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 types of particle physics experiments ? • 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(from the Appendix) • 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 in the methane (CH4) 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 model’s 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.Planck’s 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 • Wavemechanics • Introduced in 1926 by E.Schrodinger • Based on L. deBroglie’s probability waves. • Matrices mechanics • Introduced in 1926 by W.Heisenberg • An abstract translation of Schrodinger’s 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) • DeterministicUniverse • 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-deterministicUniverse • The Uncertainty Principle shows that the Universe is at non-deterministic at atomic scale. • Hard to accept • Einstein’s “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 and quantum mechanics does not happen because of the interaction with the environment (we are bombarded all the time by cosmic particles) • However some cosmologists use these ideas in their theoretical work about the Universe. At galactic level there huge really empty spaces.

14. A New Approach to the Molecule • Explaining the valence numbers in CH4: • 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 • ionic binding • 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 • Thepositron • 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. • Einstein’s E=mc2 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 mesonsas 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.