Quantum numbers and the periodic table

• An element's location on the periodic table reflects the quantum numbers of the last orbital filled
  
• The period indicates the value of principal quantum number for the valence shell
  • the lanthanides and actinides are in periods 6 and 7, respectively.
• The block indicates value of azimuthal quantum number () for the last subshell that received electrons in building up the electron configuration.
  • blocks are named for subshells (s, p, d, f)
  • Each block contains a number of columns equal to the number of electrons that can occupy that subshell
    • The s-block (in orange) has 2 columns, because a maximum of 2 electrons can occupy the single orbital in an s-subshell.
    • The p-block (in purple) has 6 columns, because a maximum of 6 electrons can occupy the three orbitals in a p-subshell.
    • The d-block (in green) has 10 columns, because a maximum of 10 electrons can occupy the five orbitals in a d-subshell.
    • The f-block (in dark blue) has 14 columns, because a maximum of 14 electrons can occupy the seven orbitals in a f-subshell.
• questions to ponder
  • What would the periodic table look like in a hypothetical universe where:
    • there were 3 possible values of m_s, instead of 2?
    • the angular momentum quantum number could take on values from 1 to n-1 only?
    • values of m = 0 were not allowed?
    • the maximum value of n were 5?

Factors affecting the valence shell

Atomic radius

• what does atomic radius really mean?
  • atoms have no definite surface
  • a simple model: bound atoms are like touching spheres
  • adding atomic radii for two bound atoms gives an estimate of bond length
  

  Explaining periodic trends in atomic radius. See the section on factors affecting the valence shell above.

  trend	valence n	Z	# core electrons	net effect on atomic radius
  going right across main group rows...	no change	increases	no change	the increase in Z causes a decrease in radius
  going right across transition series...	no change	increases	increases	the increase in Z causes a decrease in radius, but the increase in the number of core electrons causes an increase. The two competing effects cause a small decrease, then small increase!
  going down groups...	increases	increases	increases	three competing effects; but n is strongest, so radius increases.

• using the trends
  • to compare atoms in different groups and different periods, look for atoms that must be intermediate in size
    • this isn't always possible!
    • example: Which is larger, a silicon atom, or a selenium atom?

Ionic radius

• periodic trends parallel those of atomic radius
• cations are always smaller than the parent atom
  • removing an electron decreases electron-electron repulsion, so the electron clouds contract
  • emptying the valence shell completely leaves only electrons with lower n value
• anions are always larger than the parent atom
  • adding an electron to an atom increases electron-electron repulsion and swells the electron cloud
• comparing radii for isoelectronic ions and atoms
  • size within isoelectronic series is affected only by Z
  • example
    F^-, Ne, and Na⁺ are isoelectronic, with Z = 9, 10, and 11, respectively. All have identical valence n and identical numbers of electrons, so the larger Z is, the smaller the atom or ion. Na⁺ is the smallest and F^- is the largest.

Ionization energy

• ionization energy is the minimum amount of energy required to remove an electron from an atom or ion in the gas phase
• normally, ionization removes valence electrons first
  • valence electrons are farthest from nucleus on average, so they feel the least attraction for the nucleus and are easiest to remove
  • end of valence electrons is marked by a big jump in ionization energies

    Na(g) Na+(g) + e-	H = +496 kJ	first ionization energy
    Na+(g) Na+2(g) + e-	H = +4560 kJ	second ionization energy
  • core orbitals have lower n, and are much more penetrating than valence orbitals
  • proximity to nucleus makes core electrons much more difficult to remove
  • core noble gas configurations have high stability
• factors affecting ionization energy
  • atomic radius
    • smaller atoms hang on to valence electrons more tightly, and so have higher ionization energy
  • charge
    • the higher the positive charge becomes, the harder it is to pull away additional electrons
    • second ionization energy is always higher than the first
  • orbital penetration
    • It's easier to remove electrons from p orbitals than from s orbitals
  • electron pairing
    • within a subshell, paired electrons are easier to remove than unpaired ones
    • reason: repulsion between electrons in the same orbital is higher than repulsion between electrons in different orbitals
    • example
      On the basis of gross periodic trends, one might expect O to have a higher ionization energy than N. However, the ionization energy of N is 1402 kJ/mol and the ionization energy of O is only 1314 kJ/mol. Explain.
      
      Taking away an electron from O is much easier, because the O contains a paired electron in its valence shell which is repelled by its partner.

Why metals are metals

• the ionization energy of metallic elements is very low
• valence electrons are easily lost, and shared among all atoms in the metal
• this 'sea' of valence electrons binds together the metal cations and gives metals their characteristic properties
  • mobility of electrons in the sea explains metal's ability to conduct electricity and heat
  • metals are workable because cations can slide past each other but still be bound by the electron sea
• comparing metals
  • more valence electrons means stronger metal
  • higher positive charge on cations, higher negative charge on sea = stronger bonding

Explaining elemental properties: the s block elements

• the alkaline earth metals (Group IIA)
  • soft, but harder than alkali metals
    • ns² valence configuration = more electrons in the sea = more tightly bound metal cations
  • reactive, but not as reactive as alkali metals
    • ionization energies are not as low as alkali metals
  • salts less soluble than those of the alkali metals
    • higher cation charge concentrated on smaller cations makes it hard to pull apart ionic lattices