Electronic Structure cont’d:
Representations of hydrogen-like orbitals
s orbitals
l = 0, ml= 0: one s orbital per
subshell
spherically symmetric
p orbitals
l = 1, ml = -1, 0, 1: three p orbitals
per subshell (starting at n=?)
two lobes; oriented along x, y, z
axes
d orbitals
l = 2, ml = -2, -1, 0, 1, 2: five d
orbitals per subshell (starting at
n=?)
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Many - electron atoms
H atom: 1 electron in the lowest
energy state (1s); this is the ground
state
In the H atom, all orbitals with same n
have the same energy (e.g. orbital
diagram)
We want to treat many-electron atoms (all
atoms except H)
Schrödinger's equation can be
solved exactly only for H atom!!
To a very good approximation, many
electron atoms can be described with
H-like orbitals (1s, 2p, etc.)
Presence of more than 1 electron
greatly alters orbital energies e.g.,
2s < 2p and 3s < 3p < 3d
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The essential result:
For a given value of n, orbital
energies increase with increasing l
value
As a rule, s < p < d for subshells with
the same n value
Draw an orbital diagram for manyelectron atoms – include all orbitals
from the first three shells…
How to place electrons in the orbitals?
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Electron spin & the Pauli exclusion principle
Electron possesses an intrinsic
magnetic moment called electron
spin
Electron spin is quantized –
we assign a spin quantum number ms which only can
1
have values ms = 
2
now we have 4 quantum numbers to
describe an electron in a many
electron atom: n, l, ml, and ms
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Pauli exclusion principle
no two electrons in an atom can have
the same 4 quantum numbers
for a given orbital (1s, 2p, etc.), n, l,
ml are fixed
We will assume that two electrons in
a many-electron atom may be in the
same allowed energy state (orbital)
By the Pauli principle, if more than
one electron is in the same energy
state, we MUST use different values
of ms
we conclude that a given orbital can
‘hold’ only two electrons WITH
OPPOSITE SPINS!!
We represent an electron with ms = 1/2 with an  arrow
We represent an electron with ms = -1/2 with a  arrow
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Now: use the orbital diagram we developed earlier for
many-electron atoms, and develop electron configurations
for elements H-Zn
Electron configurations
arrangement of electrons in an atom = electron
configuration
ground electron configuration: all electrons in their
lowest energy states
1s orbital is lowest in energy, followed by 2s and 2p;
electrons fill the 1s, then 2s, then 2p, 3s, 3p, 4s, 3d,
etc.
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Writing electron configurations
From the orbital diagram: write symbol for occupied
orbitals with a superscript to indicate occupancy, e.g.,
H: 1s1
He: 1s2
Li: 1s22s1
Be: 1s22s2
B: 1s22s22p1
C: 1s22s22p2
For C: does the second 2p electron go in spinpaired or unpaired?
Hund's rule: for degenerate orbitals, lowest
energy is obtained when the number of electrons
with the same spin is maximized
Electrons will occupy orbitals singly as much as
possible, with parallel spins
We continue filling the 2p orbitals from N to Ne:
N: 1s22s22p3
O: 1s22s22p4
F: 1s22s22p5
Ne: 1s22s22p6
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- what's so special about Ne?
- after Ne: start filling the 3s orbital at Na:
Write 1s22s22p63s1 or [Ne]3s1
Na has one 3s electron beyond the Ne
configuration
- what about Li? [He]2s1
Li and Na are similar in chemical and physical
properties because they have the same outershell electron configuration!
Outer shell electrons are those electrons beyond
a noble gas configuration – these are the valence
electrons
Core electrons are found in the inner shells
Filling of 4s starts at K: [Ar]4s1;
Ca: [Ar]4s2
after 4s: 3d subshell is filled
Sc: [Ar]4s23d1 :
transition metals
Ti: [Ar]4s23d2
V: [Ar]4s23d3
Cr: [Ar]4s23d4 or
[Ar]4s13d5 ?
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Mn: [Ar]4s23d5
...Zn: [Ar]4s23d10
start filling 4p at
Ga: [Ar]4s23d104p1
..
Kr: [Ar]4s23d104p6
Regions of the periodic table revisited:
Active metals (Groups 1A, 2A): filling outer s-subshell
Representative (main group) elements: filling outer psubshell
Transition metals: filling outer d-subshell
Lanthanides/Actinides: filling outer f-subshell
So: elements in the same group have the same valence
electron configuration
The periodic table thus arises from the periodic nature of
electron configurations
How does the periodic nature of electron configurations
influence chemical and physical properties of the
elements?
Next, we examine the periodic nature of chemical and
physical properties of the elements
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Problems du Jour
What is the maximum number of electrons in an atom that
can have the following quantum numbers:
n = 2, ms = - ½
n = 5, l = 3
n = 4, l = 3, ml = -3
n = 4, l = 1, ml = 1, ms = ½
Write electron configurations for the following elements.
Give the number of unpaired electrons in each.
a) Ga
b) Sb
c) Ti
d) S
e) Co
f) Rb
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