Download Lecture 20: Polyelectronic Atoms

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
– Electronic Configuration (Core and Valence
electrons)
• Problems Chapter 12 Zumdahl 5th Ed.
– 61-67, 71,72d, 75, 76, 78
1
Spin: The Fourth and final quantum number
• Electrons have spin even when
free in space; not part of an atom.
• Further experiments demonstrated
the need for one more quantum
number.
• Specifically, some particles
(electrons in particular)
demonstrated inherent (or internal)
angular momentum.
2
Electron Spin
Each and every electron has spin ½. (It is internal to the
electron)
Protons and neutrons also have spin ½.
ms = 1/2
• The new quantum number is ms
(analogous to ml).
• For the electron, ms has two values:
+1/2 and -1/2
ms = -1/2
• Half integer spin is an odd kind of
angular momentum not shared by
orbital angular momentum
(Z12.65) No it does not really spin,
but close.
3
The Aufbau Principle
• For polyelectronic (i.e. real) atoms, a direct solution
of the Schrodinger Equation is not possible. (Can’t
solve the 3 body motion problem; Z12.61)
• 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). This appx. implies effective
nuclear charges to hold electrons when there are
many electrons
• 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.
4
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).
5
First Row (Electronic Configuration)
• 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)
Number of Electrons in
the set of orbitals
2
1N
s
1s
2s
2p
E .C .
6
Second Row (E.C.)
• Lithium (Z = 3)
1s22s1
1s
2s
2p
• Berillium (Z = 4)
1s22s2
1s
2s
2p
• Boron (Z = 5)
1s22s22p1
1s
2s
2p
7
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
8
Finish 2nd row (n=2) (E.C.)
• Oxygen (Z = 8)
1s22s22p4
1s
2s
2p
• Fluorine (Z = 9)
1s22s22p5
1s
2s
2p
• Neon (Z = 10)
1s22s22p6
1s
2s
2p
full
9
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)
1s22s22p63s1
Ne
[Ne]3s1
3s
• Argon (Z = 18)
[Ne] 3s23p6
Ne
3s
3p
10
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.
11
Problems Z12.66-67
• Give the ground state: E.C. for Si, B, Al, S
• Give the first excited state E.C. for B.
2
2
2
2
• An O atom has the E.C. 1s 2 s 2 px 2 p y
– How many upaired electrons are present?
– Is this an excited state for O?
– In going from this state to the ground state would energy be
released or absorbed, why?
• Maximum number of electrons with these Q.N.s?
– (in general the max number of electrons is 2 times the number of
orbitals).
n = 4 ⇒ 16 ⋅ 2 = 32
n = 5, ms = 12 ⇒ 25 ⋅1
n = 3, A = 3 ⇒ 7 ⋅ 2 = 14
n = 2, A = 1, mA = −1, ms = −21 ⇒ 1
12
Paramagnetism (Z12.75,78)
• The number of unpaired electrons in an atom (either in
ground state or an excited state) can be measured by a
paramagnetism experiment.
• The experiments provide us with indications of the E.C. of
each atom.
• Consider the ground state E.C. of Li, Ni, Ba, Hg:
– Which is paramagnetic: Li, Ni.
– How many unpaired electrons are expected. (1,2,0,0)
• Is this an excited state E.C?
1s 2 2 s 2 2 p 4 3s1
– What neutral atom is it? (9 electrons, F)
2
2
5
0
– What is the ground state E.C? 1s 2 s 2 p 3s
– How many unpaired electrons in the ground state and excited
state? (1, and 3)
13
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.
14
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
Exceptions: Maximizes/Symmetrizes Unpairing Z12.71,72d
Z= 29, Copper: 1s22s22p63s23p64s13d10 = [Ar] 4s13d10
Z= 30, Zinc: 1s22s22p63s23p64s23d10 = [Ar] 4s23d10
15
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.
16
Lanthanides
• After Lanthanum ([Xe]6s25d1), we start filling 4f.
17
Actinides
• After Actinium ([Rn]7s26d1), we start filling 5f.
18
Column Numbering
• Heading on column given total number of valence electrons.
19
The Modern Periodic Table
20