PHYS1210 Study Guide - Final Guide: Large Hadron Collider, Higgs Boson, Peter Higgs
14 Jun 2018
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Particle Physics
Structure of the Atom
An electron (charge = -1.6x10-19 C) orbits a central positive nucleus (+1.6x10-19 C).
Techniques such as scanning tunnelling microscopy and transmission electron microscopy
allo atos to e see ee though the are only 10-10 m across.
Electromagnetic waves
James Maxwell (1831-1879) summarised all magnetic and electrical phenomena in a set of 4
equations. Visible light is an electromagnetic wave and obeys these equations.
Radioactivity and Half life
Radioactive intensity depends on mass of radioactive
material. Number of decay events (dN) per unit time (dt) is
proportional to total number of particles (N). Solution defines decay rate ().
Half-life is the average time it takes half of a given number of radioactive nuclei to decay.
Set N=N0 /2 and t= T⁄ in exponential decay equation gives:
Wave-particle duality
The photoelectric effect experiment (incident light of the correct wavelength can eject
electrons from an irradiated metal surface) was carried out by Millikan in 1913. Results
explained by Einstein (1920) by incident light comprising particles (photons) of energy
ejecting electrons with a
Matter waves
Particles can also behave as waves e.g. they can diffract or interfere. De Broglie (1923)
showed that particles can be represented by matter waves with a wavelength:
where p is the patiles oetu ad h is Plaks ostat .-34 Js).
Electron waves
Thus, electrons are not just particles but are also waves and they can diffract and interfere.
Diffatio: eas that e a uild optial o iagig istuets ased o electrons –
hence electron microscope.
Interference: constructive and destructive interference of electrons leads to electron energy
levels in materials.
Electronics
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So, electrons in solids exist in discrete energy levels. Consequence: Semiconductors and
band gaps. Determines all the properties of electronic components used in diodes,
transistors and Ics.
The discrete electron orbits in the Bohr model of the hydrogen model are explained in terms
of the stadig aes foed the eletos ae function. The visible spectrum of
hydrogen results from transitions to the n=2 level.
The functioning of neon signs (gas discharge tubes) is governed by quantisation. Strong
electrical field excites electrons in tube that collide with gas atoms. Electrons in gas atoms
are excited to higher energy states. Whe the ela to a oe stale oital a photo is
emitted. Quantisation of energy levels says that this can only have certain energy values.
Frequency of the light is related to energy and so only get certain colours.
Heisenberg and Uncertainty
When we try and measure small objects, we start to disrupt the objects we want to
measure. e.g. Where is the particle? Shine a light at it and look. But the light hitting an
ordinary object has a power typically of mW (or about 1015 photons/s hit the object). So
just fire one photon at it & observe recoiling photon. But particle will also recoil & its
momentum will change! The smaller the particle the more accurately we have to fire the
photon – the greater the momentum change. The Heisenberg uncertainty principle says we
cannot simultaneously measure the position and momentum of a particle with accuracies
better than Δx, Δp where:
So, in the quantum world, certainty is lost. Define probability of finding particles in a certain
region. So, exact radius of orbits in the Bohr model is replaced by a probability of an
electron being at a certain radius.
Particle Accelerators
Van de Graaff Accelerator: Apply high voltage (~50 kV) to pointed conductor. Pull electrons
off resulting in positive charge on belt. Charge transferred from belt to spherical conductor.
Cyclotron: Constant magnetic field to move ions in circular paths. Two D-shaped cavities
separated by a gap. AC potential difference to ions as they cross the gap. AC ensures applied
voltage in correct direction. Incremental increase in KE until max radius achieved.
Synchrotron: Mass of accelerating particle increases relativistically. To maintain constant
radius need to increase B-field. Synchronous increase - synchrotron particle accelerator.
Energy loss – synchrotron radiation.
The Large Hadron Collider (LHC) will guide protons at almost the speed of light in opposite
directions around a 27 km underground ring before smashing them into one another with
an energy of 14 TeV at four separate points. 14 TeV ~ energy of 14 mosquitoes in flight. But
resulting energy density is the highest ever produced in a laboratory. 4 large detectors:
ATLAS, LHCb, ALICE & CMS will catch and analyse the debris from these collisions.
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The Higgs Boson – The God Patile
1964: Peter Higgs (Edinburgh University) publishes landmark paper in PRL proposing that
after the big bang, many particles had no mass, but became heavy later due to the Higgs
quantum field.
What is the Higgs field?
An energy field stretches through universe.
Clings to fundamental particles
Drag that is produced makes them heavy.
Some particles feel the field stronger than others – its more "sticky" to them.
Photos dot feel it at all ad ae massless
So, all particles initially were massless but when the Higgs field switched on (shortly
after the big bang), they gained mass.
Higgs boson is signature particle of the field.
Particle Detectors
First detectors based on photographic emulsion plates – ionised atoms along path of high
energy particles leads to a chemical change in the emulsion.
A cloud chamber contains a supersaturated vapour by cooling a gas just below its
condensation point. Gas molecules then condense on any ionised species. Ions created
alog the patiles path at as uleatio sites fo odesatio – cloud tracks.
A bubble chamber contains a liquid close to its boiling point. Ions produced by particles act
as nucleation sites for bubble production. Typically more efficient than a cloud chamber
since liquid (often liq H2) density is higher than gas.
Wire drift chambers (most common now) involve closely spaced wires in gas chamber.
Ionised gas species produces an electron avalanche. Position determined by time of
detection at edge. Reconstruct path via computer.
So the atom comprises a nucleus surrounded by electrons. But are these fundamental
particles? B the 9s the uleus as ko to ade of potos ad eutos. But are
neutrons and protons fundamental particles? Wh dot the ulea potos epel eah
other? There must be a strong attractive force holding the nucleons together – the strong
nuclear force. Forces can be modelled using concept of force fields. An electron generates
an electric field (E) which interacts with another electron causing repulsive force (F). But the
electric field really propagates as an electromagnetic wave:
1. Em waves are also collections of photons
2. Or interaction can be modelled as an exchange of photons
Particle Exchange
Analogy: Attraction: kids on roller skates grabbing pillows. Repulsion: kids on roller skates
throwing pillows.
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Document Summary
An electron (charge = -1. 6x10-19 c) orbits a central positive nucleus (+1. 6x10-19 c). Techniques such as scanning tunnelling microscopy and transmission electron microscopy allo(cid:449) ato(cid:373)s to (cid:271)e (cid:862)see(cid:374)(cid:863) e(cid:448)e(cid:374) though the(cid:455) are only 10-10 m across. James maxwell (1831-1879) summarised all magnetic and electrical phenomena in a set of 4 equations. Visible light is an electromagnetic wave and obeys these equations. Radioactive intensity depends on mass of radioactive material. Number of decay events (dn) per unit time (dt) is proportional to total number of particles (n). Half-life is the average time it takes half of a given number of radioactive nuclei to decay. Set n=n0 /2 and t= t(cid:1005) (cid:1006) in exponential decay equation gives: The photoelectric effect experiment (incident light of the correct wavelength can eject electrons from an irradiated metal surface) was carried out by millikan in 1913.
