7.3 The structure of matter

How do we know the structure of the atom?

The famous Geiger-Marsden Alpha scattering experiment

In 1909, Geiger and Marsden were studying how alpha particles are scattered by a thin gold foil.

Alpha source

Thin gold foil

Geiger-Marsden

As expected, most alpha particles were detected at very small scattering angles

Alpha particles

Thin gold foil Small-angle scattering

Geiger-Marsden

To their great surprise, they found that some alpha particles (1 in 20 000) had very large scattering angles

Alpha particles

Thin gold foil Small-angle scattering

Large-angle scattering

Explaining Geiger and Marsdens’ results

The results suggested that the positive (repulsive) charge must be concentrated at the centre of the atom. Most alpha particles do not pass close to this so pass undisturbed, only alpha particles passing very close to this small nucleus get repelled backwards (the nucleus must also be very massive for this to happen).

nucleus

Angle of deviation

Rutherford did the calculations!

Rutherford (their supervisor) calculated theoretically the number of alpha particles that should be scattered at different angles. He found agreement with the experimental results if he assumed the atomic nucleus was confined to a diameter of about 10-15 metres.

Rutherford did the calculations!

That’s 100 000 times smaller than the size of an atom (an atom is about 10-10 metres).

7.3 The Rutherford model (video)

If the nucleus of an atom was a ping-pong ball, the atom would be the size of a football stadium (and mostly full of nothing)!

Nucleus (ping-pong ball

The Particle zoo!

• Following Rutherford’s discovery physicists kept smashing particles into each other discovering hundreds of different particles.

The Standard Model

• The Standard Model explains all particles and complex interactions with only:

• 6 quarks.• 6 leptons. (The electron is a lepton). • Force carrier particles (bosons). (like

the photon). • All the known matter particles are

composites of quarks and leptons, and they interact by exchanging force carrier particles.

Matter and anti-matter

• For every type of matter particle there also exists a corresponding antimatter particle.

• Antiparticles look and behave just like their corresponding matter particles, except they have opposite charges. For instance, a proton is electrically positive whereas an antiproton is electrically negative.

• When a matter particle and antimatter particle meet, they annihilate into pure energy.

Quarks

• Quarks are one type of matter particle. Most of the matter we see around us is made from protons and neutrons, which are composed of quarks.

• There are 6 quarks (3 pairs) up/down, charm/strange, top/bottom. (For each of these quarks, there is a corresponding antiquark.)

• (Quarks also carry another type of charge called color charge which you don’t need to study!)

Quarks

7.3 What are quarks? (video)

Data booklet reference

Quarks make HADRONS

• Although individual quarks have fractional electrical charges, they combine such that hadrons have a net integer electric charge.

• There are two classes of hadrons;

HADRONS: Baryons & Mesons

Baryons

• Contain 3 quarks

You need to know the quarks in a proton and a neutron

Mesons

• contain one quark (q) and one antiquark (q).

• One example of a meson is a pion (π+), which is made of an up quark and a down antiquark (ud). The antiparticle of a meson just has its quark and antiquark switched, so an antipion (π-) is made of a down quark and an up antiquark (du).

Mesons

• Because a meson consists of a particle and an antiparticle, it is very unstable. The K meson lives much longer than most mesons, which is why it was called "strange" and gave this name to the strange quark, one of its components.

Conservation of baryon number

In all nuclear processes, baryon number is conserved (protons and neutrons both have a baryon number of 1)

Leptons

• There are 6 leptons, 3 with charge and 3 without. The charged leptons are the electron (e-) the muon(μ) and the tau(τ). The muon and tau are like electrons but have a lot more mass. The uncharged leptons are the neutrinos (ν). They have no electrical charge and very little mass.

• For each lepton there is a corresponding antilepton.

Data booklet reference

Lepton decays

• The heavier leptons are not found in ordinary matter at all because they quickly decay into lighter leptons. Sometimes the tau lepton will decay into a quark, an antiquark, and a tau neutrino.

• When a heavy lepton decays, one of the particles it decays into is always its corresponding neutrino. The other particles could be a quark and its antiquark, or another lepton and its antineutrino.

Lepton decays

• Some types of lepton decays are possible and some are not. In order to explain this, they divided the leptons into three lepton families: the electron and its neutrino, the muon and its neutrino, and the tau and its neutrino. The number of members in each family must remain constant in a decay. (A particle and an antiparticle in the same family "cancel out" to make the total of them equal zero.)

Lepton number conservation

• Electrons, muons and taus and their neutrinos have lepton number +1. Their antiparticles (positrons, antimuons etc) and their antineutrinos have lepton number -1.

• One important thing about leptons, is that lepton number is always conserved when a massive lepton decays into smaller ones.

Conservation of lepton number

7.3 What are neutrinos? (video)

Conservation of strangeness

• The presence of a strange quark in a particle is denoted by a quantum number S=-1. Particle decay by the strong or electromagnetic interactions preserve the strangeness quantum number.

