Introduction to spectroscopy

1. Introduction to spectroscopy Introduction: the Unity of Science Electromagnetism (textbook: Griffiths, Jackson) Electrostatics (Coulomb’s Law) in vacuum and dielectrics Magnetostatics (Ampère’s Law) Electromagnetism (Faraday’s Law and Maxwell’s equations) The wave-equation, simple radiating systems Optics (Fresnel’s Law) Mid-term Exam 2/9/12 (30%) Quantum Mechanics (textbooks: Feynman, Bohm, Dirac,….) The problem of atomic spectra and black-body radiation QM formalism Two-body systems: the Amonia maser Dirac’s and Schroedinger’s equations Atoms and molecules: the Periodic Table The chemical bond and perturbation theory Final Exam (40%)

2. The Unity of Science To explain almost everything with almost nothing David Bensimon

3. Mathematics is a game with rules like chess, go, backgammon, … These arbitrary rules are the rules of logics. logics ~ arithmetics (Russel, Whitehead, Gödel) arithmetics ~ computing (Türing, Von Neuman) Mathematics: the language of Science Within mathematics there exists sub-fields with their own arbitrary additional rules (axioms), for example Euclidian or Riemannian geometries that differ in their axioms of parallels. Contrary to Kant’s assertion no mathematical proposition is informative. Science investigates the quantitative (measurable) relations between objects (mass, speed, position, charge, …). Mathematics by dealing with numbers provide a conceptual framework for their formulation.

4. Gravitation – Newton, Einstein (free fall, motion of planets, tides, expansion of the Universe, etc.) Electromagnetic theory– Maxwell, Faraday, Ampère, … (electricity and electrical motors and generators, radio waves, optics, rainbow, ….) Quantum mechanics- Einstein, Bohr, Schrödinger, Heisenberg, … (atoms, molecules, chemistry, transistors, conduction, magnetism, etc.) Statistical mechanics-Boltzman, Einstein, Gibbs, … (heat, engines, refrigerators, lasers, phase transitions, plastics, blackbody radiation of the Universe, etc.) The fundamental theories

5. NGC4414 F = G m M / r2 Gravitation Every gravitational system is unstable → Big-Bang

6. Maxwell’s equation determine the electric and magnetic fields E and Bas a function of the charges and currents densities: r and J Electromagnetic theory These equations unify electricity, magnetism and optics (light). They predicted radio-waves and X-rays. The force exerted by the electromagnetic field on a charge q is: It explains the movement of electrons in a TV tube, electrical motors and generators, lightning, aurora borealis, particle accelerators, etc.

7. Electromagnetic spectrum

8. Quantum mechanics describes the motion of isolated particles: Schrodinger’s equation iћ∂tΨ = H Ψ Quantum mechanics Ψ is known as the particle wave-function. Only the probability|Ψ|2 of finding the particle at a given place and time can be known. Quantum mechanics explains the chemical properties of elements, the origin of magnetism, light emission, electrical conduction, etc. Quantum mechanics is the foundation of chemistry, electronics (transistors, computers), lasers, medical imaging (MRI), nuclear power, etc.,

9. Direct observation of the wave-like behaviour of electrons Electronic wave in an atom corral Fe corral on Cu Don Eigler, IBM Radius: 72Å

10. Quantum Mirage Co corral on Cu By placing a Cobalt atom in one of the focii of the ellipse, one creates a replica of that atom in the other focus.

11. High energies The Bohr atom E = h n Low energies The electrons move around the nucleus like planets orbiting the sun. Because the electron is also a wave only certain orbits allow for a stationary wave. The transition from one orbit to an other is accompanied by emission (or adsorption) of a photon of well defined energy.

12. The Rosetta stone of the Universe See: Omnilingual by H.Beam Piper (how to decipher a Martian civilization with the periodic table)

13. Chemistry and Quantum mechanics n =1 n =2 n =3 The solution of Schrödinger’s equation for a hydrogen-like atom has the electron orbiting the nucleus on orbitals characterized by their quantum numbers: n = 1,2, ….; l= 0,…n-1; m=-l,…,l. Each orbital can be occupied by at most two electrons (with opposite spin). The maximal number of electrons on the orbitals with quantum number n is thus 2 n2. The chemical properties of atoms is determined by the number of electrons on its not fully filled outer orbitals.

