Particles and Radiation

nuclide notation

a nucleon is a proton or a neutron (a particle inside the nucleus)

nucleon number, A, is the combined number of protons and neutrons inside that nucleus

proton number, Z, the number of protons in the nucleus. this defines the element

nuclide and isotope

nuclide — a specific type of nucleus defined by its number of protons and neutrons

isotopes — atoms of the same element (same proton number, Z) but with different neutron numbers

changing neutron number doesn’t affect the atom’s chemical properties but rather it affects the stability of the nucleus

(in general, the greater the number of neutrons compared to protons, the more unstable the nucleus)

specific charge

the ratio of a particle’s charge (C) to its mass (kg)

charge / mass

electromagnetic force in the nucleus

causes the positively charged protons

to repel each other

extends over an infinite range - longer than other fundamental mental forces - particles don’t have too be as close together to interact via this force

gravitational force in nucleus

causes all the nucleons on the nucleus to attract each other due to their mass

this is much smaller in magnitude (due to the very small masses of nucleons) than the electromagnetic force — negligible

strong nuclear force in nucelus

an attractive force that is stronger than the electromagnetic force

keeps nuclei stable by overcoming the electrostatic force of repulsion between protons

acts between all nucleons

very short range of only a few fm — can’t hold together very large, unstable nuclei

repulsive for very small nucleon separations of less than 0.5fm

0 at 0.5fm

as separation increases to between 0.5-3fm, snf is attractive and reaches a maximum attractive value

rapidly falls towards 0 above 3fm

nuclear decay

the process of unstable nuclei emitting particles to become more stable

alpha decay

usually happens only in heavy nuclides with proton number greater than 82

emit an alpha particle from their nucleus

energy is released, with most transferred to the alpha particle as kinetic energy. a small amount goes to the decayed nucleus.

nucleon number decreases by 4

proton number decreases by 2

alpha particles have a very short range of only a few cm in air and can be stopped by a sheet of paper

beta decay

beta minus

• neutron is changed into proton

• high speed electron ejected from the nucleus along with an antineutrino particle which carries away some energy and momentum

• happens in neutron rich nuclei

• nucleon number doesn’t change

• proton number increases by 1

beta plus

• a proton is changed into a neutron

• high speed positron ejected from the nucleus along with a neutrino

• nucleon number doesn’t change

• proton number decreases by 1

both types of beta decay have a range of a few metres in air and can be stopped by an aluminium sheet

gamma radiation

• emitted following alpha or beta emission

• by unstable nucleus with too much energy

• no mass or charge

hypothesis of neutrinos

• whilst the nucleus of any particular nuclide is known to release a fixed amount of energy during beta decay,

• kinetic energies of emitted beta particles varied up to a maximum value

• missing energy violated conservation of energy

• suggested that a third particle, antineutrino, must be produced which shares a proportion of released energy with the beta particle, carrying it away

• so another particle must be emitted alongside the beta particles and thus should be neutral ( to conserve charge) and have zero or negligible mass (as it had never been detected) 

antiparticles

• every particle had corresponding antiparticle

• equal in rest mass and rest energy but opposite in charge (if charged)

electron volt eV

1eV = 1.6 x 10^-19 J

the energy transferred when an electron is moved through a potential difference of 1V

rest energy

• energy equivalent to the rest mass of the particle

total energy conserved in interaction =

total energy = rest energies before interaction + kinetic energies before interaction = rest energies after interaction + kinetic energies after interaction

pair production

photon passing near nucleus / atom

when energy is converted into mass, equal amounts of matter and antimatter are produced. 

it must always produce a particle and its corresponding antiparticle because certain quantities must be conserved.

E_min = 2E₀

2E because each particle has the same rest energy as the other as they are a particle and antiparticle pair

• minimum energy of photon needed to produce at least the combined rest mass of the the particle and its antiparticle

• If the photon has greater than the required minimum energy, then the remaining energy is transferred to the particle and antiparticle pair as kinetic energy, carried away by them

annihilation

when a particle comes into contact with its corresponding antiparticle, the combined rest mass of the particle and the antiparticle is converted into energy in the form of two gamma ray photons which move in opposite directions to conserve momentum

• a minimum energy of photon produced, corresponding to an annihilation taking place at rest

electromagnetic spectrum

a continuous spectrum of all the possible frequencies of electromagnetic radiation.

• frequency - number of waves passing a point per second

• wavelength - distance between adjacent crests of a wave

• the higher the frequency of EM radiation, the greater its energy.

photon model of EM radiation

photon - a discrete packet, quanta, of EM energy / waves ( em waves emitted as short burst of waves, each packet leaving source in different direction)

0 rest mass

the four fundamental forces

• strong - gauge boson is pion. affects hadrons only

• electromagnetic - gauge boson is the virtual photon. affects charged particles only

• weak - gauge boson is the W+ and W- bosons. affects all types of particles

• gravitational is incredibly weak in comparison to all of these. affects all particles with mass.

exchange particles / gauge bosons

• how forces act between two particles

• virtual particles, cannot be directly detected - existing only for a very short time - long enough to transfer energy, momentum and other properties during an interaction

• they have momentum. resultant force acting on the particles from the transfer of exchange particle causes a change in momentum - the paths of interacting particles change - to conserve momentum

• the charge on a W boson must allow for conservation of charge before and after interaction on both sides of feynman diagram

• the size of the exchange particle determines the range of the force - heavier have shorter range - force itself has shorter range

electron capture

• proton in a proton rich nucleus can capture an inner shell electron

• proton changes into a neutron

• electron changes into neutrino and emitted

• the proton is acting on the electron so the W+ boson comes from the  proton.

electron proton collision

• electron collides with high speed with a proton.

• proton becomes a neutron

• electron becomes a neutrino and is emitted.

• the electron acts on the proton so the W- boson comes from the electron.

weak nuclear force involved in beta decays

• they involve leptons which do not feel strong nuclear force

• involves quark change

• W+ and W- bosons have rest mass

decay of muon

• produces electron, electron antineutrino and muon neutrino

strangeness and strange quarks

• S and anti S quarks are heaviest

• kaons and antikaons are not the same particle as their strangeness differs

• k + has strangeness +1

• strange particles are created in strong interactions and created in pairs to conserve charge and strangeness

• strange particles decay via the weak interactions

• strangeness conserved in strong interactions

• strangeness can only change by +1, -1 or 0

quark structures of hadrons and stability

• hadrons not fundamental - consist of quarks - smaller particles that are fundamental

• baryons - 3 quarks

• mesons - quark and antiquark pair

• proton is the only stable hadron and the only stable baryon - all other baryons eventually decay into protons

• all mesons are unstable:

• kaons most unstable, short lifetime and decay into pions or a muon and antineutrino or an antimuoun and a neutrino

• charged pions decay into muon and antineutrino or an antimuon and neutrino

• neutral pions decay into high energy photons

• baryon number always conserved

• charge always conserved

leptons

• fundamental - don’t break down into smaller non leptons

• electrons, muons and neutrinos

• lepton numbers for electrons and muons considered seperately and is always conserved

• charge always conserved