• Electron has intrinsic angular momentum - ``spin''. It behaves as if it were ``spinning'', i.e. rotating around its axis.
• rotating charge magnetic field - the electron is a magnetic dipole.

  

• Remember:

  

• (In units of angular momentum,) the electron has ``spin ''; it is a member of the family of particles with ``half-integer spin'', called ''.
• Fermions obey Pauli's exclusion principle.
• direction of spin is ``quantized'', i.e. only certain directions are allowed. For spin 1/2, only two directions are allowed - called ``up'' and ``down''.
  

PAULI'S EXCLUSION PRINCIPLE
No quantum mechanical state can be occupied by more than one fermion of the same kind (e.g. more than one electron).

The hydrogen atom, having only one electron, is a very simple system; this is why Bohr's simple model worked for it.
Complications in atoms with many electrons:

• in addition to the force between electron and nucleus, there are also forces between the electrons;
• ``shielding'':
  electrons in outer orbits are shielded from the force of the nucleus by electrons in the inner orbits.
  

  need to solve Schrödinger equation to describe multi-electron atoms.

QUANTUM NUMBERS
Schrödinger equation applied to atom :

• electron's energy, magnitude and direction of angular momentum are quantized (i.e. only certain values allowed)
• no well-defined orbit, only probability of finding electron at given position ``orbital''
• the state of an electron is described by a set of four quantum numbers:
  • n, the principal quantum number
  • , the orbital quantum number
  • , the orbital magnetic quantum number
  • , the spin quantum number

  Meaning of quantum numbers:

  • the energy level of a state is determined by n and
  • most probable value of distance grows with n
  • 
  • (i.e. n different values);
    measures magnitude of angular momentum in units of ;
    value of influences the energy and the shape of the orbital:
    : spherical
    : dumbbell shaped,....
  • , i.e. different values;
    specifies direction of angular momentum (gives component of angular momentum vector in specified direction)
    determines orientation of orbital
  • denotes direction of spin:
    

    

    

Some definitions:

• collection of orbitals with same n = ``electron shell'';
• one or more orbitals with same and = ``subshell'';
• spectroscopic notation for orbitals:
  orbitals denoted by value of n and a letter code for the value of :

  ,

  ,

  ,

  ,

  ,

  and alphabetic after that;

  e.g.: ``2s'' refers to the subshell ;

  number of electrons in the subshell is added as a superscript;

  e.g.: `` '' means a configuration where 6 electrons are in the subshell 2p, i.e the subshell .
  

PAULI EXCLUSION PRINCIPLE :

• No two electrons in the same atom can have the same set of four quantum numbers
• the number of electrons in a given subshell is limited to
  (factor of 2 is due to orientation of spin),
  number of electrons in a given shell is limited to .
• in multi-electron atom, electrons cannot all sit in the lowest energy levels.

• The periodic system can be understood in terms of the possible electron states, as predicted by the solution of the Schrödinger equation, and the Pauli principle.
• for a given kind of atom (i.e. given total number of electrons), the ground state of the atom is that in which electrons occupy the states with the lowest possible energy.
• the electron configuration in the outer subshells of an atom determines its chemical properties.
• the beginning of every ``period'' of the periodic table corresponds to the beginning of a new shell
• the end of every period corresponds to the ``noble gases'', in which the outer electrons are in a particularly stable configuration, called ``noble gas configuration'' or ``octet structure''.
• the noble gas configuration is , i.e. 2 electrons in the s subshell, and 6 electrons in the p subshell of the shell n (except for n = 1, where there is no subshell).
• plot of ionization energy vs atomic number Z shows minima at the Z values corresponding to the beginning of periods (hydrogen, and the ``alkali metals'' Li, Na, K, Rb, Cs),
  and maxima at the end of the periods (the noble gases He, Ne, Ar, Kr, Xe, Rn).
  (ionization energy = energy necessary to liberate loosest bound electron of the atom).

