Atoms
Where are the electrons?
RPI - ERTH 2330
Louis Victor de Broglie (1925) said that
the wavelength of any particle of mass
(m) and velocity v is l = h/mv
h is equal to 6.6262 E -34 Js.
Electrons as waves…
E.B. Watson
the wavelength of any particle
l = h / mv
Standing Waves
A free electron moves in a traveling wave, like a
ripple across the water.
When it becomes captured by an atom, its movement
is that of a standing wave.
n=1
n=2
n=3
n=4
E.B. Watson
A variable that is allowed by the system to
have only certain discrete values is said to
be quantized. The variable n, which
enumerates these permitted values is
called a quantum number.
Heisenberg uncertainty principle
Uncertainty
Problem – we cannot measure the position and
velocity of a small particle at the same time.
E.B. Watson
Remember l = 2L/n? (2D
wave – guitar string)
Meet Y (3D wave)
Quantization
Integers n, l, m
Describe r, q, and f
E.B. Watson
Principle (n)
distance
1, 2, 3, 4,…
Angular mo. (l )
shape
0 to n – 1, 0 is spherical
Magnetic (m)
orientation
-l to +l
Wave function
distance sphericity orientation
We are forced to describe the position of the
electron in terms of probability
Y 2n,l,m
The electron around a nucleus is highly likely to
be in a quantized standing wave.
E.B. Watson
s orbital
E.B. Watson
E.B. Watson
p orbital
E.B. Watson
n>2
l=1
m = -1 , 0 , 1
d orbital
for n > 2, l = 2
m = -2, -1, 0, 1, 2
balloons extending from nucleus at right
angles
f orbital
m = -3, -2, -1, 0, 1, 2, 3
for n > 3, l = 3
Geometry is very complex
Image from Kotz
and Purcell, 1987
Hydrogen (H)
Energy for
position for one
electron
In other words,
the electron
could be in any
one of these
circles - but only
as a function of
available energy
BTW – an eV is an
electron volt and is
1.60217646 E -19
Joules
DE = 10.25 eV
Energy and electron
position.
•lowest 1s orbital - ground
state for hydrogen.
•2s and 2p are same energy,
greater than that of the 1s,
and are energetically
equivalent (for hydrogen).
•there is a direct relationship
between orbital size and
energy level.
•Increasing n means
decreasing DE.
So – a single electron’s position may be defined by
its probability to be in a certain orbital (s, p, d, or f),
as defined by Y2 n, l , m.
It’s position caries a certain energy.
Beyond Hydrogen: Multiple electron atoms
The wave function must define only one electron.
Two unidentical electrons may occupy one orbital.
We need one more number in our wave function!!
We have three n, l, m. However, we
may place two electrons in each wave
number (orbital).
Introducing s, the term for the spin of the
electron
Two values +1/2 and -1/2. Terms carry
a direction component (pos or neg) and
a symmetry component (1/2).
The spin is related to the angular momentum of the electron.
Electrons are spinning particles, and they may spin in
one orbital in either positive or negative directions.
But they may not spin in the same direction within one
orbital – thus, n, m, l, s combine to describe a unique
place for an electron (Pauli Exclusion Principle)
Table of electron wave functions
Note: the orbital letter is
determined by the value of l.
Remember
Any single object
with mass and
velocity can be
defined as a wave
The uncertainty
of observing the
mass requires a
probability
treatment
Nick Kim’s
cartoon pokes
fun at getting
carried away with
this…
Ground State
The lowest amount of
energy used to retain
the electrons is called
a ground state.
On the graph on the
right, what are the two
possible ground states
for a hydrogen atom?
Hund’s rule: electrons retain parallel spin
as much as possible.
We end up with this :
2px 2py 2pz
1s 2s
not this:
2px 2py

2pz
B
C
N
O
2p
Predicting the arrangement of atoms
He- 2 electrons - both share the 1s orbital
Li - 3 electrons - two share 1s, and one in 2s
There is an increased nuclear charge with
greater Z.
Therefore, spatial equivalency doesn’t mean
equivalent energies!
4s is lower than 3d!
Notation:
Notation:
Size of Atom
Increase down a group
Decrease across a period.
When moving across a period of main group elements, the size decreases
because the effective nuclear charge increases.
