Recap Observations inside Matter

1
Recap Observations inside Matter

• What is an electronic microscope ?
• How can small objects be seen with a microscope
  and with an electronic microscope ?
• How do you explain the X ray diffraction
  experiments on salt (NaCl) ?
• How do we know that electrons move as probability
  waves?
• What are the two main components of a particle
  physics experiment ?
• Explain an experiment in a supercollider using
  electrons and positrons.

2
The Universe at the Molecule Level

• Molecules
• At the end of the 19th century the molecule was
  the most important brick of matter. It explained
  why a substance is a liquid or has a certain
  smell or colour.
• The structure of molecules
• X ray diffraction measurements by Roentgen
  established that atom stick together according
  to their valence numbers.
• These numbers predicted that a carbon atom would
  stick to 4 hydrogen atoms or that a helium atom
  would prefer to be unattached.
• What was behind these laws will be seen at the
  end of this lecture.

3
The Universe at the Atom Level (I)

• Indivisible atoms
• Democritus of Abdera and Leucip of Milet more
  than 2000 years ago.
• The valence numbers describing molecules did not
  change their definition of atoms.
• Divisible atoms
• 1897 - in the Cavendish lab of the Cambridge
  University J.J.Thomson showed that from an atom
  one can extract electrons leaving a positive ion.
  
• His atomic model implies uniform distribution of
  electrons, which oscillated with the emission of
  radiation.
• But the optical spectra and his theory did not
  agree.

4
Two Bricks for the Universe

• The electron
• 1911 P.Millikan measures the electrical charge
  of an electron,
• The electron becomes the elementary unit of
  charge.
• The planetary model of the atom
• 1911 E.Rutherford at the University of
  Manchester scatters alpha particles of metal
  targets.
• The proton
• 1912 - Rutherford baptizes the hydrogen nucleus
  proton and suggests that the other 92 elements
  have their nuclei built of protons.
• Like the electron a proton has an elementary
  unit of charge (but positive) and a mass 1836
  times bigger than the electron. Atoms have an
  equal number of protons and electrons.

5
Explaining atomic spectra

• What is an atomic spectrum ?
• Distinguishing absorption and emission
  spectra. (Both are used in astronomy)
• A new theory is needed
• 1913 - the 2nd Solvay congress in Bruxelles
  discusses the planetary models predictions on
  atomic spectra.
• According to the laws of electromagnetism
  electrons would radiate energy until they fall on
  the nucleus.
• Experiments showed a spectrum constant in time.
• Also, atoms should always radiate and not only
  when heated.

6
The Quantum Model of an Atom

• Origin
• 1913 - N.Bohr explains the hydrogen optical
  spectrum with M.Plancks 1900 model of quanta.
• How does it work ?
• Electrons stay only in some quantum states and
  cannot continuously gain or loose energy.
• For an electron to jump from an orbit with the
  energy E1 to a higher orbit of energy E2 the atom
  has to get the energy E2-E1.
• If the amount of energy passed to the atom does
  not correspond to a difference between two
  orbital energies nothing will happen.

7
Quantum Numbers

• Elliptical orbits for electrons
• Introduced by A.Sommerfeld.
• Ellipses are described with the help of 3
  quantum numbers.
• Spin the 4th quantum number
• W.Pauli introduces the exclusion principle only
  two electrons can occupy an elliptic orbit.
• The two electrons were made distinct through a
  4th quantum number related to their spin
  movement.
• With these quantum numbers physicists were able
  to explain the electronic structure of all atoms
  and the experimental atomic spectra.
• .

8
Quantum Mechanics

• Wave mechanics
• Introduced in 1926 by E.Schrodinger
• Based on L. deBroglies probability waves.
• Matrices mechanics
• Introduced in 1926 by W.Heisenberg
• An abstract translation of Schrodingers work
  into matrices.

