orbit
around it.
The Rutherford
Scattering
experiment consists
of a piece of gold
foil, which is
bombarded with
positively charged
alpha particles
Rutherford Scattering
Rutherford found the following occurred:
Most alpha particles are undeflected
A few alpha particles are slightly
deflected
A few alpha particles bounce off
Nucleus
Constituents of the Atom
For most elements, a sample contains a mixture of different
versions. These have the same number of protons, and
electrons, but a different number of neutrons.
Isotopes
Nuclide
e = electron (–)
Nuclide
3e
p = proton (+)
3e
3p
3n
n = neutron
Nucleon number
6
Proton number
3
3p
4n
Li (Lithium)
7
3
Li (Lithium)
Mass of proton
= 1.00728 u
Charge of proton
= +1.60x10-19 C
Mass of neutron
= 1.00867 u
Charge of electron
= - 1.60x10-19 C
Mass of electron
= 0.00055 u
Diameter of an atom ~ 10-10 m
1 u (unified atomic mass unit) = 1.66x10-27 kg
Diameter of a nucleus ~ 10-14 m
Constituents of the Atom
Nuclide - This is a particular version of an atom. The previous
example shows a simple model of the two naturally occurring
nuclides of Lithium, along with the symbols used.
Nucleon Number A - This number is made up of the total
number of protons and neutrons in the nucleus, also called
nucleons. Once called the mass number.
Proton Number Z - This is the number of protons in the
nucleus, and also the number of electrons in a neutral atom.
Once called the atomic number.
Isotopes - These are atoms with the same proton number,
but different nucleon numbers. They have the same electron
arrangement and, therefore, the same chemical properties
“Four Force” Model
Force
Strength
Range
Comments
Strong interaction
Very Strong
1x10-15m
Affects protons
and neutrons only
Weak interaction
Weak
1x10-18m
Affects all
particles
Gravitational
forces
Very Weak
Infinite range
Affects all objects
with mass
Infinite range
Affect all objects
with static or
moving charge
Electromagnetic
forces
Strong
Quarks and Antiquarks
Quarks and Antiquarks are the fundamental particles. They
are what make up nucleons, i.e. protons and neutrons, as well
as other particles
There are 6 types of quark, of which two occur in protons and
neutrons. These are shown below in the examples. These
quarks are known as UP (u) and DOWN (d). They have
charges of +2e/3 and -1e/3 repectively.
u
u
d
u
d
d
Nucleons containing UP and DOWN quarks
Quarks and Antiquarks
The 6 quarks along with their antiquarks, make up the quark
family. The properties of antiquarks are similar to those of the
corresponding quark, but with the opposite sign.
Quark /
Antiquark
Symbol
Charge/e
Baryon
number, B
Strangeness,
S
up
u
u
+2/3
-2/3
1/3
-1/3
0
0
down
d
d
-1/3
+1/3
1/3
-1/3
0
0
charm
c
c
+2/3
-2/3
1/3
-1/3
0
0
strange
s
s
-1/3
+1/3
1/3
-1/3
-1
1
top
t
t
+2/3
-2/3
1/3
-1/3
0
0
bottom
b
b
-1/3
+1/3
1/3
-1/3
0
0
Particles and antiparticles
Most types of particles have a corresponding antiparticle.
This has the same rest mass, but at least one property which is
opposite to that of the particle.
For example:
Particle
Antiparticle
Electron
Positron
(antielectron)
Proton
Antiproton
Neutrino
Spin
Antineutrino
When a particle and its antiparticle meet, in most cases they
annihilate each other and their mass is converted into energy.
Particle Families
force)
Spin ½
1
Electron
e-e
2
Muon
μ
Baryons Spin ½ or 3/2
Electronneutrino
νe
0
Muonneutrino
-
-e
3
Hadrons
Leptons (not Strong
Tau
νμ
0
-e
ντ
Charge
Mesons Spin 0 or 1
Proton
p
Pion-zero
π0
+e
Neutron
π+
0
Lamda
Κ+
0
Sigma-plus
0
Κ0
+e
Σ0
Others
0
Omega-minus
Others
+e
Kaon-zero
Sigma-zero
Ω-
+e
Kaon-plus
Λ
Σ+
0
Pion-plus
n
Tauneutrino
τ-
nucleus
Generation
-e
Charge
0
Particle Exchange
The interaction between particles that results in attractive and
repulsive forces is due to continual exchange of exchange
particles. They have a short existence on borrowed energy, and
are often referred to as virtual particles.
The diagram below is a Feynman Diagram of two electrons
interacting. The straight lines show the paths of the electrons,
and the squiggly line shows the virtual photons that move
between them.
e-
e-
This is an example of the
electromagnetic force
interactions.
γ
e-
e-
Particle Exchange
There is a similar interaction for the other forces. For
Gravitational Forces, the exchange particles are called gravitons
but these haven’t been observed yet.
The Strong Force is what holds quarks together in a nucleon,
and their exchange particles are called gluons.
n
n
n
π0
n
p
p
π+
n
p
n
πn
n
p
The above Feynman diagrams show the interactions that are responsible for
the Strong Force between nucleons. These are called pions or pi-mesons and
are some of the Strong Force interactions. The - + 0 represent the charge.
Particle Exchange
For Weak Force interactions, there is an exchange of one of
three kinds of particles called intermediate vector bosons. The
symbols for these are W+, W -, Z0 and like pions the - + 0
represent the charge.
e-
p+
W+
νe
n
p+
n
e-
e-
νe
e-
νe
π-
W-
νe
The above Feynman diagrams show the neutino-neutron interaction, βdecay interaction, and the electron-antineutrino collision interaction,
respectively.
