QM ATOM QUARK F2011

QM ATOM QUARK F2011 - Survival of concept of ‘Atom’...

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Unformatted text preview: Survival of concept of ‘Atom’ è༎ Democritus (460 –370 BCE) Epicurus (341 – 270BCE) è༎ Titus Lucre&us Carus (99 - 55 BCE) Poggio Bracciolini (1380- 1459) Survival of concept of ‘Atom’ Schrödinger Hydrogen Atom The potential energy of the electron-proton system is electrostatic: V (r ) = − e2 4πε 0 r Use the three-dimensional time-independent Schrödinger Equation. ⎡ྎ ∂ 2ψ ( x, y, z ) ∂ 2ψ ( x, y, z ) ∂ 2ψ ( x, y, z ) ⎤ྏ h2 1 − + + ⎢ྎ ⎥ྏ = E − V ( r ) 2 2 2 2m ψ ( x, y, z ) ⎣ྏ ∂x ∂y ∂z ⎦ྏ For Hydrogen-like atoms (He+ or Li++), replace e2 with Ze2 (Z is the atomic number). Schrödinger Hydrogen Atom • The wave function ψ is a function of r, θ, φ. This is a potentially complicated function. • Assume optimistically that ψ is separable, that is, a product of three functions, each of one variable only: ψ (r, θ , ϕ ) = R(r ) f (θ )g(ϕ ) m = Rn,l (r )Yl (θ , ϕ ) E0 − µ ⎛ྎ e 2 ⎞ྏ 1 ⎜ྎ ⎟ྏ 2 = − 2 En = 2 ⎜ྎ 4πε 0 ⎟ྏ n n ⎝ྎ ⎠ྏ A negative energy means that the electron and proton are bound together. Hydrogen Atom Radial Wave Functions • First few radial wave functions Rnℓ Sub-scripts on R specify the values of n and ℓ. Spherical Harmonics Hydrogen Atom Quantum States Schrödinger Hydrogen Atom E0 En = − 2 n • The three quantum numbers: – n: Principal quantum number – ℓ : Orbital angular momentum quantum number – mℓ: Magnetic (azimuthal) quantum number The energy levels are: 114 atoms with distinct properties reflecting the internal structure of the atoms themselves Pauli Exclusion Principle => Constructing Matter Rutherford: atoms are not elementary particles! Precursor of modern scaFering experiments at accelerator Rutherford: atoms are not elementary particles! proton electron neutron From the atom to the quark <10-18 m <10-1 8 m ~ 10-10 m ~ 10-14 m ~ 10-15 m To learn about the sub-atomic structure we need particle accelerators From the atom to the quark <10-18 m <10-1 8 m ~ 10-10 m ~ 10-14 m u quark: electric charge = 2/3 d quark: electric charge = -1/3 ~ 10-15 m Proton = uud electric charge = 1 Neutron = udd electric charge = 0 If each proton were 10 cm across, each quark would be 0.1 mm in size and the whole atom would be 10 km wide. Protons and neutrons in the quark model Quarks have fractional electric charge! u electric charge + 2/3 d electric charge -1/3 proton (charge +1) u d u neutron (charge 0) u d d ⎛ྎ 2 ⎞ྏ ⎛ྎ 2 ⎞ྏ ⎛ྎ 1 ⎞ྏ ⎛ྎ 2 ⎞ྏ ⎛ྎ 1 ⎞ྏ ⎛ྎ 1 ⎞ྏ u⎜ྎ + ⎟ྏ u⎜ྎ + ⎟ྏ d ⎜ྎ − ⎟ྏ = p(+ 1) u⎜ྎ + ⎟ྏ d ⎜ྎ − ⎟ྏ d ⎜ྎ − ⎟ྏ = n(0) ⎝ྎ 3 ⎠ྏ ⎝ྎ 3 ⎠ྏ ⎝ྎ 3 ⎠ྏ ⎝ྎ 3 ⎠ྏ ⎝ྎ 3 ⎠ྏ ⎝ྎ 3 ⎠ྏ The particles of ordinary matter charge 0 Leptons: n = neutrino e = electron νe -1 e- +2/3 u -1/3 d Quarks: u = up d = down All stable matter around us can be described using electrons, neutrinos, u and d “quarks” 3 Families (or Generations) – Reason Unknown! 1st generation 0 νe -1 e 2nd generation +2/3 u -1/3 d Ordinary matter 0 νm -1 µ- 3rd generation +2/3 c s Cosmic rays -1/3 0 νt τ -1 t b +2/3 -1/3 Accelerators 3 generations in everything similar but the mass We believe these to be the fundamental building blocks of matter Anti-matter •  For every fundamental parKcle of maFer there is an anK- parKcle with same mass and properKes but opposite charge MaFer 0 AnK- MaFer +2/3 u νe - 1 e- - 1/3 d - 2/3 0 u νe +1 e+ +1/3 d positron •  Correspondent anK- parKcles exist for all three families •  AnK- maFer can be produced using accelerators Bar on top to indicate anK- parKcle Quarks and Colour All quark flavours come in 3 versions, called “colours” u +2/3 d - 1/3 u d u d up down Quarks combine together to form colourless parKcles -  Baryons (three quarks: red+ green + blue = white) Strong forces “glue” quarks together in bound states proton p -  Mesons (quark- anKquark pair) such as red+anK- red u- ubar state pion π u u The Eightfold Way  Neutron and proton form part of the octoplet which gave the theory its name  (8 particles)‫ .‏‬Different multiplets put all together 20 Neutron β- decay – Discovery of another force At quark level: d→ u e- νe u d n d 15 min p u u d e- νe A (free) neutron decays after 15 min Long life time ⇒ “weak” without such weak interactions the Sun would shut down! The 4 Forces of Nature Weak •  Beta-decay •  pp fusion Weak charge Strong •  Quark binding Strong (color) charge Electromagnetic • TV, PCs , iPhone •  Magnets • Power Electric charge Gravity Responsible of keeping us on earth Mass Electromagnetism e- e- γ e- e- Weak Force: W-,W+,Z0 β-decay n→peνe W- Strong Force: Gluons Gluons interact with quarks Gluons interact with other gluons Quark Confinement •  There are no free quarks, quarks and anKquarks are “confined” in colourless doublet (mesons) or triplets (baryons) by the exchange of gluons Decay Z0 Gluon hold quarks together as they move further apart unKl the gluon connecKon snaps, and other quark- anKquark pairs are created out of the energy released The new quarks bound to the old quarks and form new mesons ® S.Ward Force Particles Particles interact and/or decay thanks to forces. Forces are also responsible of binding particles together. Strong: gluons Weak: W+, W-, Z0 Only quarks (because of their colour charge) Leptons and quarks (only force for neutrinos) Electromagnetic:γ Gravity: graviton? Quarks and charged leptons Still to be discovered (no neutrinos) Negligible effects on particles The Standard Model Framework which includes: Matter •  6 quarks •  6 leptons Grouped in three generations Forces •  Electroweak: -  g (photon) -  Z0, W± •  Strong -  g (gluon) H= the missing ingredient: the Higgs Boson Not gravity! No quantum field theory of gravity yet.. Very successful to describe all observed phenomena in the subatomic world so far. But there ought to be more.. ...
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This note was uploaded on 01/02/2012 for the course PHYSICS 2214 at Cornell.

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