# THE ELECTRON

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```					The Electron
Part 2
The Quantum Model of the Atom
• In 1927, Werner Heisenberg
proposed his uncertainty principle.
– You can’t know both the velocity &
position of a particle at the same time
– Meaning we can’t predict
the exact location of an e-
or it’s path in the atom
– Whatever you use to
measure the location of
an electron will cause the
electron to move
To detect the position of an electron you might use a photon.
Unfortunately, when the photon collides with the electron the
force of the collision causes the electron to change position,
so the best you can tell is where the electron was.
The Quantum Model of the Atom
• The biggest effect of the Uncertainty
Principle on Bohr’s model is that
there is no way to define the path of
the e- around its nucleus with any
accuracy.
– The best we can do is make an educ-
ated guess within a certain range of
probability that the e- is in a particular
region around the nucleus.
The Quantum Model of the Atom
• In 1926, the physicist Erwin Schrod-
inger took the atom 1 step further.
– He proposed a mathematical
equation to describe the location &
energy of the e- in a H atom.
– He used calculated the “wave func-
tion” of the e-, or the probability of
locating the e- a certain distance from
the nucleus
• the quantum mechanical model is
based on Schrodinger’s work.
The Quantum Model of the Atom
The Quantum Model of the Atom
• Like the Bohr model, the quantum
mech model of the atom restricts the
energy of e-’s to quantized values.
– But, the quantum mechanical model
doesn’t define a specific path an elec-
tron takes around the nucleus.
• Instead it estimates the probability of
finding an electron in a certain
position.
Bohr’s model gave
the e- specific paths
around the nucleus,
based on the energy
of the electron

