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.
Thin gold foil
Alpha
source
Geiger-Marsden
As expected, most alpha particles were
detected at very small scattering angles
Thin gold foil
Alpha particles
Small-angle
scattering
Geiger-Marsden
To their great surprise, they found that
some alpha particles (1 in 20 000) had
very large scattering angles
Thin gold foil
Alpha particles
Large-angle
scattering
Small-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
(pingpong 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+
γ
e+
Feynman diagrams
An electron and a positron collide and
annihilate each other producing a photon.
e+
γ
e-
Feynman diagrams
An photon “pair produces” an electron and
a positron (antielectron)
e+
γ
e-
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-
γ
e-
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-
eγ
e+
e+
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.