• Particles that decay via the weak interaction DO NOT CONSERVE STRANGENESS!

The four interactions

Exchange particles (bosons)

• All the force interactions are “mediated” by force carrying particles called exchange particles (bosons).

Electromagnetism

• The exchange particle of the electromagnetic force is the photon (γ).  Photons of different energies span the electromagnetic spectrum.

• Photons have zero mass and always travel at the speed of light, c.

Forces in the nucleus

The Electromagnetic Force

• The repulsive force between protons in the nucleus

+

+

The Strong Force

The nucleons (protons and neutrons) in the nucleus (and the quarks inside them) are bound together by the strong nuclear force

Helium nucleus

The Strong Force

• acts over short distance (10-15 m)• acts only between adjacent particles in the

nucleus• is carried by gluons• becomes stronger with increased distance

Quark confinement

• If one of the quarks in a given hadron is pulled away from its neighbors, more and more energy is added to the force field as the quarks are pulled apart. At some point, this energy is converted into a new quark-antiquark pair. In so doing, energy is conserved because the energy of the strong field is converted into the mass of the new quarks.

• Quarks cannot exist individually because the strong force increases as they are pulled apart.

Quark confinement

Weak interaction

• Weak interactions are responsible for the decay of massive quarks and leptons into lighter quarks and leptons.

• When a quark or lepton changes type (a muon changing to an electron, for instance) it is said to change flavor. All flavor changes are due to the weak interaction.

• The carrier particles of the weak interactions are the W+, W-, and the Z bosons. The W's are electrically charged and the Z is neutral.

Gravity

• Gravity is clearly one of the fundamental interactions, but the Standard Model cannot explain it.

• The gravity force carrier particle, the graviton, has not been found.

• The effects of gravity are extremely tiny compared to the other three interactions, so theory and experiment can be compared without including gravity in the calculations.

Data booklet reference

7.3 Standard model questions

Feynman diagrams

• Developed by Nobel prize-winning Physicist and Bongo player Richard Feynman to show particle decay and interactions.

Feynman diagrams

A straight line represents a particle

Feynman diagrams

A wavy line represents a photon (EM force)

Feynman diagrams

A curly line represents a gluon (strong force)

Feynman diagrams

A dotted line represents a W or Z boson (weak interaction)

Feynman diagrams

• You may only connect these lines if you have two lines with arrows meeting a single wiggly/curvy/dotted line. You must have exactly one arrow going into the vertex and exactly one arrow coming out.

Feynman diagrams

• Your diagram should only contain connected pieces. That is every line must connect to at least one vertex. There shouldn’t be any disconnected part of the diagram.

Feynman diagrams

Common mistakes

Feynman diagrams

• In IB we read the diagrams from left to right. This is not an internationally recognised convention and many books and videos (including the one I’m going to show you!) has time going from bottom to top!

Feynman diagrams

• This left-to-right reading is important since it determines our interpretation of the diagrams. Matter particles point from left to right. Antimatter particles have arrows pointing in the other direction.

Feynman diagrams

An electron emits a photon and keeps going

e- e-

γ

Feynman diagrams

A positron absorbs a photon and keeps going

e+ e+

γ

Feynman diagrams

An electron and a positron collide and annihilate each other producing a photon.

e+

e-

γ

Feynman diagrams

An photon “pair produces” an electron and a positron (antielectron)

e+

e-

γ

Feynman diagrams

So we see that the external lines correspond to incoming or outgoing particles. What about the internal lines? These represent virtual particles that are never directly observed. They are created quantum mechanically and disappear quantum mechanically, serving only the purpose of allowing a given set of interactions to occur to allow the incoming particles to turn into the outgoing particles.

Feynman diagrams

An electron and a positron meet, annilhate to produce a (virtual) photon, which then produces another electron/positron pair

e+

e-γ

e-

e+

Feynman diagrams

An electron tosses a photon to a positron (without touching the positron). The force particles are just weird quantum objects which mediate forces.

e+

e-

e+

e-

γ

Feynman diagrams

`Electron and positron annilhate via Z0 boson producing a muon and antimuon pair.

Common questions!

• What is the significance of the x and y axes?By reading these diagrams from left to right, we interpret the x axis as time. You can think of each vertical slice as a moment in time. The y axis is roughly the space direction.

Common questions!

• The particles travel in straight lines?• No, the point of the Feynman diagram is to

understand the interactions along a particle’s path, not the actual trajectory of the particle in space.

Conservation laws

The Feynman diagrams must obey the conservation laws we discussed earlier (conservation of lepton number, baryon number and strangeness).

Examples

Examples

Examples

• Time going up!

7.3 Feynman diagrams

• A nice explanatory video – but BEWARE – this uses the bottom to top time axis!

Feynman diagram questions

• Now let’s try some Feynman diagram questions from your textbook.