Chapter 4
Arrangement of Electrons in Atoms
Section 1 – The Development of a
new Atomic Model
Properties of Light
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
Before 1900, scientists thought light behaved as a wave
Changed when it was discovered that light also had
particle-like characteristics
Visible light is a kind of electromagnetic radiation 
form of energy that exhibits wavelike behavior as it
travels through space
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
X-rays, UV, infrared, etc.
Together, all forms of electromagnetic radiation form the
electromagnetic spectrum
Properties of EM Radiation

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All forms of EM radiation travel at a constant speed (3.0
× 108 meters per second (m/s)) through a vacuum and at
slightly slower speeds through matter
It has a repetitive nature, which can be described by the
measurable properties  wavelength and frequency
Wavelength (λ)  the distance between corresponding
points on neighboring waves
Frequency (ν)  the number of waves that pass a given
point in a specific time, usually one second
λ
λ
Frequency and Wavelength


Frequency and wavelength are mathematically related to
each other
This relationship is written as follows
c = λν
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c is the speed of light
λ is the wavelength of the electromagnetic wave
ν is the frequency of the electromagnetic wave
Because c is the same for all electromagnetic radiation,
the product λν is a constant
The Photoelectric Effect
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
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Early 1900s, scientists
conducted two
experiments involving
relations of light and
matter that could not be
explained by the wave
theory of light
One experiment involved
a phenomenon known as
the photoelectric effect
Photoelectric effect 
the emission of electrons
from a metal when light
shines on the metal
The Mystery

For a given metal, no electrons were emitted if the light’s
frequency was below a certain minimum—regardless of
how long the light was shone

Light was known to be a form of energy, capable of
knocking loose an electron from a metal

Wave theory of light predicted light of any frequency
could supply enough energy to eject an electron

Couldn’t explain why light had to be a minimum
frequency in order for the photoelectric effect to occur
The Particle Description of Light

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
Explanation  1900, German physicist Max Planck was
studying the emission of light by hot objects
Proposed a hot object does not emit electromagnetic
energy continuously, as would be expected if the energy
emitted were in the form of waves
Instead, Planck suggested the object emits energy in small,
specific amounts called quanta
Quantum  the minimum quantity of energy that can be
lost or gained by an atom

Planck projected the following relationship between a
quantum of energy and the frequency of radiation
E = hν

In the equation,



E is the energy, in joules, of a quantum of radiation
ν is the frequency of the radiation emitted
h is a constant now known as Planck’s constant

h = 6.626 × 10−34 J• s
1905 Albert Einstein
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Expanded on Planck’s theory by introducing the idea that
electromagnetic radiation has a dual wave-particle
nature
Light displays many wavelike properties, it can also be
thought of as a stream of particles
Einstein called these particles photons
Photon  a particle of electromagnetic radiation having
zero mass and carrying a quantum of energy
The energy of a specific photon depends on the
frequency of the radiation
Ephoton = hν
The Hydrogen-Atom Line-Emission
Spectrum



When current is passed
through a gas at low
pressure, the potential
energy of some of the gas
atoms increases
The lowest energy state of
an atom is its ground
state
A state in which an atom
has a higher potential
energy than it has in its
ground state is an excited
state
Example: Neon Signs

When an excited atom
returns to its ground
state, it gives off the
energy it gained in the
form of electromagnetic
radiation

Excited neon atoms emit
light when falling back to the
ground state or to a lowerenergy excited state.
Line-Emission Spectrum

Scientists passed electric current through a vacuum tube
containing hydrogen gas at low pressure, they observed
the emission of a characteristic pinkish glow

Emitted light was shined through a prism, it was separated
into a series of specific frequencies of visible light

The bands of light were part of what is known as
hydrogen’s line-emission spectrum
Quantum Theory
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
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The hydrogen atoms should be excited by whatever
amount of energy was added to them
Scientists expected to see the emission of a continuous
range of frequencies of electromagnetic radiation, that is,
a continuous spectrum
Why had the hydrogen atoms given off only specific
frequencies of light?
Attempts to explain this observation led to an entirely
new theory of the atom called quantum theory


Whenever an excited hydrogen
atom falls back from an excited
state to its ground state or to a
lower-energy excited state, it
emits a photon of radiation
The energy of this photon
(Ephoton = hν) is equal to the
difference in energy between the
atom’s initial state and its final
state

Changes of energy (transition of an electron from
one orbit to another) is done in isolated quanta

Quanta are not divisible

There is sudden movement from one specific
energy level to another, with no smooth transition

There is no ``in-between‘‘

Hydrogen atoms emit only specific frequencies of
light  showed that energy differences between
the atoms’ energy states were fixed

The electron of a hydrogen atom exists only in very
specific energy states
Bohr Model of the Hydrogen Atom


Proposed a model of
the hydrogen atom that
linked the atom’s
electron with photon
emission
According to the
model, the electron can
circle the nucleus only
in allowed paths, or
orbits

When the electron is in one of these orbits, the atom has
a definite, fixed energy

The electron, and therefore the hydrogen atom, is in its
lowest energy state when it is in the orbit closest to the
nucleus

This orbit is separated from the nucleus by a large empty
space where the electron cannot exist

