Atoms are made up of:
- Protons - +1 charge, relative mass 1.
- Neutrons - 0 charge, relative mass 1.
- Electrons - -1 charge, relative mass 0.0005.
The proton number defines the element. In a neutral atom, the number of protons = the number of electrons.
Atoms with the same number of protons but different numbers of neutrons are called isotopes.
- Changing the number of neutrons doesn't affect the atom's chemical properties, though it can affect the atom's stability.
- The greater the number of neutrons compared with the number of protons, the more unstable the nucleus.
- Unstable nuclei may be radioactive and decay to become more stable.
The Strong Nuclear Force
- The strong nuclear force holds the nucleus together. To do this it must be stronger than the electrostatic force.
- It is an attractive force that has a very short range (3-4fm).
- This force works equally between all nucleons. The size of the force is the same whether it's proton-proton, neutron-neutron or proton-neutron.
- At a very close distance the strong nuclear force must be repulsive to prevent nucleons crushing inwards continuously.
- Alpha emission happens in very big atoms (with more than 82) protons, such as Uranium and Radium. This is because the atoms are too big for the strong force to keep them stable.
- When an alpha (α) particle is emitted, the proton number decreases by two and the nucleon number decreases by four.
- 2 protons and 2 neutrons are emitted.
- Beta-minus (β-) decay occurs in isotopes that are 'neutron rich' (too many more neutrons than protons in their nucleus).
- In the decay, a neutron changes into a proton, and an electron and antineutrino are emitted.
- The proton number increases by one, and the nucleon number stays the same.
- In beta decay, a neutral particle called an 'anitneutrino' is released. this antineutrino carries away some energy and momentum.
Antiparticles and Mass-Energy
- Every particle has a corresponding antiparticle with the same mass but opposite charge.
- Energy can turn into mass and mass can turn into energy.
- When energy is converted into mass you get equal amounts of matter and antimatter.
- Firing two protons at each other at high speed will result in a lot of energy upon impact. This energy may be converted into more particles.
- If an extra proton is formed then there will always be an antiproton to go with it - pair production.
- Pair production can only happen if one gamma ray photon (γ) has enough energy to produce that much mass.
- It tends to happen near a nucleus, which helps to conserve momentum.
- Electron-positron pairs are the most commonly produced because they have a relatively low mass.
- When a particle meets its corresponding antiparticle the result is annihilation.
- All the mass of the particle and antiparticle gets converted back to energy.
- Antiparticles do not exist in ordinary matter because it only takes a fraction of a second for them to annihilate with a particle.
- Hadrons experience the strong nuclear force.
- Hadrons are not fundamental particles - they are made up of quarks.
- There are two types of hadron - baryons (3 quarks) and mesons (2 quarks).
- Examples of baryons include protons and neutrons.
- The proton is the only stable baryon. All other baryons decay to a proton.
- The antiparticles of protons and neutrons are antibaryons.
- The baryon number is the number of baryons. The proton and neutron each have baryon number = +1.
- Antibaryons have a baryon number = -1, non-baryons have a baryon number = 0.
- Baryon number is always conserved in an interaction (the total baryon number on one side of the equation is equal to the baryon number on the other side).
- Quarks have baryon number +1/3.
- All mesons are unstable and have baryon number B = 0 (they're not baryons).
- Pions (π-mesons) are the lightest mesons - there are 3 versions (π+, π0, v-).
- They were discovered in cosmic rays and occur in high-energy collisions, such as those at CERN.
- Kaons (K-mesons) are heavier and more unstable than pions.
- Mesons interact with baryons via the strong force.
- Leptons are fundamental particles that don't experience the strong force.
- They interact with other particles mainly via the weak force.
- There are three leptons: the electron (e-), the muon (μ-) and the tau (τ-).
- Muons and taus are unstable, and decay into electrons.
- The electron, muon and tau leptons come with their own neutrinos.
- Neutrinos have zero or almost zero mass, and zero electric charge. They only take part in weak interactions.
- Each lepton (including lepton neutrinos) is given a lepton number of +1, but the electron, muon and tau have to be counted separately.
- There are 3 different lepton numbers - Le, Lμ and Lτ.
- The up quark (u) has a charge +2/3, baryon number 1/3 and a strangeness of 0.
- The down quark (d) has a charge -1/3, baryon number 1/3 and a strangeness of 0.
- The strange quark (s) has a charge -1/3, baryon number 1/3 and a strangeness of -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.
- Proton = uud. Total charge = 2/3 + 2/3 - 1/3 = 1. Baryon number = 1/3 + 1/3 + 1/3 = 1.
- Neutron = udd. Total charge = 2/3 - 1/3 - 1/3 = 0. Baryon number = 1/3 + 1/3 + 1/3 = 1.