For more
than one
electron:
Electrostatic
repulsion
between
electrons
Increased
nuclear
charge
(larger # of
protons)
Stripping off an electron
A certain quantity of energy is needed to
evict an electron from its home.
Ionization Energies
Mendeleev’s Table
Image from Kotz
and Purcell, 1987
E.B. Watson
Electron configuration and periodicity
For more
than one
electron:
Electrostatic
repulsion
between
electrons
Increased
nuclear
charge
(larger # of
protons)
f
d
The periodic table
Elements 1 through 20 easily divide the behavior into
8 periods based on the numbers of electrons in the
highest energy orbital
Group 3b-2b - The transition elements
Beyond 20 - the d orbital; room for 10 electrons with
no or little change in energy. However, the d orbital
can split energies (2 up, 3 down or inverse) if needed.
Transition state
Lanthanides and Actinides
The f orbital - naturally occurring lanthanides
are known as the Rare Earth Elements (REE’s).
6s provides valence (+2; except divalent Eu)
Valence
The number of bonds that an atom can form as part
of a compound is expressed by the valence of the
element.
Goal -atoms want to end up in compounds that give
them a noble-gas-like configuration.
• Singles (like Na) form only one bond, and are
therefore monovalent
• Magnesium has a valency of two (divalent)
For elements on the right side of the periodic table
and sub 20 III-V elements, valence is the number of
outermost electrons.
Group VI-VII elements require additional electrons, as
they have nearly complete valence shells. Their
valence is determined by what they lack (O is
divalent).
Transition elements may have multiple valences.
Fe is best example. So do may heavy elements in
p-block - these depend on what and how they are
bonded.
Notation
We may denote how many electrons are present in a
neutral ground-state atom a number of different
ways.
One presentation - dots surrounding the atomic
symbol - Lewis Structures
Potassium has 19 electrons
[Ar] 4s1
K
Sulfur has 16, [Ne] 2s2 2p4 - Four
electrons in p, two in s
Strontium has 38
[Kr] 5s2
Sr
S
Ions are atoms that carry a charge as
valence electrons are lost/gained
Cation - Atom loses electron(s)
(becomes positive)
[Ca]2+
Calcium Ca2+
Anions - Atom gains electron(s)
(becomes negative)
[
O
]
2-
Oxygen O2-
Ionization
Valence electrons are those easiest to move from their lowenergy orbital away from the attraction of the Atom.
As such, its relatively cheap to move the electron(s) out of the
s-orbital or into the p-orbital
Column IA (1) has 1 valence electron - ions may be created by
removing the s orbital electron
Column IIA (2) has 2 valence electrons at the same ionization
energy, ions may be removing both electrons from the s orbital.
Column VIA (15) lacks two electrons to complete the p-orbital.
Column VIIA (16) lacks one electron to complete the p-orbital
Group IA, 1 valence electron (p1), form +1 cation
Group IIA, 2 valence electrons (p2), form +2 cations
Group VIA, 6 valence electrons (p2 d4), form -2 anions
Group VIIA, 7 valence electrons (p2 d5), form -1 anions
Okay, why does
this work?
Low DE between
electron
configurations
This works when
one considers
the shape of the
orbitals as they
interact with
those of adjacent
atoms (oxygen)
Ionization occurs either by losing or gaining
electrons
Linus Pauling quantified the ability of an
atom to attract (gain) electrons. He termed
this quantity electronegativity.
Electronegativity
capacity of an atom to attract extra electrons
Image from Gill, 1996
How big is an ion?
Ionic Radius - the size
A cation is always smaller than the
atom from which it is derived (because
it has lost an electron)
Example: Li 1.52 Å Li+ 0.82 Å
An anion is always bigger than the
atom from which it is derived.
Example: F 0.64 Å F- 1.25 Å
Ionic radii are not fixed - they depend on the degree of ionization
and any adjacent atoms to which they are bonded.
Similar Behavior
Image modified from Gill, 1996
•Electron movement may be modeled with standing
waves
•Position and velocity are simultaneously uncertain,
probabilities are used
•Ground state is the lowest-energy configuration
•Orbitals are functions of discreet energies - movement
to lower energies produce an electromagnetic photon
•Periodicity matches orbital configuration
•Removal or addition of outermost (valence) electrons
produces ions
•Affinity to attract ions is electronegativity
•Ionic radii are dependent on both the electron
structure and its interactions in bonding.