• Atoms try to acquire particularly stable electron configuration (i.e the configuration maximizing binding energy) for their outer electrons
• form ions or molecules.
• Most stable configuration for outer electrons is noble gas configuration (octet structure)

  

• strategies to achieve more stable configuration:
  • give away electrons
  • accept electrons
  • share electrons
• this leads to formation of chemical bonds
• types of bonds:
  • ionic bond
  • covalent bond
  • metallic bond
    

IONIC BOND

• atoms achieve noble gas configuration by by giving up or accepting electrons (usually electron transfer from metal to non-metal) formation of ion;
• chemical bond is formed due to electrostatic attraction between two oppositely charged ions;
• bond is strong, but becomes quickly weak when ion is displaced;
  materials usually brittle (e.g. glass, rock, egg shells,..)
• compounds formed by ionic bond: e.g. NaCl, CaCl ,
• examples of ions with noble gas configuration:
  

  

METALLIC BOND

• atoms give up electron, to be shared by all
• metallic lattice = positive ions at fixed positions, in ``sea'' or ``gas'' of mobile electrons
• electrons mobile good thermal and electrical conductivity
• electron not tied down in particular bond can absorb and re-emit light over wide frequency range good reflector
• bond is ``elastic'' since attraction due to mobile electrons bond holds even if ions displaced metals are malleable
  

COVALENT BOND

• well-defined cluster of neighboring atoms share electrons - form ``molecule''
• state with shared electrons has lower energy than individual atoms
• ``valence electrons'' = outer electrons
  group number = number of valence electrons
• ``valence of element'' = number of electron pairs shared to complete octet of electrons
• examples:

  in , H atoms share one electron pair;

  in , O atoms share two electron pairs;

  in , N atoms share three electron pairs;

  single H, O, N (``in statu nascendi'') are much more reactive than pair

• Carbon
  Carbon's outer electron configuration is it needs 4 electrons to complete octet
  shares 4 pairs of electrons
  e.g. methane (``swamp gas'')
  possibility of 4 covalent bonds large variety of possible compounds with C organic chemistry

POLAR BONDS

• Electron pairs shared between two different atoms not necessarily shared equally - sharing ratio depends on electronegativity;
• ``electronegativity'' = ability of atom to attract an electron to itself;
• electronegativity increases from left to right (i.e. grows with group number) in every row of the periodic table;
  alkali metals (group 1) are least electronegative, halogens (group 7) are most electronegative;
• non-polar bond = bond in which electrons are shared equally
• polar covalent bond = bond in which one of the atoms exerts greater attraction for the electrons than the other (has larger electronegativity)
• if difference in electronegativity is large enough, bond becomes ionic bond

GEOMETRY OF BONDS

• electron-pair repulsion rule(EPRR):
  Electron pairs surrounding an atom (be they shared or un-shared with other atom) repel each other and are directed to be as far apart as possible.
• water molecule:

  oxygen in water has 4 electron pairs, 2 shared and 2 unshared;

  EPRR e-pairs point to corners of tetrahedron, with O atom in center of tetrahedron,

  H atoms sit at two of the corners of the tetrahedron;

  constituents of water form triangle; angle between the two lines from O to H is 105 (109 predicted from this model);
  ``Mickey Mouse shape'' of water molecule

  O is more electronegative than H water is polar molecule, more negative near O atom, more positive near H atoms.

  polarity of water molecule good solvent

INTER-MOLECULAR FORCES

• electric dipole forces:
  polar molecules exert electric dipole forces on each other;
  e.g. water molecule:
  attracted to (-) partner of other molecule (oxygen of other water molecule, or solute constituent)
  ``hydrogen bond'';
  hydrogen bond is reason for water to be liquid at ``normal'' temperatures
  (note e.g. are gases!)
• Van der Waals forces:
  fluctuations, shifts of charges within covalent molecule temporary dipole moment electrostatic dipole forces;
  charge unbalances small forces weak (Van der Waals binding energies are )
  most liquids held together by VdW forces,
  cohesion, surface tension