Particle+Physics

Topics:

 * Constituents of the atom
 * Stable and unstable nuclei (only a link to Nuclear notes)
 * Particle accelerators and matter/anti-matter facts
 * Particles, anti-particles and photons / Classification of particles
 * Particle interactions
 * Quarks and anti-quarks (//to be completed//)

**Constituents of the atom**
An atom is the smallest neutral particle that represents an element. Atoms can be visulaised as being made up of the following particles (remembering that in fact the proton and neutron are made up of smaller fundamental particles (quarks):


 * Neutron (n) - has no charge. Unstable in isolation and decays into a proton (see next section). Rest mass 1.67 x 10 -27 kg. Rest energy 939 MeV.


 * Proton (p) - has charge of +1, or +1.60 x 10 -19 C (the same as an electron, but with opposite charge. Rest mass 1.67 x 20 -27 kg (actually slightly lighter than a neutron. Rest energy 938 MeV.


 * Electron (e - ) - has charge of -1, or -1.60 x 10 -19 C. Rest mass 9.11 x 10 -31 kg. Rest energy 0.51 MeV.

Note: 'u' is a symbol used for atomic mass units, and has the value 1.661 x 10-27 kg. So the masses of the constituents of an atom in atomic mass units are:
 * n 1.00867u
 * p 1.00728u
 * e - 5.5x10 -4 u

The size of a nucleus is of the order of femto metres (10 -15 m), while the size of an atom is of the order of tens of nanometres (10 -10 m). The nucleus is therefore around 100 000 times smaller than an atom, so if an atom was the size of an Airbus A380 (the worlds largest airliner, at 70-80m in length and wingspan) the nucleus would be less than a millimetre wide (so about the size of a grain of sand on the shoe of one of the 555 passengers).


 * Summary**


 * = Particle..... ||= Mass/kg.......... ||= Charge/C............. ||= Specific......... Charge (Ckg -1 ) ||= Mass/u... ||
 * = neutron ||= 1.675x10 -27 ||= 0 ||= 0 ||= 1 ||
 * = proton ||= 1.673x10 -27 ||= +1.60x10 -19 ||= 9.56x10 7 ||= 1 ||
 * = electron ||= 9.11x10 -31 ||= -1.60x10 -19 ||= 1.76x10 11 ||= 5.5x10 -4 ||
 * m p /m e ~ 1840 (i.e. the proton and neutron are approximately 1800 times the mass of the electron)
 * The electron has a greater charge per unit mass than the proton (approximately 1840 times, as they have the same charge per particle), and so is deflected proportionately more by an electromagnetic field.


 * Nuclear Notation**

A X X  Z

The X is the element being referred to. A is the nucleon number (the total number of neutrons and protons). Z is the proton number. The proton number is fixed for a specific element, while different isotopes of the element have a different number of neutrons. An atom is neutrally charged (see the definition at the top), and so has the same number of electrons as protons. An **ion** is a charged atom, so an atom that has lost or gained one or more electrons (so the number of electrons does not equal the number of protons). All the protons and neutrons are contained in the **nucleus**, so if you are considering a nucleus only, then if would have a charge of +1.6x10 -19 x #protons (as there are no electrons).


 * Other terminology:**

molecule: a molecule of a substance is the smallest particle of it which can exist under normal conditions. For example, oxygen is normally found as a pair of oxygen atoms, while argon is found as a single atom. So a molecule of argon is the same as an atom of argon, but a molecule of oxygen is made up of two oxygen atoms. Note that the idea of a molecule often breaks down when considering solids as the sharing of electrons means that is is not possible to identify when one molecule ends and another begins.

