Section 1 - Particles - complete

- inside every atom theres a nucleus containing protons and neutrons (nucleons)
- orbiting the nucleus are electrons
- the particles within an atom all have different properties (e.g. charge, mass etc)

(Particle - Charge (coulombs, C) - Mass (kg) - Relative Charge - Relative Mass)
- Proton - +1.6 x 10^-19 - 1.67 x 10^-27 - +1 - 1
- Neutron - 0 - 1.67 x 10^--27 - 0 - 1
- Electron - -1.6 x 10^-19 - 9.11 x 10^-31 - -1 - 0.0005

- the proton number is also known as the atomic number and has the symbol Z
- the proton number is what defines the element
- in a neutral atom, the number of electrons will equal the number of protons
- the element's reactions and chemical behaviour depend on the number of electrons

- the nucleon number is also known as the mass number and has the symbol A
- the nucleon number tells you how many neutrons and protons are in the nucleus
- therefore, the number of neutrons = mass number - proton number
- also, as both protons and neutrons have a mass of ~1, mass number = atoms relative mass

- atoms with the same number of protons but different numbers of neutrons are called isotopes
Example
hydrogen has three natural isotopes, hydrogen, deuterium and tritium. hydrogen has 1+ and 0 neutrons. deuterium has 1 proton and 1 neutron. tritium has 1 proton and 2 neutrons
- changing the number of neutrons doesnt affect the atom's chemical properties
- the number of neutrons does affect the stability of the nucleus
- unstable nuclei may be radioactive and decay over time into different nuclei that are more stable

- all living things contain the same percentage of radioactive carbon-14 taken in from the atmosphere
- after they die, the amount of carbon-14 inside them decreases over time as the carbon-14 decays to stable elements
- scientists can calculate the approximate age of archaeological finds made from dead organic matter (e.g. wood, bone) by using the isotopic data (amount of each isotope present) to find the percentage of radioactive carbon-14 that's left in the object

- the specific charge of a particle is the ratio of its charge to its mass, given in coulombs per kilogram (Ckg^-1)
- to calculate specific charge, just divide the charge, in C, by the mass (in kg)

Example
calculate the specific charge of a proton
charge = 1.6 x 10^-19
mass = 1.67 x 10^-27
specific charge = 1.6x10^-19 / 1.67x10^-27 = 9.58 x 10⁷ Ckg^-1 (3 s.f.)

- there are several different forces acting on the nucleons in a nucleus
- two commonly known ones are electrostatic forces from the protons electric charges, and gravitational forces due to the masses of the particles
- repulsion from the electrostatic force is much bigger than the gravitational attraction
- if these two forces were the only ones, the nucleons would fly out of the nucleus
- therefore there must be another force keeping the nucleus together (strong nuclear force)

- to hold the nucleus together, it must be an attractive force thats stronger than the electrostatic force
- it has a very short range and can only hold nucleons together when they're separated by up to a few femtometres (1x10^-15m)  (the size of a nucleus)
- the strength of the SNF quicly falls beyond this distance
- SNF works equally between all nucleons (whether its proton-proton, neutron-proton or neutron-neutron
- at very small distances apart, the SNF must be repulsive or it would crush the nucleus to a point

- the SNF can be plotted on a graph showing how it changes with the distance of separation between nucleons
- if the electrostatic force is also plotted, you can see the relationship between these two forces
- the SNF is repulsive for very small separations of nucleons
- as nucleon separation increases past about 0.5 fm, the strong nuclear force becomes attractive
- it reaches a maximum attractive value and then falls rapidly towards 0 after about 3 fm
- the electrostatic repulsive force extends over a much larger range

- alpha emission only happens in very big nuclei like uranium and radium
- the nuclei of these atoms are too big for the strong nuclear force to keep them stable
- when an alpha particle is emitted, the proton number decreases by two, and the nucleon number decreased by four
- alpha particles have a very short range, only a few cm in air
- the range can be seen by observing the tracks left by alpha particles in a cloud chamber
- geiger counters can also be used by bringing the alpha source close
- then move it away slowly and observe how the count rate drops

- beta-minus decay is the emission of an electron from the nucleus along with an antineutrino
- beta decay happens in isotopes that are unstable due to being 'neutron rich' (i.e. they have too many more neutrons than protons)
- when a nucleus ejects a beta particle, one of the neutrons in the nucleus is changed into a proton
- the proton number increases by 1 and the nucleon number stays the same
- in beta decay, you get a tiny neutral particle called an antineutrino
- the antineutrino carries away some energy and momentum