14. The chemical bond The chemical bond between two atoms is established by the sharing of a pair of electrons that fill up the unfilled orbitals of the respective atoms. Thus Oxygen which lacks two electrons to fill up its n=2; l=1 orbital will bind to two Hydrogen atoms, each of which lacks one electron to fill up its n=0; l=0 orbital. The resulting molecule H2O (H-O-H: water) is stable because it minimizes the energy of the Oxygen and Hydrogen atoms.

15. The unity of life Life is a set of chemical reactions driven in fine by the Sun’s energy. In contrast with physical phenomena which unity is derived from general principles (EM, QM, StatMech), Life derives its unity from evolution. ADN Since all life forms evolved from the same source (ancestor), they share the same components (amino-acids, nucleotides, proteins), the same genetic code, the same chemical reactions, etc. DNA « What is true for a bacteria is true for an elephant», J.Monod

16. Statistical mechanics addresses the behaviour of a large number of particles. This large number and the collisions between the particles randomizes their motion. The fundamental concept is entropy. Statistical mechanics S = log(6) S = log(37) The entropy S of a system measures the lack of information on the system: it is defined as the logarithm of the number of its possible states. For a regular dice: S = log(6) For a loaded dice: 0 < S = -∑ pm log pm ≤log(6)

17. If one assumes that Nature is not « loaded » (ergodic hypothesis) then the dynamics of a system of many particles will tend to maximize its entropy S under some fixed constraint (total energy E, volume V, number of particles N, etc.). Law of ideal gases Mathematically this is done by maximizing the function: F= S – b (E + g V + d N) For a system of m states of energy Em occupied with probability pm with the constraints ∑ pm = 1 and total energy E = ∑ pm Em : F= S – b E – l = -∑ pm log pm – b ∑ pm Em – l ∑ pm Maximizing F: ∂ F/ ∂ pn = 0 → pn = e-bEn/ ∑ e-bEmBoltzmann distribution

18. T,P V1, T1,P1 V2, T2,P2 V’1,T P, V’2 V’1,T,P Law of ideal gases F= S – b(E + g V) = S’1+S’2 – b(E’1+E’2) + g (V’1+V’2)= F1= S1 – b1(E1 + g1V1) F’1= S’1 – b(E’1 + g V’1) F2= S2 – b2(E2 + g2V2) F’2= S’2 – b(E’2 + g V’2) The temperature is definedas: kBT = b-1 = ∂S/∂E , which is the parameter that is equaled when the vessels are brought in contact. Similarly the pressure is: P = g = b-1 ∂S/∂V = kB T N/V This is the law of ideal gases, where we used the fact that for an ideal gas of N particles in a volume V, the entropy S ~ N log(V).

19. According to the laws of QM, electromagnetic waves (e.g. light) are also particles: photons. In contrast with atoms their energy (E) is not linked to their speed (the speed of light cwhich is fixed), but to their frequency (n). Temperature of a gas of photons E = h n Like the atoms of a gas, confined photons thermalize at the temperature of their container. Their energy (and thus their frequency) are proportional to that temperature: E = h n ~ T By observing the light emitted by a body one can thus deduce its temperature, be that a human body (infrared), the Sun (visible) or the Universe (radio waves).

20. Sun’s spectrum and temperature

21. The universe is expanding The Doppler shift to the red indicates that galaxies are moving away from us: the Univers is expanding.

22. The temperature of the Universe is 2.7°K Intensité The Universe is the best example of a black body

23. N DT ~ 0.001 °K (as a result of the galaxy’s motion (Doppler effect) at à 600 km/sec. ) 360° 0° Spatial distribution of primordial radiation S After susbstracting the galaxy’s motion. The equatorial contribution is due to the stars in our galaxy (the Milky Way). After susbtracting radiation from the Milky Way DT ~ 0.00001 °K The residual radiation inhomogeneities served as nucleation points for the formation of galaxies Temperature map T ~ n max

24. The mind-boggling enigma “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve“ E.Wigner. Why can we predict the temperature of the Universe but not next week’s weather? Why can we predict the behaviour of an electron but not our dog’s? The mathematical equations of our fundamental theories (EM, QM) are soluble because they are linear (the field of a sum of particles is the sum of the particles’ fields). This might not have been so (hydrodynamics). The Universe would then have remained mysterious and unpredictable, like the weather.