Stable and unstable nuclei
Nuclear Physics

Particle accelerators and matter/anti-matter facts



 * Matter and Anti-matter - 10 facts**


 * 1) Matter and antimatter – are produced together. Think of a coin factory, printing coins of different values (but not all values) – when the coin is stamped out it leaves behind a hole in the material. The hole is an “anticoin”.
 * 2) Bring matter and anti-matter together and they annihilate.
 * 3) Equal amounts of matter and anti-matter must have been created at the start of the Universe, but somehow there was an asymmetry so that matter won the fight. The cosmic background radiation is the leftover from the matter-antimatter annihilations.
 * 4) Brain scanning machines use antimatter (PET scans).
 * 5) Research projects have investigated the use of antimatter fuel.
 * 6) When an electron and a positron meet they annihilate, turning into energy which, at high energies, can rematerialise as new particles and antiparticles. This is what they do at CERN.
 * 7) In 1995 CERN researchers were able to create antihydrogen atoms by speeding antiprotons past normal atoms at close to the speed of light.
 * 8) The Sun regularly creates anti-matter, and in 2002 NASA’s RHESSI spacecraft saw the creation of roughly half a kg of anti-matter in a solar flare – its subsequent destruction generated enough energy to power whole countries for years.
 * 9) NASA estimates the energy produced by a gram of antimatter meeting a gram of normal matter would equal that of the thrust behind 1 000 external space shuttle fuel tanks. For that reason research into anti-matter engines has been conducted. The problem is antimatter is hard (e.g. costly) to produce: about 20 nanograms have been produced so far by humans (10-9 grams).
 * 10) Bananas give off anti-matter as they contain potassium-40, a radioactive isotope which undergoes b + decay (where a proton is converted, via the weak force, to a neutron, releasing a positron (the anti-matter version of an electron) and a neutrino.

Background
Rutherford's experiments in 1911 with gold leaf provides evidence that the nucleus of an atom is very small and positively charged. This is due to the back scattering of alpha particles (helium ions).

If you know the kinetic energy of the alpha particle then Coulomb's law (F = kQ 1 Q 2 /r 2 ) can be used to estimate the maximum radius of the nucleus.

Electron diffraction can provide a more precise estimate (i.e. fast electrons have a small wavelength - about that of a nuclear diameter, and analysis of the diffraction pattern provides an estimate of the size of the nucleus of about 10 -15 m.

The four forces of nature:

 * Gravity**
 * applies to all objects with mass.
 * Infinite range.
 * Weak (relative strength 10 -38 ).
 * Most important force on scale of Universe, negligible effect on atomic scales)


 * Electromagnetic force**
 * applies to all objects with charge.
 * Infinite range.
 * Strong (relative strength 10 -2 ). NB: most materials have zero net charge, so strength is not apparent between every day objects.
 * Holds atoms and molecules together
 * Responsible for friction, buoyancy, tension and contact forces


 * Strong nuclear force**
 * affects hadrons (e.g. protons and neutrons) but not leptons (e.g. electrons).
 * Limited range (up to 10 -15 m).
 * Strong (relative strength 1)
 * Balances repulsive electromagnetic forces between protons in nucleus.


 * Weak nuclear force**
 * Effects ALL particles (i.e. hadrons and leptons).
 * Short range (10 -18 m).
 * Weak (relative strength 10 -5 )
 * Responsible for radioactive (ß) decay.

Fundamental and non-fundamental particles (and their anti-particles)




There are two groups of fundamental particles, fermions (the matter particles) and the bosons (the force carriers). The fermions (whether matter or antimatter) are fundamentally made up of quarks and leptons (from the Greek for 'light'). However quarks have never (yet) been observed individually, and the particles that are made up of quarks are called Hadrons (this is from the Greek for 'heavy'). Furthermore, Hadrons are either made of of groups of three quarks (all matter, or all anti-matter) or in pairs (one matter and one anti-matter). These sub-groups are called Baryons and Mesons.

One point to note in preparation for the section on matter and anti-matter is that Mesons, which are made up of matter and anti-matter particles can exist and matter/anti-matter annihilation will only occur when the particles meet. In a Meson the matter/anti-matter pairs are 'orbiting' each other, so do not annihilate (even so these particles are not usually stable for long). Particles made up of an antimatter and matter particle are often referred to as -onium partciles, eg positronium (an electron and anti-electron - although this is not a Meson) or charmonium (made up of c and cbar quarks).


 * Quarks**

Evidence of the structure of neutrons and protons comes from deep inelastic scattering, where very high energy electrons are fired at nucleons. Some backscattering occurs (like with the gold leaf experiment, only on a smaller scale), indicating that the nucleons contain small regions of intense charge. These regions of intense charge are called quarks, which are thought to be fundamental particles (like the electron). Quarks come in various flavours (up, down, charm, strange, top and bottom, with the first letter of the word being the symbol for each quark).

Protons are made up of uud. As u quarks have a +2/3 charge and d quarks have a -1/3 charge the overall charge is +1. Neutrons are made up of ddu. It therefore has no net charge.