9
The Uncertainty Principle (I)

• The Uncertainty Principle
• Introduced by W.Heisenberg
• the position and the velocity of an atomic
  electron cannot be determined accurately
  determined at the same moment in time. Our
  efforts to determine accurately one of them will
  make the other quantity undetermined.
• The Relativistic Uncertainty Principle
• Introduced by P.Dirac
• It produces another it is impossible to
  determine the energy of a particle at an exact
  moment in time in other words, if we talk about
  a very small period of time the energy of a
  particle is undetermined.

10
The Uncertainty Principle (II)

• Deterministic Universe
• Marquis de Laplace in early 1800s argued that the
  Universe should be completely deterministic.
• Although not supported by church this theory
  lived for almost 200 years.
• Non-deterministic Universe
• The Uncertainty Principle shows that the Universe
  is at non-deterministic at atomic scale.
• Hard to accept
• Einsteins God does not play dice did not stop
  quantum mechanics to become a highly successful
  scientific theory which underlies nearly all
  modern science and technology.

11
Entangled Atomic States

• Quantum states
• Atomic electrons are described by quantum
  states, which are some combinations of position
  and velocity.
• Entangled states
• Their states depend also on the states of the
  other atomic electrons

12
Entangled Atomic Processes

• No single theoretical predictions
• Quantum mechanics does not predict a single
  definite result for an observation.
• Instead it predicts a number of possible outcomes
  and tells us how likely each of these is.
• Example an electron scattering from an atom is
  represented by a wave function containing 3
  processes elastic scattering, excitation,
  ionization
• Entanglement
• corresponds to the 3 states interacting with each
  other
• an experiment collapses the wave function to
  reveal only one state

13
Entanglement in Macro-Universe

• The many worlds interpretation of quantum
  mechanics
• At macro level quantum entanglement of states
  does not happen because of the interaction with
  the environment
• However some cosmologists use these ideas in
  their theoretical work about the Universe

14
A New Approach to the Molecule

• Explaining the valence numbers
• Carbon has 4 unpaired electrons on the highest
  orbit, which can be snatched by other atoms
  hydrogen has only one electron and is interested
  to get an extra electron.
• Helium has just 2 paired electrons and is not
  interested to couple with other atoms.
• Types of atomic binding
• Examples above correspond to ionic binding of
  atoms (Lewis 1916).
• 1927 - Heitler and London formulate the covalent
  binding (ex. hydrogen molecule)
• metallic binding conduction electrons

15
Explaining the Electrical Force (I)

• Electromagnetic force.
• Matter at the molecular and atomic level is
  governed by the electromagnetic force.
• How do two electrical charges interact ?
• The answer requires relativistic quantum
  mechanics
• The fact that an electron has an electric charge
  means that it pulses radiation (photons).
• Why does the electron pulse photons is explained
  by the relativistic uncertainty principle (ex. a
  gamma photon only 10-20 seconds).
• These photons are virtual, meaning that they
  cannot be oberved/measured.

16
Explaining the Electrical Force (II)

• How does the virtual photon interact with the
  electron? The answer is related to
  antiparticles.
• An experiment in 1932 showed that a photon can
  break into an electron and a positron
  (anti-electron).
• Experiments also showed that an electron will
  annihilate a positron producing photons.
• The mysterious interaction from a distance of
  the two electrons becomes an exchange-type
  interaction.

e-
e-
e- e
virtual photon
e-
e-
Feynman diagram
17
Two New bricks for the Universe

• In 1932 Curie discovers artificial nuclear
  transmutations, Chadwick discovers the neutron
  and Anderson discovers the positron.
• Neutrons were assumed to collide with charged
  particles in ionization chambers. These particles
  were produced through nuclear transmutations
  created with particle accelerators (Cockcroft
  Walton 1928).
• Neutrons were needed in the structure of the
  atomic nucleus.
• Positrons were seen in cosmic rays with
  observation chambers mounted on balloons.

18
Antiparticles

• The positron
• was the first anti-particle found experimentally.
  