- scientists originally thought that the only particle emitted from the nucleus during beta decay was an electron
- however, they found that the energy of the particles after beta decay was less than it was before meaning that it didnt fit with the principle of conservation of energy
- 1930 - wolfgang pauli suggested another particle was being emitted too, and it carried away the missing energy
- the particle had to be neutral or the charge wouldn't be conserved in beta decay
- it also had to have (~)0 mass as it had never been detected
- other discoveries led to pauli's theory becoming accepted and the particle was named the neutrino (antineutrino)
- the neutrino was eventually observed 25 years later, proving Pauli's hypothesis

- visible light is just one type of electromagnetic radiation
- the electromagnetic spectrum is a continuous spectrum of all the possible frequencies of electromagnetic radiation
- the frequency 'f' and wavelength are linked by f = speed of light in a vacuum / wavelength
- c  = speed of light = 3.00 x 10⁸ ms^-1
- electromagnetic radiation exists as photons of energy
- the energy of a photon depends on the frequency of the radiation

E = hf = hc/wavelength
(h = Planck constant = 6.63 x 10^-34 Js

- every particle has an antiparticle with the same mass and rest energy 
- example: an antiproton is a negatively-charged particle with the same mass as a proton
- example 2: an antineutrino is the antiparticle of the neutrino
(particle > antiparticle)
- proton > antiproton
- neutron > antineutron
- electron > positron
- neutrino > antineutrino

- neutrinos and antineutrinos are incredibly tiny so assume they have 0 mass and 0 rest energy

- energy can turn into mass and mass can turn into energy
- the rest energy of a particle is just the 'energy equivalent' of the particle's mass, measured in MeV
- you can work out the rest energy using the formula E=mc²
- when energy is converted into mass you get equal amounts of matter and antimatter

- fire two protons at each other at high speed
- you end up with a lot of energy at the point of impact
- this energy might be converted into more particles
- if an extra proton is formed then there will always be an antiproton to go with it
- this is called pair production

- energy that gets converted into matter and antimatter is in the form of a photon
- pair production only happens if one photon has enough energy to produce that much mass
- only gamma ray photons have enough energy for this
- pair production tends to happen near a nucleus, which helps conserve momentum
- the most common pair is electron-positron because they have a relatively low mass
- the minimum energy for a photon to undergo pair production is the total rest energy of the particles produced
- the particle and antiparticle each have a rest energy of E₀, so: E_min = hf_min = 2E₀
- the particle tracks are curved because there's usually a magnetic field present in particle physics experiments
- they curve in opposite directions because of the opposite charges on the electron and positron

- when a particle meets its antiparticle the result is annihilation
- all the mass of the particle and antiparticle gets converted back to energy
- antiparticles can usually only exist for a fraction of a second before this happens, so they dont exist in ordinary matter
- an annihilation is between a particle-antiparticle pair, which both have a rest energy E₀
- both photons need to have a minimum energy, E_min, which when added together equals at least 2E₀ for energy to be conserved in this interaction
- so, 2E_min = 2E₀ and E_min = hf_min = E₀

EXAMPLE
Calculate the maximum wavelength of one of the photons produced when an electron and positron annihilate each other
minimum photon energy = E_min = hf_min = E₀ 
f = c/wavelength so hc/wavelength_max = E₀
so max wavelength = hc/E₀ = (6.63x10-34)x(3.00x10⁸) / (0.511x10⁶)x(1.60x10^-19) = 2.43 x 10^-12m

- you cant have instantaneous action at a distance
- when two particles interact, something must happen to let one particle know that the other one is there

Example: 1) Ball 2) Boomerang
1) repulsion - each time the ball is thrown or caught the people get pushed apart, which happens because the ball carries a momentum
(particle exhange also explains attraction)
2) attraction - each time the boomerang is thrown or caught the people get pushed together

- these exchange particles are called gauge bosons
- the repulsion between two protons is caused by the exchange of virtual photons, which are the gauge bosons of the electromagnetic force
- gauge bosons are virtual particles, meaning they only exist for a very short time

- all forces in nature are caused by four fundamental forces
- strong nuclear force, weak nuclear force, electromagnetic force, gravity
- each one has its own gauge boson
(force - gauge boson - particles affected)
- electromagnetic - virtual proton - charged particles only
- weak - W⁺ or W^- - all types
- strong - pions (pi⁺, pi^-, pi⁰) - hadrons only
- gravity is feeble compared with the other types of interaction (forces) so is not really mentioned
- gravity only really matters when using big masses like stars and planets
- pions are described as being exchanged between nucleons OR gluons being exchanged between quarks