Anti-quarks have the opposite charge, but are otherwise identical.


 * Leptons**

Electrons are fundamental particles from the family called Leptons. Electrons also have an associated electron-neutrino (//v,// pronounced "new"). The electron anti-particle is called the positron. This family also includes the muons (which are 200 times the mass of the electron, but are unstable) and their associated anti-particles, and the Tauons (and their neutrinos) which have twice the mass of a proton(!).


 * Hadrons**

Hadrons are not fundamental particles and are made up of either three quarks (baryons, like protons and neutrons) or a quark and an anti-quark (mesons).


 * Gauge Bosons (aka virtual particles)**

Although fields can be used to describe the forces, the interaction that results in attractive and repulsive forces is due to a continual exchange of other particles. These exchange particles have a very short lifetime and owe their existence to borrowed energy, so they are often referred to as virtual particles. The interactions between particles can be represented by Feynman diagrams.

Photons are the force carriers for the electromagnetic force. Photons have no mass. The W and Z particles are the force carriers of the weak nuclear force. These bosons have mass.

See the next section on particle interactions for more on Feynman diagrams.


 * Anti-partciles**

Every matter particle has a corresponding anti-particle. The anti-particle is a 'mirror' image of the, matter particle. It has the same mass but the opposite charge. By colliding together high energy protons another proton and an anti-proton may be produced:

p + p -> p + p + p + pbar

(NB: pbar is usually written but this is difficult (for me) to show on a webpage). All anti-matter particles are written as the matter particle but with a line above the symbol (//exception//: leptons - the matter leptons electron, muon and tau are written as a symbol with a superscript '-' as they have negative charge; the antimatter versions are written with a superscript '+'. Presumably this is because the bar could be confused with the '-' symbol).

Anti-matter particles do not exist in large quantities as when matter and anti-matter particles meet they annihilate into high energy electromagnetic radiation (typically a pair of gamma photons). This is called **pair-annihilation**. The opposite of this is **pair production** - where a high energy gamma ray photon is converted into a pair of particles, one an particle and the other its anti-particle twin.

Despite the difficulty of creating and storing antipatter particles, they have practical uses. For example positrons (obtained from b + radioactive decay) are used to identify different diseases with the Positron Emission Tomography (PET) scanner [|CERN antimatter info - PET scanner]. The annihilation of the positron with electrons in the patient's body are at low energy, so there is not enough energy for particles to be created, so the energy is given off as two high energy photons with opposite vectors (as a result of conservation of momentum).

E=mc 2 can be used to calculate the minimum energy required for pair production to happen. For example

What is the minimum energy that a high energy gamma ray photon must have in order to change into an electron-positron pair?

mass of an electron (and positron) = 9.11 x 10 -31 kg Energy required = 2 x (9.11x10 -31 ) x (3.00x10 8 ) 2 = 1.6398x10-13 = 1.64x10 -13 J  OR  Rest energy in MeV = 2 x 0.51 = 1.02 MeV. Check (convert J to eV by dividing by the charge on an electron): 1.6398x10 -13 /1.6x10 -19 = 1024875 eV = 1.02MeV. **The quantum nature of Electromagnetic radiation** Max Planck proposed in 1900 that radiation is emitted and absorbed in discrete packets, or quanta. This enabled him to solve the 'black-body radiation problem', i.e. that the then current theoretical models of how radiation intensity should vary with wavelength matched the experimental results only for long wavelenghts (infra-red and longer). For short wavelengths, e.g. in the visible range, the theory provided no explanation of why the intensity peaked. These quanta have become known as photons. Photons are: The energy carried by a photon is given by: E = hf, where E = energy (J) h = Planck constant (6.63x10 -34 ) f = frequency (or equivalently (using s=fl ), E=hc/l. Gamma rays (very short wavelength EM radiation) are often referred to simply as high energy photons as a result.
 * of different types (radio waves, microwaves, infra-red, visible, UV, x-ray and gamma rays - note: x-rays and gamma rays differ in their source. Gamma rays come from changes of energy levels in the nucleus, while x-rays come from rapid deceleration of fast moving electrons, or from changes in energy of the the innermost orbital electrons).
 * all travelling at the same speed (in a vacuum)
 * made of oscillating electric and magnetic fields (at 90o to one another)
 * are of different frequencies and wavelengths. The wavelength of visible light falls between 10 -6 and 10 -7 m (micro metres, m m). Frequency and wavelength are inversely related (as one goes up the other goes down).

