Particle Physics

AS Physics

Particle Physics

Electromagnetic Radiation and Quantum Phenomena

Particle Physics

Tracks left in a particle detector.

Contents

Constituents of the Atom
Stable and Unstable Nuclei
Alpha decay
Beta decay
Gamma rays
Particles, Antiparticles and Photons
Converting from Energy into Frequency/Wavelength
"Stamp Collecting" and the "Particle Zoo"
Leptons
Neutrinos... the ghost particle
Hadrons
Mesons
Baryons
Fundamental Forces
Conservation Rules
Feynman Diagrams
Some Real Decays...

Constituents of the Atom

Atoms are made of protons, neutrons and electrons.

Element is the name used for a 'type' of atom i.e. an atom defined by the number of protons it has e.g. Carbon has 6 protons.

Protons are positively charged
Electrons are negatively charged
Neutrons have NO charge

Schematic drawing of an atom..... in reality it doesn't look like this! Remember that this is a model. Electrons very rarely occupy very specific locations, rather they form probability clouds at discrete distances from the centre of the atom... You should think about what it means to 'see an atom', we see collections of them all the time (like a turnip or a tractor or Boris Johnson!), however, to 'see' individual atoms we need equipment and once you need equipment (like STM or TEM) is this really considered seeing... enter the philosopher!

Protons and neutrons (also called 'nucleons') are found in the nucleus (centre of the atom) and contain (almost!) all the mass of the whole atom.

Here is a summary of some key properties:

e and p have equal but opposite charge.

Charge is a unit measured in Coulombs, not to be confused with 'relative charge'.

The relative charge of e:p:n is -1:+1:0

The relative mass of e:p:n is 0:1:1

An atom has a net zero charge. If it loses an electron it becomes a positive ion, if it gains an electron it becomes a negative ion.

A = the 'nucleon' number or 'atomic mass number' or 'atomic mass unit' = p + n

Z = the 'atomic' number or 'proton number' = p

X = symbol for a particular element

e.g. If Carbon has A=12 and Z=6, then it must have 6 neutrons

Isotopes = "atom with the name number of protons but different number of neutrons"

Example = Carbon has several isotopes, the most common being Carbon-12. Carbon-13 and Carbon-14 are unstable and not found in abundance.

The isotope listed on the periodic table takes into account (percentage-wise) the ratio of naturally occurring isotopes.

Example of different isotopes of Carbon. C-12 is the most common. In more advanced periodic tables you will see Carbon-12.011, this is the summed average of carbon isotopes.

Stable and Unstable Nuclei

From basic intuition you would expect two things from the atom:
1) Since positively charge protons are packed together in the nucleus, why doesn't the nucleus just explode apart...?
2) Since electrons are attracted to protons, why don't the electrons fall into the nucleus...? (Not covered in A-level courses)

The answer to 1 is called the 'Strong Nuclear Force'. Since positive charges (i.e. protons) should repel each other because of electrostatic forces, there must be a short-range attractive force that keeps these nucleons together.

Example - When protons are 'far' apart they repel each other via repulsive electrostatic forces. As protons are brought close together (e.g. with fusion in the sun) the attractive strong force begins to 'win' against the repulsive electrostatic force. The strong force becomes significant at ~3 femto-meters. If those protons are then brought EVEN closer, then they will repel i.e. an atom has a radius of ~0.5fm, and since you cannot overlap one atom with another, they, in fact, repel each other. This is shown in the graph below:

This graph shows that at large separation electrostatic forces dominate.

As we bring those protons together the strong nuclear force makes them attract.

Finally, at really short distances those protons repel each other.

As atoms get bigger, the more influence the electrostatic force has, because protons from opposite sides of the atom will begin to repel each other, even though they are bound to their neighbours via the strong force.

The image on the right show how short distance forces are dominated by the strong force, whereas longer distance separations are influenced more by electrostatic forces.

To become more stable, an atom could decay in one of three ways: Alpha(α) , beta (β) and gamma (γ)

Alpha Decay

An alpha particle has 2p and 2n i.e. it is the same as a helium nucleus and is written as:

A convenient equation for alpha decay is:

i.e. element X decays into element Y and emits an alpha

Alpha particles are ‘heavy’ and have a relative charge of +2. It is therefore highly ionising and doesn’t go far without interacting with something.

Beta Decay

When a neutron decays into a proton it emits a fast moving electron; this is a beta- (β-) particle.