- the larger the mass of the gauge boson, the shorter the range of the force
- the weak bosons have a mass of ~100x bigger than a proton
- this means they have a very short range
- creating a virtual W particle uses so much energy that it can only exist for a very short time and cannot travel far
- however, a photon has zero mass meaning it has a force with infinite range (can travel very far)

- gauge bosons are represented by wiggly lines
- other particles are represented by straight lines

Rules
- incoming particles start at the bottom of the diagram and move upwards
- the baryons and leptons cant cross from one side to the other
- make sure the charges on both sides balance (W bosons carry charge from one side to the other)
- a W^- particle going to the left has the same effect as a W⁺ particle going to the right

Electromagnetic Repulsion
- when two particles with equal charges get close to each other, they repel

Beta-plus and Beta-minus Decay
- n -> p + e^- + ^-v_e  (beta-minus decay)
- p -> n + e⁺ + v_e (beta-plus decay)
- you get an antineutrino in beta^- decay and a neutrino in beta⁺ decay so the lepton number is conserved

- electrons and protons are attracted by the electromagnetic interaction between them
- if a proton captures an electron, the weak interaction can make this interaction happen
- p + e^- -> n + v_e 

- electron-proton collisions are where an electron collides with a proton
- the equation is the same as electron capture
- in the diagram, a W^- boson replaces the W⁺ boson and travels in the opposite direction (electron to proton instead of proton to electron)

- a nucleus has nucleons in it
- since the protons are positive they need the SNF (strong interaction) to hold them together
- particles which can feel the SNF are called hadrons
- hadrons are not fundamental particles and are made up of quarks
- there are two types of hadrons: baryons (and anti-baryons) and mesons
- they're classified according to the number of quarks that make them up

- protons and neutrons are both baryons
- there are other baryons that dont exist in normal matter (e.g. sigmas)
- all baryons (except the proton) are unstable and they decay to become other particles
- the partices a baryon ends up as depends on what it is, but a proton is always included as they are the only stable baryons
- antiprotons and antineutrons are antibaryons
- because antiparticles are annihilated when they meet their particle, antibaryons dont exist in ordinary matter

- the baryon number is the number of baryons (i.e. similar to the nucleon number but including unusual baryons like sigma)
- protons and neutrons each have a baryon number B = +1
-antibaryons have a baryon number B = -1
- things that arent baryons have a baryon number B = 0 
- baryon number is a quantum number meaning it must be conserved in any interaction
- this means it can only take on a certain set of values 
- when an interaction happens, the baryon number on either side of it has to be the same
- this can be used to predict if an interaction will happen or not
- if the numbers dont match, the interaction cant happen
- the total baryon number in any particle interaction never changes

- beta decay involves a neutron changing into a proton which happens when there are a lot more neutrons than protons or when a neutron is outside of the nucleus
- when this happens it forms a proton, electron and antineutrino (beta+ decay)
- electrons and antineutrinos are leptons so they have a baryon number of 0
- neutrons and protons are baryons so B=1
- therefore, on both sides of the equation B = 1 meaning the interaction can happen

- all mesons are unstable and have baryon number B = 0
- pions (pi-mesons) are the lightest mesons
- there is a +ve, -ve and neutral pion
- there are lots of pions in high-energy particle collisions
- Kaons (K-mesons) are heavier and more unstable than pions
- you get kaons like K⁺ and K⁰
- kaons have a very short lifetime and decay into pions
- pions and kaons were discovered in cosmic rays 
- cosmic ray showers are a source of pions and kaons
- you can observe their tracks with a cloud chamber
- mesons interact with baryons via SNF
- pion interactions swap protons with neutrons and neutrons with protons, but leave the baryon number unchanged

- leptons are fundamental particles and dont feel SNF
- they only really interact with other particles via the weak interaction, along with gravitational and electromagnetic if theyre charged
- electrons are a type of stable lepton
- muons are heavy electrons
- muons are unstable and eventually decay into ordinary electrons
- electron and muon leptons each have a neutrino v_e and v
- neutrinos have (~)0 mass and 0 electric charge
- neutrinos only take part in weak interactions 

- the lepton number is the number of leptons
- each lepton is given a lepton number of +1 but the electron and muon types of lepton have to be counted seperately
- you get different lepton numbers for each: L_e and L
- all leptons and lepton neutrinos have antiparticles too
- the antiparticles have the opposite charge and lepton numbers to their counter-particles
- for example, a muon has a charge of -1 so the antimuon has a charge of +1

