# Chapter 4: Arrangement of Electrons in Atoms ```Warm-Up
 Lithium
has an atomic weight of
6.941 g/mol. When 10.4115 g of
lithium is heated, it emits an energy
measured at 262,500 joules. What is
the energy given off by one atom?

Wave Theory
Particle Theory
Light has measureable
characteristics of frequency (ν)
and wavelength (λ)
When matter is heated, it emits
depends on the temperature.
Planck showed that energy can
only be released by atoms in
“chunks” of some minimum size
(quantum). E=hν
Properties of Light
Wave Theory
Particle Theory
Photoelectric effect: light shining on a
clean metal surface causes the surface to
emit electrons, but only if the frequency of
the light is greater than some minimum
frequency. Einstein showed that light
comes in small energy packets called
photons. The photon must have enough
energy (E=hν) to overcome the attractive
forces holding the electron within the
metal atom. If the photon does not have
enough energy (does not have the
minimum frequency), no electron will be
emitted.
Emission Lines – Bohr Model of the atom
Properties of Light
 To
explain why energy states of an
atom are quantized, scientists had to
change the way they viewed the
nature of the electron.
 The photoelectric effect, and
hydrogen emission lines showed that
light could behave as both a wave
and a particle.
 What does this mean for the
electron??
4-2 The Quantum Model of the Atom
Louis de Broglie – 1924
 Suggested that electrons were
waves confined to the space
around the nucleus
 the waves could only exist at
certain frequencies that
corresponded to specific
energies—the quantized energies
of Bohr’s orbits (where E = hν).

4-2 The Quantum Model of the Atom
A beam of electrons
passed through a crystal
shows the pattern to the
right.
 Why is there a pattern
of light and dark rings?
 What would you expect
to see if you passed light
through a tiny slit?
 Video

 The
pattern is due
to wave
Interference and
Diffraction.
Wave Interference
 Interference
is when two waves overlap
(superpose) to form a resultant wave of
greater or lesser magnitude.
Constructive Interference –
Destructive Interference –
in a smaller (or no) wave
larger wave
Wave Interference
 diffraction
involves a change in
direction of waves as they pass
through an opening or around an
obstacle in their path.
 As the waves bend around the
obstacle, they experience
interference (constructive
and destructive)
Wave Diffraction

Electron beam diffraction
experiments showed the
bending of an electron wave
as it passes by the edge of
an object, such as an atom
in a crystal. The resulting
interference pattern occurs
when waves overlap,
resulting in a reduction of
energy in some areas and an
increase of energy in others.
Further Evidence Shows That The Electron Also
Acts As A Wave
 Diffraction shows
that
light behaves like a
wave, and electrons
also behave like a
wave.
Take Home Message…
Bohr showed that
electron orbits are
quantized (only exist at
certain frequencies).
 If we think of the
electron wave as being
like a wave that is
confined to a box of a
specific distance, the
wave can only exist
stably if it is showing
harmonics.

Why only certain frequencies?
What Does The Wave Have To Fit?
There is a restriction
on the wavelengths
that the electron can
have. In successive
revolutions, the
waves must be
exactly in phase with
each other. Why?
Oh Joy, Another Formula
The wavelength of any
orbital can be related to
size of the orbit. How?
2πr = nλ;
for n = 1, 2, 3, 4…
This IS Why It’s Quantized
Since each orbital
can only have a
specific wavelength
associated with it,
the energy of that
orbital is fixed by
the equation E = hν.
 The
value of n gives the first quantum
number, which indicates the main energy
level occupied by the electron.
Think 3-D, Not 2
The Heisenberg Uncertainty Principle (1927)
 It
is impossible to
determine
simultaneously both
the position and
velocity of an
electron or any other
particle.
 Video
Werner Heisenberg
Think of the waveparticle duality of
matter as this:
A quantum entity,
such as a photon or
an electron travels as
a wave, but arrives
as a particle.
Wave-Particle Duality
Together with the
uncertainty principle, the
wave equation laid the
foundation for modern
quantum theory.
 Quantum theory
describes
mathematically the wave
properties of electrons
and other very small
particles.