However, we can only
guess within a certain
degree of probability the
location of an e-
The Quantum Model of the Atom
• The probability of finding an electron
within a certain volume of space
surrounding the nucleus can be
represented by a fuzzy cloud
– The cloud is more dense
where the probability of
finding the e- is higher.
The Quantum Model of the Atom
• Each electron in a given atom is
given a set of 4 values called
quantum numbers, that describe an
electron’s behavior.
– The 1st 3 quantum numbers map the
electron’s location, the 4th describes
the electron’s orientation.
– No 2 electrons have an identical set
of four quantum numbers.
The Quantum Model of the Atom
• You can assign every electron in a
given atom (element) a set of 4 quan-
tum numbers
• The quantum numbers act as the
• Quantum #’s can be described as a
kind of coordinate system to map the
location of an e- in the atom.
The Quantum Model of the Atom
• The problem with e- in the atom is
that they can’t be pinned down to a
precise location because of Heisen-
berg’s Uncertainty Principle
– So the quantum #’s only give a fuzzy
or probable location of the electron in
the atom.
The Quantum Model of the Atom
• An analogy of quantum numbers
might help.
– We can think about the quantum #’s
as perhaps like trying
to find our seat in
Rupp Arena
using a ticket stub.
The Quantum Model of the Atom
• Each piece of information on your
ticket stub gets you closer and closer
– Each quantum number gets us closer
and closer to the probable location of
an electron
The Quantum Model of the Atom
• The 1st quantum number is the
“Principle Quantum Number”
– symbolized by n.
– can values of 1 to infinity.
• The larger the value of n, the farther
from the nucleus the electron is.
– These electrons are more energetic
so the volume of their appearance is
larger
The Quantum Model of the Atom
• Each energy level has a limit to the
number of electrons it can hold.
–   n=1 can hold 2 electrons
–   n=2 can hold 8 electrons
–   n=3 can hold 8 electrons
–   n=4 can hold 18 electrons
–   n=5 can hold 18 electrons
–   n=6 can hold 32 electrons
The Quantum Model of the Atom
• The Principle quantum number can
be compared to the level of Rupp.
– The Upper Arena is farther from the
floor than the Lower Arena
– The larger the principal quantum
number the farther from the nucleus.
The Quantum Model of the Atom
• The 2nd Quantum number is the
“Azimuthal Quantum number”
– Symbolized with an “l,”
– can have numbers of 0, 1, 2, 3 which
correspond to the letters s, p, d, f.
– indicates a shape of an orbital
– “l” is expressed with letters rather
than numbers.
• An s orbital is spherical
• A p orbital is dumb-bell
• A d is mostly clover-leaf
• An f is really complicated
The Quantum Model of the Atom
• Each l is called an orbital
– An orbital is the region or volume
around the nucleus of an atom where
an electron with a given energy is
likely to be found.
The Quantum Model of the Atom
• Every energy level (quantum # - n)
contains 1 and only 1 s sublevel
– The number of sublevels in any given
n is theoretically related to the value
of n
• n=1has 1 sublevel…only the s
• n=2 has 2 sublevels…s & p
• n=3 has 3 sublevels…s, p, & d
• n=4 has 4 sublevels…s, p, d, & f
The Quantum Model of the Atom
• The quantum # l might correspond to
the section number on our stub
– It narrows down for us to the specific
area in the upper arena that our seat
is in.
– The l quantum number gives us the
sublevel of the electron on the energy
level.
The Quantum Model of the Atom
• The 3rd Quantum number is the
“Orientation/Orbital quantum
number”
– Symbolized by ml
– Within each sublevel, are orbitals –
each with a different orientation.
– Each orbital higher than ml = 1 can
have a different orientation on the
Cartesian axis (x, y, & z)
The Quantum Model of the Atom
• On a map ml might be thought of as
the row our seat is located on.
– The row narrows down for us where
in the section our seat is.
– In the atom, ml gives the direction that
the shape of the volume that the
electron occupies points.
The Quantum Model of the Atom
• Together the l and ml quantum
numbers give valuable info about the
electrons probable location
• The “s” sublevel (l =0; ml = 0):
– Spherical shape and only one
allowed in each energy level.
– As the energy increases (n) the “s”
orbital also gets bigger.
The Quantum Model of the Atom
• The p-sublevel: (l =1; ml=-1,0, or 1)
– Shaped like a dumbbell.
– There are 3 orbitals designated px, py,
or pz in each energy level. (Based on
axis on the cartesian coordinates)
– The p orbitals are higher energy then
s orbitals
– Only found in ground state atoms
containing 5 electrons or more
The Quantum Model of the Atom
• The d-orbital (l =2; ml= -2, -1, 0, 1, 2):
– The d orbitals have more
complicated shapes.
– There are 5-d orbitals in each energy
level that they appear.
– The d-orbitals appear only after the
2nd energy level, and beyond
Proposed
composite
of 5 d-orbitals
The Quantum Model of the Atom
• The f-orbital
(l = 3; ml = -3, -2, -1, 0, 1, 2, 3)
– Most energetic and complicated
– There can be 7 “f” orbitals for each
energy level that they occupy.
The Quantum Model of the Atom
• There is a limit to how many electrons
that each sublevel can hold, which
limits the number of electrons that
can have the same relative energy
Sublevel    # of      Maximum #
Orbitals   of Electrons
s         1             2
p         3             6
d         5            10
f         7            14
The Quantum Model of the Atom
• The 4th and final Quantum Number,
is the Spin quantum number
– Symbolized by ms
– Each orbital can hold at most 2
electrons,
• They must spin in opposite directions
on their axes designated (+½ & -½)
The Quantum Model of the Atom
• The spin quantum number might
work somewhat like the seat number
on the ticket stub.
– There is only one possible seat that
corresponds to the information on
– There is only one possible electron
that matches a given set
of quantum numbers
The Quantum Model of the Atom
Set of (n, l, ml, ms)
• H only has 1 electron, and it is on the
n=1 energy level, and it’s in the s-
sublevel
– (1,0,0,+½)
• He has 2 electrons, and they are both
on the n=1 energy level, and in the s
sublevel
– (1,0,0,+½)(1,0,0,-½)
The Quantum Model of the Atom
• Lithium has an electron in the n=2
energy level and so on….
– 3Li: (1,0,0,+½) (1,0,0,-½)
(2,0,0,+½)
– 4Be: (1,0,0,+½) (1,0,0,-½)
(2,0,0,+½) (2,0,0,-½)
– 5B: (1,0,0,+½) (1,0,0,-½)
(2,0,0,+½) (2,0,0,-½)
(2,1,-1,+½)
The Quantum Model of the Atom
• Continuing With n=2
– 6C: (1,0,0,+½) (1,0,0,-½)
(2,0,0,+½) (2,0,0,-½)
(2,1,-1,+½) (2,1,0,+½)
– 7N: (1,0,0,+½) (1,0,0,-½)
(2,0,0,+½) (2,0,0,-½)
(2,1,-1,+½) (2,1,0,+½)
(2,1,1,+½)
The Quantum Model of the Atom
– 8O: (1,0,0,+½) (1,0,0,-½)
(2,0,0,+½) (2,0,0,-½)
(2,1,-1,+½) (2,1,0,+½)
(2,1,1,+½) (2,1,-1,-½)
– 9F: (1,0,0,+½) (1,0,0,-½)
(2,0,0,+½) (2,0,0,-½)
(2,1,-1,+½) (2,1,0,+½)
(2,1,1,+½) (2,1,-1,-½)
(2,1, 0,-½)
The Quantum Model of the Atom
–   10Ne:   (1,0,0,+½) (1,0,0,-½)
(2,0,0,+½) (2,0,0,-½)
(2,1,-1,+½) (2,1,0,+½)
(2,1,1,+½) (2,1,-1,-½)
(2,1, 0,-½) (2,1,1,-½)
Not every orbital
is found in every
energy level.
(ie.The n=1 level
only contains
the s orbital)
Electron Configurations
• The distribution of electrons among
the energy levels, sublevels,
orientations, and spins of an atom is
known as the electron configuration.
– Having a basic understanding of how
the electrons are configured helps us
determine the interaction of atoms of
elements to other elements
– When they come into contact it’s the
outer electrons that do the chemistry.
Electron Configurations
• Electron configurations are determin-
ed by distributing electrons among
levels, sublevels, & orbitals, in order
of lowest in energy to highest.
• We can predict the location of the
electrons in the atoms by following 3
important principles:
Electron Configurations
• The Aufbau Principle
– Electrons are added one at a time to
the lowest energy orbitals available
until all electrons are distributed.
– The # of electrons distributed,
depends on the atomic # of the atom.
– We’ll use a diagram to help
placement in the proper order
Electron Configurations
• The Pauli Exclusion Principle
– An orbital can hold a maximum of
2 electrons.
– To occupy the same orbital the
electrons must spin in opposite
directions.
• Depicted with arrows         orbital
pointed in opposite
directions.