Particle interactions
When objects interact they exert equal and opposite forces on each other. For example, if two protons approach each other they repel each other (due to the electrostatic repulsion) and move away from each other.

At a subatomic scale, this interaction takes place via the exchange of 'virtual' particles. (Note they are termed 'virtual' as if you try to measure them, you will stop the interaction taking place, so the particles will then not exist, however (with the exception of the graviton) they have been observed in experiments). Two analogies that may help think about attractive and repulsive forces in these terms are:

Two ice-skaters face each other and one throws a ball to the other. Effect: they move away from one another. The exchange of the ball (force carrier) has resulted in a repulsive force.
 * Repulsive forces**

Two ice-skaters face away from each other. One throws a boomerang away from the other, and it circles around and the other catches it before it hits the first on the back of the head. Effect: the ice-skaters move towards each other. The exchange of the boomerang (force carrier) has resulted in an attractive force.
 * Attractive forces**

The strong nuclear exchange particle (gluon) and the electromagnetic exchange particle (photon) are stable, massless and without charge. The weak force has three charge carriers, W+,W-, and Z. These have charge, are massive (83 to 93 GeV, compared to 0.9 GeV for a proton or neutron), but are not stable, lasting only 10 -25 s.

Four important nuclear reactions that involve the weak force are shown in the embedded word document below (downloads):



Extension topics / unfiled / incomplete notes:

 * Higgs field and Higgs bosons.**

Peter Higgs, a Scottish scientist, thought of the idea, that become known as, the Higgs field as a mechanism for giving particles mass (and explain why some bosons don't have mass, and other bosons do). The Higgs field does not have a zero value at its lowest energy state. Other particles moving through the field interact with the Higgs field and are slowed down by it. This gives them apparent mass (different properties). E.g. drop a ball bearing into a bottle of water, it moves more slowly than if the bottle was empty. The water is analogous to the Higgs field, changing the behaviour of particles (the ball bearing), from how it would behave in the absence of the field. The Higgs field is quantised as a Higgs boson. The Higgs boson has mass, but the standard model does not predict the mass.


 * Symmetry**

Is an important concept in particle physics. In this sense it means that certain properties remain unchanged as you change other things. Spontaneous symmetry breaking. A blank piece of paper can be any way up. It is symmetric in as much you don't know if it is up or down. However if you write on it, you break the symmetry as the paper then has an up and down.

Hot magnet, each atom is a little magnet, but in random direction. As it cools they line up, you get a magnetic field outside, so the magnet has a preferred direction. Similarly, at the start of the universe the Higgs field was random and symmetric. However the symmetry was broken at a certain time and it then had a particular direction and particles then had mass.

For more on this see the Solar and Cosmology section on the evolution of the Universe.


 * Standard Model**

Notation (for the table below) - for the fermions:

c P **P** s

Here c = charge; a = spin (note this does not actually represent the particles rotation, but is a quantum property of the particle) ; P = particle notation.

I II III IV

Columns I, II and III are the ** fermions ** - particles with spin 1/2 which obey Fermi-Dirac statistics and the Pauli exclusion principle.

The repulsive force between atoms is partly a result of the exclusion principle - note that electrons are fermions - which means that as atoms get close the electron shells cross over. As two electrons cannot occupy the same quantum state, electrons are forced to a higher quantum state, increasing the system energy as if a repulsive force existed between the atoms. The repulsive force is also partly electrostatic, due to the negative charge of both electron shells.


 * Radioactive decay**

Activity, A = l N where A is the change in N over time (//d//N///d//t), and l is the decay constant. This relationship shows that the activity of a sample is only related to the number of particles and the decay constant for that type of particle.

Note that the decay constant is related to the half-life by the expression: l t 1/2 = ln2 = 0.69 (approx).


 * beta - decay -** is written o -1 e where the -1 is included as the nucleus which has given rise to the decay has had a neutron change into a proton, so the mass number of that atom has increased. As the mass number is conserved, the electron is written with a -1 mass number. (So for beta minus decay the mass number of the atom //increases//).

Note //Source of material on this page: much of the material on this page was taken from Letts, Revise AS & A" Physics.//