When a proton is converted into a neutron a positron ('positive electron') is emitted (more on this later...)

This is possible because the mass of a neutron is slightly higher than that of a proton.
mass of proton = 1.6726 × 10-27kg
mass of neutron = 1.6749 × 10-27kg

When a neutron decays there are other by-products which account for the remaining mass loss.

Beta particles are less ionising than alpha particles because they are smaller and have only a relative charge of -1.

The equation for Beta- decay is:

i.e. element X decays into element Y and emits a β- and an anti-electron-neutrino (see 'conservation laws' later)

Gamma Rays

Any excess energy that is left over from a decay is given out as electromagnetic radiation in the form of gamma rays.

These waves are highly penetrating; only impeded by thick metal.

Gamma often follows alpha and/or beta decay. The equation for gamma emission is:

Since no nucleons decay, A and Z remain the same

For a fuller description of these radioactive processes, see the Nuclear and Radioactivity section.

Particle, Anti-particles and Photons

For every particle there is an antiparticle.

A particle and anti-particle's (rest) mass is the same, however, their charges are opposite. Here is the basic logic behind this proposition

Any particle with mass (m) and velocity (v) has momentum (p):

One of Eintstein's most famous equations described the total energy (E) of a particle in terms of the speed of light (c):

For an object at rest, v = 0 ms-1

This means that the energy, E, can both a positive and a negative value... the origin for particles and anti-particles. When a particle meets its anti-particle they annihilate i.e. all their rest-mass energy is converted into energy. This energy can be calculated using Einstein's famous E=mc^2 equation.

Examples of particles/antiparticles:
- electron/positron
- proton/anti-proton
- neutron/anti-neutron
- neutrino/anti-neutrino....... etc.

Energy can be positive or negative because when we take the square root of a number its product can either be both positive or both negative e.g. -2x-2=4 as well as 2x2=4. Likewise (mass)x(mass)xc^2=E so too (-mass)x(-mass)xc^2=E

Annihilation = When a particle and antiparticle meet, converting their mass into energy.

Pair production = With enough energy, a photon can turn into a particle/anti-particle pair

Converting from energy into frequency/wavelength

c = speed of light
f = frequency
λ = wavelength
E = wave energy
h = Planck's constant = 6.63 x 10^-34

Electron volt (eV) = Work done on an electron in accelerating it through a potential difference of 1 Volt. It is a convenient unit for energy where 1eV = 1.6x10^-19 Joules

Example of pair production:

An electron has a rest mass energy of 0.511MeV.
To make an electron-positron pair you would need:
2 × 0.511MeV = 1.022 MeV
1.022MeV = 1.022 × (10^6)× (1.6×10^-19)
= 1.64 10^-13J

Frequency? Use E=hf
1.64 ×10^-13 = 6.63×10^-34×f
f = 2.5 × 10^20Hz

"Stamp collecting" and the "Particle Zoo"

Particles make up our universe and they interact with each other in very specific ways. The 'standard model' for particle physics is the phrase used to describe the fundamental interactions (/forces) between all the particles that we know. Before we get to those forces, lets group them into categories with similar properties. Firstly, elementary particles can be considered either matter/antimatter (known as fermions) or force particles (more commonly known as 'gauge' bosons). Matter/anti-matter can be subdivided into EITHER Hadrons (which are made up of quarks) OR Leptons (which cannot be divided further).

Leptons

There are three charged ('electron', 'mu' (pronounced like 'new') and 'tau') and three neutral leptons (the 'neutrinos'). Because of 'conservation laws' (see later) each lepton comes with an accompanying neutrino, because they are associated with the same decays. Neutrinos have a very small mass

Notice that the charge of the electron, muon and tau particle are all the same. However, their masses are very different. In fact, all leptons are stable apart from the muon and tau particle (and their antiparticles).

Muons can decay into electrons.

Neutrinos... the ghost particle

Neutrinos and anti-neutrinos are probably the most numerous particles in the universe. Created in β decay and nuclear fusion. They are very weakly interacting, which makes them difficult to detect. Neutrinos were hypothesised in order to take account of some missing energy in β decay. It was initially assumed that β particles would be emitted in β decay with the same amount of energy each time. However this wasn’t the case. There was some energy missing. This energy was later accounted for by including a very small mass that has no charge and doesn’t interact with much = neutrinos.

Hadrons

Hardons are made up of QUARKS (it is a debatable how this is pronounced!).