The Schr&ouml;dinger Wave Equation (1926)
The wave functions
give only the
probability of finding
an electron at a given
place around the
nucleus.
Solutions to the equations = Wave Functions
 The
electrons do not travel around the nucleus
in neat orbits, as Bohr had thought.
 Instead, the electrons exist in certain regions
called orbitals.
 An orbital is a three dimensional region
around the nucleus that indicates the probable
location of an electron.
Orbitals
 In
order to completely describe
orbitals, quantum numbers are used.
 Quantum numbers specify the
properties of atomic orbitals and the
properties of electrons in orbitals.
 The first 3 quantum numbers result
from solutions to the Schrodinger
equation.
Atomic Orbitals and Quantum
Numbers
 Indicates
the main energy level
occupied by the electron.
 Values of n are positive integers (1,
2, 3…)
 As n increases, the electron’s energy
and average distance from the
nucleus increases.
Principal Quantum Number (n)
 Indicates
the shape of the orbital.
 For each n the number of orbital
shapes possible is equal to n.
 The values of l that are allowed are
zero and all positive integers less
than or equal to n-1.
Angular Momentum Quantum
Number (l)
 l=0
designates
an s orbital
 l=1 designates
a p orbital
 l=2 designates
a d orbital
 l=3 designates
an f orbital
Angular Momentum Quantum
Number (l)
 Indicates
the orientation of an
orbital around the nucleus.
 The values allowed are
m = -l……0…….+l
Magnetic Quantum Number (m)
 Only
two possible values, +&frac12; or -&frac12;
 Indicates the two fundamental spin
states of an electron in an orbital.
 A single orbital can hold a
maximum of two electrons, which
must have opposite spins.
Spin Quantum Number
 Improves
upon Bohr’s model
because it describes the
arrangement of electrons in atoms
other than hydrogen.
 The arrangement of electrons in an
atom is known as the atom’s
electron configuration.
The Quantum Model
 Electrons
in atoms tend to assume
arrangements that have the lowest
possible energies - ground state
electron configuration
The Quantum Model
Some background info…

To simplify things, we show
electrons in orbits around
the nucleus (it’s really 3-D
orbitals).

There can be a
maximum of 8
electrons in the outer
shell!!!
◦ But only the noble gases
(Group 18) are full (ex.
Neon)
Rules Governing Electron Configurations
The energy levels of the
orbitals are determined and
orbitals one by one
according to 3 basic rules:
1. Aufbau principle
2. Pauli exclusion principle
3. Hund’s rule

Aufbau (“Build-up”) Principle
An electron occupies the
lowest-energy orbital that can
Note: Starting with the third
main energy level (n = 3), the
energies of the sublevels begin
to overlap (see diagram on p.
105).

Pauli Exclusion Principle (1926)
 No
two electrons in the same
atom can have the same set of
four quantum numbers. Thus
electron pairs in orbitals must be
of opposite spin.
Wolfgang Pauli:
Hund’s Rule
Notice how the “3p” electrons
are all up arrows before you
start filling with down
 Orbitals
of equal
energy are each
occupied by one
electron before any
orbital is occupied
by a second electron,
and all electrons in
singly occupied
orbitals must have
the same spin.
 The rule above
minimizes electronelectron repulsion.
 Orbitals
are like clouds showing
the most probable region of
electron locations.
 The sizes and shapes of electron
clouds depend on the energies of
the electrons that occupy them.
Orbitals are like clouds…
n
(principle quantum number) –
the main energy level (shell or
orbit)
 l (angular momentum QN) – the
shape of each sublevel
 m (magnetic QN) – how many
orbitals are in each sublevel
 Spin QN – direction of spin for an
electron in an orbital
Quantum Numbers – Like GPS
Coordinates for an electron
Orbital Notation
2. Electron-Configuration Notation
3. Noble-Gas Notation
4. By the quantum numbers associated with each
electron (you will NOT be held responsible for this
on a test).
1.
Terminology that you need to know follows:
Four Ways of Representing Electron
Configurations
Highest Occupied Energy Level

