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Quantum Phenomena II: Revision Quantum Phenomena II: Revision Chris Parkes April/May 2003 Hydrogen atom Quantum numbers Electron intrinsic spin Other atoms More electrons! Pauli Exclusion Principle Periodic Table Particle Physics The fundamental particles The fundamental forces Cosmology The big bang The evolution of the universe Fundamental PhysicsAtomic Structure

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2 Quantum Numbers Atom can only be in a discrete set of states n,l,m Diff. From classical picture with any orbit Principle n fixes energy - quantized Integer >=1 l fixes angular momentum L Integer in range 0 to n-1 m (or m l ) fixes z component of angular momentum Integer in range –l to +l

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3 Total Angular momentum 1. Orbital angular momentum L, e orbiting nucleus L 2 =l(l+1)h 2. Quantum number l notation l=spdfg…., l=0,1,2,3,4… 3. l has z-component m l, (-l….+l) Interacts with magnetic field, U=m l B B Zeeman effect gives splitting of states 4. Spin s=1/2, intrinsic property of electron Has m s =-1/2, +1/2 So splits an l state into two 5. Total Angular Momentum J Sum of orbital and spin Anomalous Zeeman effect / Stern-Gerlach Expt

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4 Energy levels Hydrogen Energy levels 1/n 2, scale is eV In a magnetic field E will depend upon other quantum numbers (m l,m s ), for Zeeman effect this is: [For anomalous zeeman effect from electron spin it is Where g is gyromagnetic ratio ~ 2]

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5 Energy Levels cont.. For multi-electron atoms Energy splitting depends on l even in absence of magnetic field. occurs due to screening effect Central field approximation Pauli Exclusion principle No two fermions in same state …Structure of Periodic table electrons nucleus

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6 Particle Physics Forces are due to exchange of the fundamental force carrying bosons Photon,gluon,W +,W -,Z o (and presumably graviton) Know the fundamental particles Three generations of quarks and leptons Don’t observe free quarks Confined in colourless hadrons Added some more conservation laws Energy, momentum, electric charge Baryon number, lepton number Particle interactions can be written as Feynman diagrams Know the basic vertices, and conservation laws to see whether or not a reaction will occur.

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7 Particle interactions Some basic standard model vertices:

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8 The Big Bang Evidence for the Big Bang It is dark at night! See Olbers Paradox Universe expanding Cosmic microwave background Relative abundance of elements in universe Universe Expanding – Hubble’s law Hence universe ~ 15 billion years old v = Hx d, Velocity Hubble const. distance

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9 Evolution of the universe Controlled by Quantum Phenomena Early stages dominated by basic particle physics Later stages by gravitational effects Starts at high temp., high density Cools down and expands…. Key stages Separation of forces into the four basic forces Formation of nuclei Formation of atoms Microwave background radiation, remnant photons from when atoms formed Then gravitation dominates and stars and galaxies form

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