• It was predicted theoretically by Paul Dirac in
  1929.
• Other antiparticles
• In the next years new anti-particles were
  discovered and the Universe had a new symmetry.
• Particle-antiparticle pairs
• Where ever there is enough energy (radiation,
  colliding particles) Nature creates them.
• Einsteins Emc2 gives the masses of these pairs.
  
• Anti-matter
• There is no evidence that the Universe contains
  anti-matter, that is anti-atoms such as
  anti-hydrogen.

19
Nuclear Force

• Nuclei
• about 100,000 times smaller than atoms
• are described by the quantum mechanics.
• Gamma rays spectra
• As the nuclear force is much stronger than the
  electrostatic force the energy differences
  between possible states are large, corresponding
  to gamma rays spectra.
• Using accelerated particles to hit nuclei one
  moves nucleons (protons or neutrons) to more
  energetic states, and the release of gamma rays
  corresponds to the return to less energetic
  states.
• Nuclear models are not as good as the atomic
  models.
• Nuclear collisions can produce the nuclear fusion
  and fission energy.

20
Nuclear Binding Energy

• Binding tighter particles is equivalent to
  freeing energy, as their separation needs energy.
  A body will always be lighter than the sum of its
  components.
• All forces can produce energy by freeing binding
  energy.
• Burning wood produces energy/heat corresponding
  to the rearrangement of electrons and release of
  electrostatic energy.
• The birth of new stars corresponds to the
  condensation of cosmic dust with the release of
  gravitational energy.
• The energy radiated by the Sun corresponds to
  nuclear and not gravitational forces.

21
Fusion Energy

• The Sun
• radiates the equivalent of about 4 million tons
  of mass/energy per second
• that energy is produces through the fusion of
  hydrogen and helium nuclei.
• Hydrogen fusion
• is a thermonuclear reaction (it needs extreme
  heat, which in the Sun has produced through its
  gravitational collapse).
• The fusion creates first a proton-neutron pair
  (deuteron). The weak nuclear force changes a
  proton into a neutron.
• In a second stage deuterons fuse to create nuclei
  of helium (with 2 protons and 2 neutrons).

22
Fission Energy

• Nuclear radioactivity
• Heavy nuclei (heavier than lead with its 82
  protons) are becoming unstable because the
  electric repulsion of protons compensates the
  nuclear binding.
• Natural radioactivity eliminates protons from
  nuclei such as uranium.
• Nuclear fission
• Hit with a neutron the uranium nucleus splits
  into 2 nuclei and a few neutrons, which can
  further fission other uranium nuclei.
• This the chain reaction used in nuclear fission
  reactors.

23
Nuclear Binding Energy
Iron
uranium
Binding energy per nucleon (in MeV)
hydrogen
100
200
number of nucleons
24
The Nuclear Force Carrier

• The Pion
• 1934 H. Yukawa introduces the mesons as carriers
  of the nuclear force, but the full picture of the
  exchange of mesons was produced only in 1970s.
• In 1945 ionization chambers in the Pyrenees
  mountains recorded the first meson, the pion.
• The life of a pion is only about 10-8 seconds
  after that time it disintegrates into a muon and
  a neutrino.
• The muon is a heavy electron (about 200 times
  heavier), which lives only about 10-6 seconds
  before disintegrating into a normal electron.

25
The Weak Nuclear Force

• The Universal Alchemist
• The weak nuclear force is in action each time
  that one particle disintegrates into another.
  Without it nature could not manufacture nuclei
  heavier than hydrogen.
• This force was there to change protons into
  neutrons.
• The Weak Force is Universal
• the same force that disintegrates nucleons will
  disintegrate mesons or muons.

26
The Universality of Forces
p
p
e-
e-
virtual photon
virtual photon
The electromagnetic force
no
muonic neutrino
p
muon
virtual weakon (w-)
virtual weakon
positron
(w)
e-
anti-electronic neutrino
electronic neutrino
The weak nuclear force