The electron-containing
main energy level with the
highest principal quantum
number.
AKA: The outermost
shell/orbit
Inner-shell Electrons
Electrons that are not in
the highest occupied
energy level.
AKA: Everything that is
NOT in the outer
shell/orbit
Orbital Notation

An unoccupied orbital is
represented by a line. The
lines are labeled with the
sublevel (principal quantum
number and orbital shape).
◦
◦
◦
◦
Why 1 line for s-orbitals?
Why 3 lines for p orbitals?
Why 5 lines for d orbitals?
Why 7 lines for f orbitals?
 Draw
and label the sublevels (see
Fig 4-16 p. 105)
 Make sure your energy levels are
spaced appropriately!
 Add electrons to the orbitals one by
one following the 3 rules.
Orbital Notation
 Draw
the orbital notation for Boron
 First, determine how many electrons
Boron has – 5
 Next draw &amp; label the sublevels
2p
2s
1s
Orbital Notation - Example
 Draw
the orbital notation for
Nitrogen
 First, determine how many electrons
Nitrogen has – 7
 Next draw &amp; label the sublevels
2p
2s
1s
Orbital Notation - Example
 Draw
the orbital notation for
Oxygen
 First, determine how many electrons
Oxygen has – 8
 Next draw and label the sublevels
2p
2s
1s
Orbital Notation - Example
 Draw
the orbital notation for
Magnesium
 First, determine how many electrons
magnesium has – 12
 Next draw and label the sublevels
3s
2p
2s
 Don’t
have to draw the lines and
arrows 
 The number of electrons in a
sublevel is shown by adding a
superscript to the sublevel
designation
Electron Configuration Notation
 Draw
the electron configuration
notation for Boron
2p
2p
2p
1s22s22p1
2s
1s
Orbital Notation for Boron
Electron Configuration Notation
 Draw
the electron configuration
notation for Nitrogen
2p
2p
2p
1s22s22p3
2s
1s
Orbital Notation for Nitrogen
Electron Configuration Notation
 Draw
the electron configuration
notation for Oxygen
2p
2p
2p
1s22s22p4
2s
1s
Orbital Notation for Oxygen
Electron Configuration Notation
 Draw
the electron configuration
notation for Magnesium
3s
2p
2p
2p
1s22s22p63s2
2s
1s
Orbital Notation for Magnesium
Electron Configuration Notation
WARNING!!!
The electron-configuration
in the book is NOT in the
proper order!!!
 Do not copy from the table,

 The
electron configuration for an
atom is 1s22s22p63s23p5
 How many electrons does it have?
 What is the atomic number? 17
 What element is it? Chlorine
 In the 3rd main energy level, how
many p orbitals are filled? 2
 How many unpaired electrons does
this atom have? 1
Example
17
Noble Gas Configuration
The outer main energy level
is fully occupied, in most
cases, by eight electrons
(sometimes called
“completing the octet”).
Which noble gas does not
complete the octet?
Noble Gas Notation

This is a shorthand method to show electron
configurations, usually for atoms in the 3rd period and
beyond. You show the nearest previous noble gas as
the core, and then only denote the outermost
electrons.
Weird Variations
Chromium (Cr) expect [Ar]4s23d4, is [Ar]4s13d5
 Copper (Cu) expect [Ar]4s23d9, is [Ar]4s13d10

The reason is that mixes of half and/or fully filled orbitals are
more stable (in a lower-energy state), than a combination of
fully or half filled orbital with a partially filled orbital.
Assignment
Electron-configuration
worksheet
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