Download - Quantum Phenomena II: Revision
Quantum Quantum Phenomena Phenomena
II:II:RevisionRevision
Chris Parkes April/May 2003
Hydrogen atomHydrogen atom Quantum numbers Electron intrinsic spin
Other atomsOther atoms More electrons! Pauli Exclusion Principle Periodic Table
Particle PhysicsParticle Physics The fundamental particles The fundamental forces
CosmologyCosmology The big bang The evolution of the
universe
Fundamental PhysicsAtomic Structure
http://ppewww.ph.gla.ac.uk/~parkes/teaching/QP/QP.html
2
Quantum NumbersQuantum Numbers
Atom can only be in a discrete set of states n,l,mAtom can only be in a discrete set of states n,l,m Diff. From classical picture with any orbit
Principle n fixes energy - quantizedPrinciple n fixes energy - quantized Integer >=1
l fixes angular momentum Ll fixes angular momentum L Integer in range 0 to n-1
m (or mm (or ml l ) fixes z component of angular ) fixes z component of angular momentummomentum
Integer in range –l to +l
3
Total Angular momentumTotal Angular momentum
1.1. Orbital angular momentum L, Orbital angular momentum L, e orbiting nucleuse orbiting nucleus L2=l(l+1)h
2.2. Quantum number lQuantum number l notation l=spdfg…., l=0,1,2,3,4…
3.3. ll has z-component mhas z-component mll,, (-l….+l) (-l….+l) Interacts with magnetic field, U=mlBB Zeeman effect gives splitting of states
4.4. Spin s=1/2Spin s=1/2, intrinsic property of electron, intrinsic property of electron Has ms =-1/2, +1/2 So splits an l state into two
5.5. Total Angular Momentum JTotal Angular Momentum J Sum of orbital and spin Anomalous Zeeman effect / Stern-Gerlach Expt
4
Energy levelsEnergy levels
Hydrogen Energy levels Hydrogen Energy levels 1/n 1/n2 2 , scale is eV, scale is eV
In a magnetic field E will depend upon other In a magnetic field E will depend upon other quantum numbers (mquantum numbers (mll,m,mss), for Zeeman effect this ), for Zeeman effect this is:is:
[For anomalous zeeman effect from electron spin it is[For anomalous zeeman effect from electron spin it is
Where g is gyromagnetic ratio ~ 2]Where g is gyromagnetic ratio ~ 2]
eVn
E2
6.13
BmU Bl
BgmU Bs
5
Energy Levels cont..Energy Levels cont..
For multi-electron atomsFor multi-electron atoms Energy splitting depends on l even in absence of Energy splitting depends on l even in absence of
magnetic field.magnetic field. occurs due to screening effect Central field approximation
Pauli Exclusion principlePauli Exclusion principle No two fermions in same state
……Structure of Periodic tableStructure of Periodic table
electrons
nucleus
6
Particle PhysicsParticle Physics
Forces are due to exchange of the fundamental Forces are due to exchange of the fundamental force carrying bosonsforce carrying bosons
Photon,gluon,W+,W-,Zo (and presumably graviton)
Know the fundamental particlesKnow the fundamental particles Three generations of quarks and leptons
Don’t observe free quarksDon’t observe free quarks Confined in colourless hadrons
Added some more conservation lawsAdded some more conservation laws Energy, momentum, electric charge Baryon number, lepton number
Particle interactions can be written as Feynman Particle interactions can be written as Feynman diagramsdiagrams
Know the basic vertices, and conservation laws to see whether or not a reaction will occur.
7
Particle interactionsParticle interactions
Some basic standard model vertices:Some basic standard model vertices:
8
The Big BangThe Big Bang
Evidence for the Big BangEvidence 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 lawUniverse Expanding – Hubble’s law
Hence universe ~ 15 billion years oldHence universe ~ 15 billion years old
v = H x d,
Velocity Hubble const. distance
9
Evolution of the universeEvolution of the universe
Controlled by Quantum PhenomenaControlled by Quantum Phenomena Early stages dominated by basic particle physics Later stages by gravitational effects
Starts at high temp., high densityStarts at high temp., high density Cools down and expands….Cools down and expands…. Key stagesKey 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