Pauli and the Elements

1
Lecture 17

• Pauli and the Elements

2
Periodic Table by Mendeleev
Properties of the elements repeat periodically
as the atomic number is increased, but why?
3
Zeeman Effect (1894)

• Spectral lines are split in a magnetic field
  (e.g., in a sunspot)
• Could be explained in terms of angular momentum
  of electron around the nucleus
• This is related to the existence of the quantum
  numberm. Recall when l 1, m can take the
  values -1, 0, 1

4
Anomalous Zeeman Effect (1897)

• Too many lines were observed in some cases
• Explanation by Goudsmit and Uhlenbeck electron
  is also spinning on its axis

5
Stern-Gerlach Experiment (1922)

• A beam of silver atoms split into two directions
  when passed through a magnetic field
• Shows that electrons can spin in only two
  directions in space (since silver is made up of
  an odd number of electrons)

6
What We Know About Electron Spin Today

• Can only spin in two directions either spin
  up or spin down
• Spin quantum number takes value 1/2
• Takes a rotation of 720 to complete one round!

7
Bosons and Fermions

• Bosons are particles with integer spins
• e.g., photons (spin 1)
• Fermions are particles with half-integer spins
• e.g., electrons, protons, neutrons, neutrinos ...
• Ordinary matter are made out of fermions, while
  radiation is made out of bosons

8
The Pauli Exclusion Principle (PEP)

• Two or more fermions cannot be in the same
  quantum state (i.e., have the same quantum
  numbers)
• Does not apply to bosons

Wolfgang Pauli (1900-1958)
9
The Difference Between Bosons and Fermions
10
Consequences of the PEP

• Existence of atoms and molecules
• Existence of white dwarfs and neutron stars

It is the fact that electrons cannot all get
on top of each other that makes tables and
everything else solid. Richard
Feynman
11
Quantum Numbers of an electron in an atom
12
Energy Levels of an Atom
13
Hydrogen Atom
14
Hydrogen Atom (contd)

• Electron can either be spin up or down
• Two hydrogen atoms can combine to give a hydrogen
  molecule H2 the two electrons have opposite
  spins
• By PEP, three hydrogen atoms cannotcombine
  together to give H3

15
Hydrogen Molecule Orbital Diagram
16
Helium Atom

• The two electrons fill the 1s state, with
  opposite spins
• By PEP, there is no more room for other
  electrons in the 1s state forms a closed shell
• Makes helium chemically inert
• Similar situation for the other inert noble gases

17
Lithium Atom

• First two electrons fill the 1s state, and form
  a closed shell
• Third electron must go to the next level 2s
• Thus, similar chemical properties as hydrogen

18
Oxygen Atom (Z8)

• 1s and 2s shells are closed four remaining
  electrons in 2p state
• There is room for two more electrons in 2p state,
  e.g., from two hydrogen atoms
• That is why we have water H2O

19
Water Molecule Orbital Diagram
Hydrogen atoms join up with the 2px and 2py states
20
Sodium Atoms Orbital Diagram

• A sodium atom in the groundstate has a partially
  filled 3s state and an empty 3p state
• A collection of sodium atomswould have
  overlapping 3p states
• Electrons in the 3s state canjump to the 3p
  state andhence move between atoms

21
Band Theory QM explains properties of
conductors, semiconductors and insulators
Conductor
Semiconductor
Insulator
22
Band Theory (contd)

• In a metal, there are many unfilled energy
  levels in the valence band (c.f. partially full
  LT). Electrons can easily move between the
  valence and conduction bands
• In a semiconductor, the valence band is full
  (c.f. completely full LT). Only a few electrons
  can jump to the conduction band
• In an insulator, the energy gap between the bands
  is too large for electrons to jump the gap