Lecture 20: Polyelectronic Atoms
• Reading: Zumdahl 12.10-12.13
• Outline:
– Spin (the 4th quantum number)
– The Aufbau (“filling-up”) Principle
– Filling up orbitals and the Periodic Table
Spin: The Fourth and final quantum number
• Further experiments
demonstrated the need
for one more quantum
number.
• Specifically, some
particles (electrons in
particular)
demonstrated inherent
(or internal) angular
momentum.
Electron Spin
Each and every electron has spin ½.
All protons and neutrons also have spin ½.
ms = 1/2
ms = -1/2
• The new quantum
number is ms
(analogous to ml).
• For the electron, ms
has two values:
+1/2 and -1/2
The Aufbau Principal
• For polyelectronic (i.e. real) atoms, a direct
solution of the Schrodinger Equation is not
possible.
• When we construct polyelectronic atoms, we use
the hydrogen-atom orbital nomenclature to discuss
in which orbitals the electrons reside.
• This is an approximation (and it is surprising how
well it actually works).
• Aufbau is German for “Building Up”. We are
building a multielectronic atom from the rules for
the 1 electron atom (so a few things get modified),
but it works pretty well.
Pauli’s Principle for many electron atoms
• When placing electrons into orbitals in the
construction of polyelectronic atoms, we use the
Aufbau Principle. (German for Up-Building)
• This principle states that in addition to adding
protons and neutrons to the nucleus, one simply
adds electrons to the hydrogen-like atomic orbitals
• Pauli exclusion principle: No two electrons may
have the same (4) quantum numbers. Therefore,
only two electrons can reside in an orbital
(differentiated by ms).
First Row (Electronic Configuration)
• Finally, orbitals are filled starting from the lowest
energy (to get the lowest total-energy atoms,
called the ground state))
• First number is the principle quantum number,
letter is the angular quantum number.
• Example: Hydrogen
1s1
1s
2s
2p
• Example: Helium (Z = 2)
1s2
1s
2s
2p
E.C.
Second Row (E.C.)
• Lithium (Z = 3)
1s22s1
1s
2s
• Berillium (Z = 4)
2p
1s22s2
1s
2s
2p
• Boron (Z = 5)
1s22s22p1
1s
2s
2p
Hund’s Rule
• Carbon (Z = 6)
1s22s22p2
1s
2s
2p
Hund’s Rule: Lowest energy configuration is
the one in which the maximum number of unpaired electrons
are distributed amongst a set of degenerate orbitals.
• Nitrogen (Z = 7)
1s22s22p3
1s
2s
2p
Finish 2nd row (n=2) (E.C.)
• Oxygen (Z = 8)
1s22s22p4
1s
• Fluorine (Z = 9)
2s
2p
1s22s22p5
1s
2s
2p
• Neon (Z = 10)
1s22s22p6
1s
2s
2p
full
Third Row (n=3)
Valence Electrons – the higher energy ones, used for chemistry
Core electrons -- those of low energy that can be the set of
electrons in the noble gas contained within the atom
• Sodium (Z = 11)
Ne
1s22s22p63s1
[Ne]3s1
3s
• Argon (Z = 18)
[Ne] 3s23p6
Ne
3s
3p
Summary: First 3 Rows
We now have the orbital configurations for the first 18 elements.
How did we know the order? Follow the periodic table.
Why not 3d before we hit noble gasses?
• Elements in same column have the same # of valence electrons!
• For Main Group elements we are filling the p orbitals
• For Alkali and Alkaline Earth elements fill the s orbitals.
th
4
Row (E.C.)
Similar to Sodium, we begin the next row of the periodic
table by adding electrons to the 4s orbital.
Order gets a bit confusing:
we have inner and outer shell valence electrons
• Why not 3d before 4s?
• 3d is closer to the nucleus;
think about electron crowding
• 4s is energetically preferred,
but the energetics are close,
more on this later.
4th Row
• Elements Z=19 and Z= 20:
Z= 19, Potassium: 1s22s22p63s23p64s1 = [Ar]4s1
Z= 20, Calcium: 1s22s22p63s23p64s2 = [Ar]4s2
• Elements Z=21 to Z=30 have occupied d orbitals:
Z= 21, Scandium: 1s22s22p63s23p64s23d1 = [Ar] 4s23d1
Z = 24, Chromium: [Ar] 4s13d5
exception
Z= 30, Zinc: 1s22s22p63s23p64s23d10 = [Ar] 4s23d10
Periodic Table: The magic of 1,3,5,7
← 2 ⋅1 →
←
←
2⋅5
←
2⋅3
→
→
2⋅7
→
This orbital filling scheme gives rise to the modern periodic table.
Lanthanides
• After Lanthanum ([Xe]6s25d1), we start filling 4f.
Actinides
• After Actinium ([Rn]7s26d1), we start filling 5f.
Column Numbering
• Heading on column given total number of valence electrons.
The Modern Periodic Table
Summary
View Aufbau principle
movie. Use the periodic
table to tell you the
proper order of filling for
the correct E.C. for each
atom.
• Electrons go into
hydrogen-like orbitals
to construct
polyelectronic atoms.
• Remember the
adjacent “trick” for
remembering how to
fill orbitals.