There are two types:
Baryons = 3 quarks
Mesons = quark and anti-quark

The quarks (u='up', d='down', s='strange') have the following properties:

The quark charges add up so that all hadrons have INTEGER CHARGE (i.e. their charge is a whole number). Anti-particles are denoted with a line above the letter.

"Strangeness" is a quantum number that is associated with strange quarks and is conserved in strong interactions.

For example, working out the charge of a proton and neutron:
A proton = Baryon = uud = 2/3 + 2/3 -1/3 = +1
A neutron = Baryon = udd = 2/3 - 1/3 - 1/3 = 0

The truth that AQA are hiding from you...

In reality there are 3 more quarks. You do not need to know about these for your exams, but its important to get the broader picture. These are called 'charm', 'top' and 'bottom' - you'll find them in all 'standard model' descriptions.

(if you are uninterested move on to the next section!).

The Meson Octet (quark+antiquark combos)

You don't "need to know" about the Meson Octet however, this is a great illustration of all the mesons you will encounter, in pictorial format. Mesons are shorted lived, because of matter/anti-matter interactions.

Notice in the picture on the left that:
blue lines connect mesons of equal charge.
red lines connect mesons of equal strangeness.

These mesons are called pions and kaons. Kaon's decay into pions and pions are the exchange particles of the strong interaction (see later).

'Strangeness' was introduced to explain the fact that some hadrons (K0 and Λ0) were created easily through the strong interaction, but decayed with lifetimes characteristic of the weak interaction. Collisions always seemed to produce pairs of these particles and so it was postulated that a new quantity called ‘strangeness’ had to be conserved in a strong interaction.

Baryons (3 quarks)

The number of baryon's before and after any decay/interaction is always conserved. The Baryon quantum number is denoted by the letter 'B'. Below are some combinations of Baryons that you could encounter, although you don't need to know about all of the quantum numbers, like isospin and spin.

In this diagram each Baryon is denoted by a pink ball with 3 quarks in it. Notice that 'strangeness' (S) goes from 0 to 1 to 2 to 3, from the top to the bottom of the diagram. And that charge (Q) goes from -1 to 0 to 1 to 2 from left to right.

The proton is the only stable Baryon into which other Baryons will decay.

Thanks wikipedia

Fundamental Forces

The fundamental forces govern all the interactions between particles. The only one missing here is the (infamous) Higgs boson.

Conservation Rules

In quantum mechanics (and particle physics) many values must be 'conserved' for an interaction to make sense e.g. in thermodynamics energy is always conserved, it is never created (out of nothing) or destroyed. So too here, there are many 'quantum numbers' that are always conserved in interactions. Particle and anti-particles have opposite quantum numbers e.g. the electron has an electron-lepton (Le) number of +1, the positron has an Le of -1.

The following are always conserved:
- charge (Q)
- lepton numbers (Le, Lmu, Ltau: where for example the electron and the electron-neutrino each have a value of 1)
- Baryon number (B) = all baryons have a baryon number = 1
- Strangeness (S) = only conserved in Strong interactions, not weak.
(- momentum and energy; but these are not quantum numbers)

This table summarises the lepton numbers:

Lepton Numbers

Anti-Lepton Numbers

Feynman Diagrams

Feynman diagrams can be used to illustrate particle interactions and decays. They represent particle motion in time. Here are a few interactions represented by Feynman diagrams. Remember: all quantum numbers are conserved.

Electron repulsion mediated by a virtual exchange photon

Beta- decay

Positron decay

Electron capture

neutron and electron-neutrino interaction

proton and anti-electron-neutrino interaction

Strong interaction

Some Real Decays...

In a cloud chamber a particle's trajectory can be tracked. Using the direction, length and splitting events of particles; a fundamental understanding of these particles can be amassed. Charged particles are deflected in magnetic fields (see Magnetic Fields), positive and negative charges deflect in opposite directions. Neutral particles follow straight paths. Fast charged particles have less curvature. Whereas heavy and charged particles will follow highly curved paths (leading to spirals)

Here is an example:

Left: Real tracks left behind in a cloud chamber/particle-detector. Right: schematic, trying to figure out which particles were where...

The incoming pion- collides with a stationary proton producing a neutral kaon and hyperon, due to charge conservation (and enough energy!).

They are neutral, not detected in the cloud chamber, but then decay. The Kaon is a meson and decays quickly.

Hyperon is a baryon and decays slowely i.e. has a longer (non-) trace.

Positive charges deflect in one direction, negative the other.