(name - symbol - charge - L_e - L )
- electron - e^- - -1 - +1 - 0
- electron-neutrino - v_e - 0 - +1 - 0
- muon -  ^- - -1 - 0 - +1
- muon-neutrino - v  - 0 - 0 - +1

- quarks are the building blocks for hadrons 
- antiparticles of hadrons are made from antiquarks
- to make protons and neutrons you need two types of quarks - the up quark (u) and the down quark (d)
- an extra one called the strange quark (s) makes more particles with a property called strangeness
- strangeness is a quantum number and can only take a certain set of values
- strange particles (e.g. kaons) are created via the SNF but decay via the weak interaction
- strangeness is conserved in the SNF but not in the weak interaction
- strange particles are always produced in pairs (e.g. K⁺ and K^-)
- one has a strangeness of +1 and the other is -1 so strangeness of 0 is conserved

Quarks
(name - symbol - charge - baryon number - strangeness)
up - u - +2/3 - +1/3 - 0
down - d - -1/3 - +1/3 - 0
strange - s - -1/3 - +1/3 - -1

Antiquarks
(name - symbol - charge - baryon number - strangeness)
anti-up - u - -2/3 - -1/3 - 0
anti-down - d - +1/3 - -1/3 - 0
anti-strange - s - +1/3 - -1/3 - +1

- evidence for quarks came from hitting protons with high-energy electrons
- the way the electrons scattered showed that there were three concentrations of charge (quarks) inside the proton
Protons & Antiprotons
- proton = uud
- total charge = 2/3 + 2/3 - 1/3 = 1
- baryon number = 1/3 + 1/3 + 1/3 = 1
- antiprotons = uud
- total charge = -2/3 - 2/3 + 1/3 = -1
- baryon number = -1/3 -1/3 -1/3 = -1

Neutrons & Antineutrons
- neutron = udd
- total charge = 2/3 - 1/3 - 1/3 = 0
- baryon number = 1/3 + 1/3 + 1/3 = 1
- antineutron = udd
- total charge = -2/3 + 1/3 + 1/3 = 0
- baryon number = -1/3 - 1/3 - 1/3 = -1

- pions are made from combinations of up, down, anti-up and anti-down quarks
- kaons have strangness as well
- pi^- meson is the antiparticle of the pi⁺ meson
- K^- meson is the antiparticle of the K⁺ meson
- antiparticle of pi⁰ meson is itself

- in beta^- decay, udd changes into uud
- only weak interaction can change a d quark into a u quark
- some unstable isotopes like carbon-11 decay by beta⁺ emission
- in this case a uud changes into a udd which can only be done by weak interaction

Charge
- the total charge before the interaction must equal the total charge after the interaction

Baryon Number
- in any particle reaction, the baryon number before and after must be equal

Strangeness
- the only way to change a type of quark is with the weak interaction
- in strong interactions there has to be the same number of strange quarks at the beginning as at the end
- in weak interactions, strangeness can change by -1, 0 or +1
- the interaction K^- + p -> n + pi⁰ is fine for charge and baryon number but not for strangeness so it wont happen
- the negative kaon has an s quark in it

Lepton Number
- the different types of lepton number have to be conserved separately
Example
- the interaction pi^- -> µ + ^-v(µ) has L(µ) = 0 at the start and L(µ) = 1-1 = 0 at the end so it works
- also, n -> p + e + ^-v_e works because L_e = 0 at the start and L_e = 1-1 = 0 at the end
However:
- v(µ) + µ -> e^- + v_e cant happen because at the start L(µ) = 2 and L_e = 0 but at the end L(µ) = 0 and L_e = 2

- if you blasted a proton with enough energy, the quarks wouldnt separate
- the energy would get changed into more quarks and antiquarks
- this would be pair production again and you would just make mesons
- quark confinement means it is impossible (atm) to get a quark by itself

- as time goes on our understanding of physics changes
- new theories are created to try to explain observations from experiments
- sometimes physicists hypothesise a new particle and the propertis they expect it to have
- experiments to try to find the existence of this new particle are then carried out
- results from different experiments are combined to try to confirm the new particle
- if it exists, the theory is more likely to be correct and the scientific community will start to accept it meaning it has been validated
- however, experiments in particle physics often need particles travelling at incredibly high speeds 
- this can only be achieved using particle accelerators
- these huge pieces of equipment are very expensive to build and run
- this means that large groups of scientists and engineers from all over the world have to collaborate to be able to fund these experiments