Particles, Radiation and Particles, Radiation and Quantum PhenomenaQuantum Phenomena

ContentsContents ParticlesParticles

– Rutherford ScatteringRutherford Scattering– Constituents of the AtomConstituents of the Atom– ““Four Force” ModelFour Force” Model– Quarks and AntiquarksQuarks and Antiquarks– Particles and AntiparticlesParticles and Antiparticles– Particle FamiliesParticle Families– Particle ExchangeParticle Exchange– Beta DecayBeta Decay– Detecting ParticlesDetecting Particles

Electromagnetic Radiation and Electromagnetic Radiation and Quantum PhenomenaQuantum Phenomena– RefractionRefraction– The Photoelectric EffectThe Photoelectric Effect– Wave Particle DualityWave Particle Duality– Spectra and Energy LevelsSpectra and Energy Levels

Rutherford ScatteringRutherford 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 ScatteringRutherford Scattering

Most alpha particles are undeflected

A few alpha particles are slightly deflected

A few alpha particles bounce off Nucleus

Rutherford found the following occurred:

Constituents of the AtomConstituents of the AtomFor 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.

3p3n

3e

3p4n

3ee = electron (–)

p = proton (+)

n = neutron

Isotopes

Nuclide Nuclide

Li (Lithium)6

3 Li (Lithium)7

3

Nucleon number

Proton number

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 AtomConstituents 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” ModelFour Force” Model

Force Strength Range Comments

Strong interaction Very StrongVery Strong 1x101x10-15-15mm

Affects protons and neutrons

only

Weak interaction

Weak 1x10-18m Affects all Affects all particlesparticles

Gravitational forces

Very Weak Infinite rangeAffects all

objects with mass

Electromagnetic forces

Strong Infinite range

Affect all objects with

static or moving charge

Quarks and AntiquarksQuarks and Antiquarks

ud

d

uu

d

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.

Nucleons containing UP and DOWN quarks

Quarks and AntiquarksQuarks and Antiquarks

Quark / Quark / AntiquarkAntiquark

SymbolSymbol Charge/Charge/ee Baryon Baryon number, Bnumber, B

StrangenessStrangeness, S, S

upup uu uu +2/3+2/3 -2/3-2/3 1/31/3 -1/3-1/3 00 00

downdown dd dd -1/3-1/3 +1/3+1/3 1/31/3 -1/3-1/3 00 00

charmcharm cc cc +2/3+2/3 -2/3-2/3 1/31/3 -1/3-1/3 00 00

strangestrange ss ss -1/3-1/3 +1/3+1/3 1/31/3 -1/3-1/3 -1-1 11

toptop tt tt +2/3+2/3 -2/3-2/3 1/31/3 -1/3-1/3 00 00

bottombottom bb bb -1/3-1/3 +1/3+1/3 1/31/3 -1/3-1/3 00 00

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.

Particles and antiparticlesParticles and antiparticlesMost 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 Antipartic

leElectron

Positron (antielectron)

Proton Antiproton

SpinNeutrino Antineutrin

oWhen a particle and its antiparticle meet, in most cases they annihilate each other and their mass is converted into energy.

Particle FamiliesParticle FamiliesGeneratiGenerati

ononLeptons Leptons (not (not Strong force)Strong force)

Spin ½ Spin ½

11 ElectronElectron

e e --

ElectronElectron--

neutrinoneutrino

ννee

22 MuonMuon

μμ --

Muon-Muon-neutrinoneutrino

ννμμ

33 TauTau

ττ --

Tau-Tau-neutrinoneutrino

ννττ

HadronsHadrons

Baryons Spin ½ or Baryons Spin ½ or 33//22 Mesons Spin 0 or 1Mesons Spin 0 or 1

ProtonProton

pp

NeutronNeutron

nn

LamdaLamda

ΛΛ

Sigma-plusSigma-plus

ΣΣ ++

Sigma-zeroSigma-zero

ΣΣ 00

Omega-minusOmega-minus

ΩΩ --

OthersOthers

Pion-zeroPion-zero

ππ 00

Pion-plusPion-plus

ππ ++

Kaon-plusKaon-plus

ΚΚ ++

Kaon-zeroKaon-zero

ΚΚ 00

OthersOthers

nucl

eu

s

-e

-e

-e 0

0

0

0

0

0

+e

+e

+e

+e

0

0

-e

Charge

Charge

Particle ExchangeParticle ExchangeThe 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.

e-

e-

e-

e-

γ

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.

This is an example of the electromagnetic force interactions.

Particle ExchangeParticle ExchangeThere is a similar interaction for the other forces. For Gravitational Forces, the exchange particles are called gravitons but these haven’t been observed yet.

n

π0

The Strong Force is what holds quarks together in a nucleon, and their exchange particles are called gluons.

n

nn

p

π+

n

pn

n

π -

p

np

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 ExchangeParticle ExchangeFor 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.

νe

W+

n

p+e-

p+

W-

n e-

π -e-

The above Feynman diagrams show the neutino-neutron interaction, β- decay interaction, and the electron-antineutrino collision interaction, respectively.

e- νe

νeνe

Beta DecayBeta DecayBeta 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 ParticlesDetecting ParticlesDetectors are needed to reveal the paths of the particles produced in experiments using particle accelerators.

Bubble ChamberFilled 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 ParticlesDetecting ParticlesDrift ChamberA 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

RefractionRefractionWhen 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.

Angle of incidence

Angle of refraction

RefractionRefractionThe 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 = c1/c2 = n1/n2

Snell’s Law states: 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 AngleCritical AngleWhen 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 stagesof refraction, from normal refraction, to the critical angle, tototal internal reflection.

Fibre OpticsFibre 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 EffectPhotoelectric 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 EffectPhotoelectric EffectThe 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 EffectPhotoelectric EffectThe 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 DualityWave Particle DualityWaves show particle-like behaviour, and particles show wave-like 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 LevelsSpectra and Energy LevelsThe 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 LevelsSpectra and Energy LevelsAn 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

SummarySummary ParticlesParticles

– Rutherford ScatteringRutherford Scattering– Constituents of the AtomConstituents of the Atom– ““Four Force” ModelFour Force” Model– Quarks and AntiquarksQuarks and Antiquarks– Particles and AntiparticlesParticles and Antiparticles– Particle FamiliesParticle Families– Particle ExchangeParticle Exchange– Beta DecayBeta Decay– Detecting ParticlesDetecting Particles

Electromagnetic Radiation and Electromagnetic Radiation and Quantum PhenomenaQuantum Phenomena– RefractionRefraction– The Photoelectric EffectThe Photoelectric Effect– Wave Particle DualityWave Particle Duality– Spectra and Energy LevelsSpectra and Energy Levels