Antiquarks are the same, with opposite baryon number and charge.
Mesons and Quarks
- Mesons are made up of a quark and an antiquark.
- Pions are made from combinations of up, down, anti-up and anti-down quarks. Kaons have strangeness.
Quark Confinement and Colour Charge
- Quarks never occur in isolation - they are always found in quark-antiquark pairs (such as in mesons) or in triads (baryons).
- Quarks are bound together by 'colour force'. It is constant, and does not decrease with distance. When two quarks are separated, at some point it becomes more energetically favourable for a new quark-antiquark pair to spontaneously appear, than to allow the two separated quarks to move further apart.
- This is a property of quarks and gluons.
- A quark's 'colour' can be red, green or blue (the primary colours).
- An antiquark's 'colour' can be anti-red, anti-green or anti-blue (represented as cyan, magenta and yellow respectively).
- Gluons are mixtures of two colours.
- The quark and antiquark colours combine to be colourless (or white). Only colourless combinations of quarks can exist.
The Weak Interaction and Positron Emission
The Weak Interaction:
- The weak interaction changes the quark type. No other interaction does this.
- Affects all fermions (all particles with half integer spin).
- The exchange particles are the W and Z bosons.
- In β- decay a neutron (udd) changes into a proton (uud). This means turning a down quark into an up quark.
- Occurs when the nucleus has too many protons compared to neutrons.
- Some unstable isotopes like Carbon-11 decay by β+ emission. Here a proton (uud) changes into a neutron (udd).
- An electron neutrino and a positron are emitted.
- Nuclei which decay by positron emission may also decay by electron capture.
Charge: In any particle interaction, the total charge before the interaction must equal the total charge before the interaction.
Baryon Number: In any particle interaction, the baryon number before the interaction must equal the baryon number after the interaction.
Strangeness: The only way to change the type of quark is via the weak interaction. In strong interactions therefore there must be the same number of strange quarks before interaction as afterwards. This means the strangeness is conserved for interactions involving the strong force. The strangeness can be changed by one value at a time via the weak force.
Lepton Number: The 3 types of lepton number (Le, Lμ, Lτ) have to be conserved separately. I.e. the Le before interaction must equal the Le after interaction.
Forces and Exchange Particles
All forces in nature are caused by four fundamental forces. Each has its own gauge boson.
- Gauge boson: Gluon
- Particles affected: Hadrons
- Gauge boson: W+, W-, Zº
- Particles affected: All types
- Gauge boson: Photon
- Particles affected: Charged particles
- Gauge boson: Graviton?
- Particles affected: All types
- The larger the mass of the gauge boson, the shorter the range of the force.
- The W bosons have a mass of about 100 times that of a proton, which gives the weak force a very short range. Creating a virtual W particle uses so much energy it can only exist for a very short time and it can't travel far.
- The photon has zero mass, which gives the electromagnetic force infinite range.
- Gravity is a very weak force compared to the other 3 fundamental forces. It is only significant when dealing with large masses such as stars. There is no evidence for the graviton yet.
- Above is the Feynman diagram for β- decay (when a neutron decays into a proton and emits an electron and anti-neutrino).
- The wavy lines represent gauge bosons, in this case the W- boson.
- The straight lines represent particles.
- In this diagram, time goes upwards. However some Feynman diagrams are drawn with time going from left to right.
Feynman Diagrams (2)
- This above is the interaction of two electrons. Each electron represents a straight line.
- They exchange a photon and repel each other (the electromagnetic force).
Feynman Diagrams (3)
- Here is the same interaction with time going from left to right.
- Generally, they are drawn with time going vertically upwards.
Feynman Diagrams (4)
Rules For Drawing Feynman Diagrams
- Incoming particles start at the bottom of the diagram and move upwards (time starts at the bottom and goes vertically upwards).
- The baryons stay on one side of the diagram, and the leptons stay on the other side.
- The W bosons carry charge from one side of the diagram to the other.
- A W- particle going to the left has the same effect as a W+ particle going to the right.
Neutrinos seldom interact with matter, but interactions do occur.
- Here is a neutrino-neutron collision. A proton and an electron are produced.
Neutrino Interactions (2)
- This is the same interaction, however a W- boson goes from the left to the right instead of a W+ boson going from the right to the left.
- A proton and an electron are produced, like before.
Neutrino Interactions (3)
- Here is a proton-antineutrino collision.
- A proton and an anitneutrino collide and produce a neutron and a positron.
- In proton-rich nuclei, a proton may turn into a neutron via β+ decay. However, another process called 'electron capture' may happen.
- The nucleus absorbs an inner atomic electron (changing a nuclear proton to a neutron) and emits a neutrino.