2 electrons
Electron Configurations
• Hund’s Rule
– Electrons occupying equal-energy
orbitals, are distributed so that the
maximum number of unpaired
electrons results.
– For ex, with Nitrogen’s 7 electrons
1        2             2
s        s             p
4d
5s
4p
3d
Energy

4s
3p

Oxygen
3s
2p
2s

1s
4d
5s
4p
3d
Energy

4s
3p

Nickel
3s
2p
2s

1s
Electron Configurations
• We generally don’t draw the energy
pattern and then fill in the boxes for
the configurations. We generally use
this type of notation:
# of electrons
Principal            in the orbital
Energy
Level

Orbital Type
Electron Configurations
• We generally don’t draw the energy
pattern and then fill in the boxes for
the configurations. We generally use
this type of notation:
# of electrons
Principal            in the orbital
Energy
Level

Orbital Type
Electron Configurations
• We generally don’t draw the energy
pattern and then fill in the boxes for
the configurations. We generally use
this type of notation:
# of electrons
Principal              in the orbital
Energy
Level

Orbital Type
Electron Configurations
• We generally don’t draw the energy
pattern and then fill in the boxes for
the configurations. We generally use
this type of notation:
# of electrons
Principal              in the orbital
Energy
Level

Orbital Type
Electron Configurations
• We generally don’t draw the energy
pattern and then fill in the boxes for
the configurations. We generally use
this type of notation:
# of electrons
Principal                   in the orbital
Energy
Level

Orbital Type
Electron Configurations
• To help write the electron configura-
tions we can use one of two tools.
• You choose the one that is most
comfortable for you.
– The periodic table
– The Aufbau diagram hanging in the
room
Electron Configurations
• Fe (Atomic Number = 26)
1s2 2s2 2p6 3s2 3p6 4s2 3d6
• Mg (Atomic Number = 12)
1s2 2s2 2p6 3s2
• Ne (Atomic Number = 10)
1s2 2s2 2p6
• Ti (Atomic Number = 22)
1s2 2s2 2p6 3s2 3p6 4s2 3d2
• Zr (Atomic Number=40)
1s2 2s2 2p6 3s2 3p64s2 3d10 4p6 5s2 4d2
Electron Configurations
• Don’t have to write out the entire
electron configuration.
• There is a short-cut:
– Keeps focus on valence electrons
– An atom’s inner electrons are
represented by the symbol for the
nearest noble gas with a lower atomic
number.
K: [Ar]4s1
Electron Configurations

For the element Phosphorus
-- 15 electrons
1s22s22p63s23p3

P:   [Ne] 3s 23p3
MUST BE A
NOBLE GAS
Electron Configurations
Let’s do a couple more:
Ba: [Xe]   6s 2

Hg: [Xe] 6s2 4f14 5d10
V: [Ar] 4s2 3d3
Exceptions to the order of filling
Electron Configurations
• The chemistry of an atom occurs at
the set of electrons called valence
electrons
• The valence electrons are the outer-
most s and p electrons of the atom.
– 2 s electrons + 6 p electrons = a full
set of valence electrons
• The arrangement of the valence e-