Beta Decay
Beta Decay is shown here in more detail:
This interaction causes a quark in the neutron to change
from down, d, to up, u, in the proton and emits a W- particle
which then decays into an electron and antineutrino.
Detecting Particles
Detectors are needed to reveal the paths of the particles
produced in experiments using particle accelerators.
Bubble Chamber
Filled with liquid hydrogen,
the pressure is suddenly
released so that the hydrogen
is ready to vaporise.
Charged particles entering
the chamber ionise the
hydrogen. This triggers
vaporisation, so a trail of
bubbles is formed along the
track of each particle.
Detecting Particles
Drift Chamber
A gas filled chamber, containing typically thousands of parallel
wires. Incoming particles cause a trail of ionisation in the gas.
Their track is calculated electronically by the length of time
ionisation electrons take to drift to the nearest sense wires. A
computer processed the signals and displays the tracks
graphically.
Particle
Refraction
Angle of
incidence
Angle of
refraction
When waves cross a boundary
between two materials, there
is a change of speed called
refraction.
If the direction of the wave is
at an angle other than the
normal line, then a change in
direction occurs.
The change in speed is
described by the refractive
index, n of the material.
n is given by:
n = cv / cm
where cv is the speed of light in a vacuum, and cm the
speed of light in the material in question. n is unitless.
Refraction
The refractive index between two materials is:
1n2
It is the ratio of speed of light in material 1, to the speed of
light in material 2, and is given by:
1n2
Snell’s Law states:
= c1/c2 = n1/n2
sini /sinr = c1/c2 = 1n2
From Snell’s law, the angle of refraction can be calculated if
the refractive index of the two materials is known. The
refractive index can be calculated from the sin of the angles
of the light measured in the materials.
Critical Angle
When light speeds up as it crosses a boundary, the change in
direction is away from the normal line. For a specific angle of
incidence, called the critical angle, the angle of refraction is
90o.
The diagram shows a the stages
of refraction, from normal
refraction, to the critical angle, to
total internal reflection.
Fibre Optics
Optical Fibres utilise total internal reflection at the boundaries
of the fibre to carry information digitally in the form of light.
The diagram below shows a straight section of optical fibre,
but the cable can bend and the light will continue to travel
down the fibre, as long as the critical angle is achieved.
The cables can be clad in a material of a lower refractive index
than the core, and this lowers the critical angle.
Examples of optical fibre usage: communications for phone
lines, and medicine for endoscopy.
Photoelectric Effect
The Photoelectric effect provides evidence that electromagnetic
waves have particle-like behaviour.
In the photoelectric effect, electrons are
emitted from a metal’s surface when it
absorbs electromagnetic radiation.
The diagram to the left shows this.
There are no electrons emitted below a certain
frequency, called the threshold frequence, fo ,
which is different for different metals.
Above this frequency, electrons are emitted with
a range of kinetic energies up to a maximum,
(½mv2)max
Photoelectric Effect
The wave model cannot explain the Photoelectric effect. The
explanation for this relies on the concept of the photon, a
quantum packet of energy. So EM radiation is given by short
bursts of energy.
The relationship between the energy of the photon, E, and its
frequency is given by:
E = hf
where h is Planck’s constant h = 6.63x10-34 Js
The energy of a photon can be measured in Joules or
Electronvolts.
One electronvolt is the energy transfer when an electron moves
through a potential difference of 1 volt, given by:
1 eV = 1.60x10-19 J
Photoelectric Effect
The minimum energy required for the electron to escape the
metal is called the work function, Φ
If energy is less than Φ, then no emission occurs
Emission is possible when hf = Φ
The photoelectric equation relates the maximum kinetic energy
of the emitted electrons to the work function and the energy of
each photon:
hf = Φ + (½mv2)
At the threshold frequency, the minimum frequency that can
cause an emission is zero, so the equation becomes:
hfo = Φ
Wave Particle Duality
Waves show particle-like behaviour, and particles show wavelike behaviour.
All particles have an associated wavelength called the de
Broglie wavelength λ
The relationship between the particle’s wavelength and its
momentum, p, is given by the de Broglie equation:
λ = h/p = h/mv
Spectra and Energy Levels
The loss of energy from an electron gives line spectra, and is
different for each material.
When current is passed through hydrogen gas, the hydrogen
spectrum is given as below:
Line spectrum are
unique for each
element, and for each
isotope of that
element.
Spectra and Energy Levels
An energy level diagram shows the amounts of energy that
electrons have at each level in an atom.
The energies are measured from a zero equivalent to a single
free electron.
The diagram shows the energy levels in a
hydrogen atom.
An orbiting electron has less energy than a free
electron, so the energies are shown as
negatives relative to the ground state.
An electron with the minimum possible energy
is in the ground state; higher energy levels are
called excited states.
When an electron moves from an energy level
E1 to a lower energy level E2 the energy of the
photon emitted is given by:
hf = E1 – E2
Summary

Particles
–
–
–
–
–
–
–
–
–

Rutherford Scattering
Constituents of the Atom
“Four Force” Model
Quarks and Antiquarks
Particles and Antiparticles
Particle Families
Particle Exchange
Beta Decay
Detecting Particles
Electromagnetic Radiation and
Quantum Phenomena
–
–
–
–
Refraction
The Photoelectric Effect
Wave Particle Duality
Spectra and Energy Levels