The energy of the electron is higher when it is in orbits
farther from the nucleus
The Rungs of a Ladder
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The electron orbits or atomic energy levels in Bohr’s
model can be compared to the rungs of a ladder
When you are standing on a ladder, your feet are on one
rung or another
The amount of potential energy that you possess relates
to standing on the first rung, the second rung…
Your energy cannot relate to standing between two rungs
because you cannot stand in midair
In the same way, an electron can be in one orbit or
another, but not in between
Summary of the Models of the Atom
Section 2 – The Quantum
Model of the Atom
The Quantum Mechanical Model of the
Atom

1) In 1924, Louis de Broglie proposed that
ELECTRONS have a dual wave-particle nature. Other
experiments soon demonstrated wave properties of
electrons.
The Quantum Mechanical Model of the
Atom

2) In 1926 Erwin Schrodinger treated
electrons as waves in a model called the
quantum mechanical model of the
atom.
a)
b)
Schrodinger’s equation applied equally well to
elements other than hydrogen.
Schrodinger’s equations: helps determine
probable electron location in an atom
The Quantum Mechanical Model of the
Atom

orbital = a three-dimensional region around the
nucleus that indicates the probable location of an
electron. (fuzzy electron clouds)
a)
The cloud has no definite boundary, it is possible that the
electron might be found at a considerable distance from the
nucleus.
The 4 Quantum Numbers:
MAGNETIC
d)
Ex. Orbitals around the Nucleus of a Neon Atom
Quantum Numbers

Electrons are not locked into fixed orbits

We can only predict the areas where electrons are
most likely to be found

Numbers are given to electrons to help with
predictions
Quantum Numbers
There are four quantum numbers. The first three
quantum numbers result from solutions to
Schrodinger’s equation and describe the orbital in which
an electron is located.
•
•
•
Principal quantum number
Angular momentum quantum number
Magnetic quantum number
The fourth quantum number describes an electron’s
spin movement within an orbital.
The 4 Quantum Numbers: PRINCIPAL
1)
The PRINCIPAL QUANTUM NUMBER
indicates the main energy level (shell) of the
orbital in which a particular electron is located.
The 4 Quantum Numbers:
ANGULAR MOMENTUM
2)
The ANGULAR MOMENTUM QUANTUM
number indicates the shape (sublevel) of the orbital in
which a particular electron is located.
a) The angular momentum quantum number is symbolized
by the letter “l”
b) Angular momentum quantum numbers are usually
designated with letters s,p,d,f
c) The order of the sublevels can be remembered as
follows: “some people don’t forget
The 4 Quantum Numbers:
MAGNETIC
The MAGNETIC QUANTUM NUMBER indicates
the spatial orientation of the orbital in which a
particular electron is located.
3)
a)
b)
The magnetic quantum number is symbolized by “m”.
The orientation of an orbital is designated using a threedimensional coordinate system with the nucleus at the
center.
The 4 Quantum Numbers:
MAGNETIC
c)
•
•
•
•
Orientation of orbitals
An “s” orbital has 1 possible orientation (a sphere centered
on the nucleus).
A “p” orbital has 3 possible orientations. (px, py, pz)
A “d” orbital has 5 possible orientations.
An “f” orbital has 7 possible orientations.
The 4 Quantum Numbers:
SPIN
The SPIN QUANTUM NUMBER indicates the spin
of an electron on its own axis
4.
The spin quantum number is symbolized by “s”.
There are two possible fundamental states (spins) for an
electron in an orbital
a)
b)

+1/2 and -1/2 are used to indicate the two possible states (spins) of
an electron in an orbital
f
s
p
s
p
4
3
d
s
2
s
1
d
p
Energy levels can be
thought of as floors in
an apartment building.
The floors that are
higher up contain
more apartments with
different numbers of
rooms. The
apartments are like
the sublevels. The
rooms in the
apartments are like
the number of orbitals
in a sublevel.
Summary of the First 4 Energy Levels
Principal
Quantum
Number:
Main Energy
Level (n)
Type(s) of
Sublevel
(orbital shapes)
# of Orbitals
per main
energy level
Maximum # of
Electrons per
sublevel
1
s
1
2
s
1
2
p
3
6
s
1
2
p
3
6
d
5
10
s
1
2
p
3
6
d
5
10
f
7
14
2
3
4
Number of
Electrons
per Main
Energy
Level (2n2)
Section 3 – Electron
Configurations

Quantum model of atom better than Bohr model b/c it
describes the arrangements of electrons in atoms other
than hydrogen
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Electron configuration  the arrangement of electrons
in an atom

b/c atoms of different elements have different numbers of
e-, the e- configuration for each element is unique

Electrons in atoms assume arrangements that have lowest
possible energies

Ground-state electron configuration  lowest-energy
arrangement of electrons for each element

Some rules combined with quantum numbers let us
determine the ground-state e- configurations
Rules Governing Electron Configurations
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1.
2.
3.
To build up electron configurations for the ground state
of any particular atom, first the energy levels of the
orbitals are determined
Then electrons are added to the orbitals one by one
according to three basic rules
Aufbau principle
Pauli exclusion principle
Hund’s rule
Aufbau Principle
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The first rule shows the
order in which electrons
occupy orbitals
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According to the Aufbau
principle, an electron
occupies the lowest-energy
orbital that can receive it
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The orbital with the
lowest energy is the 1s
orbital
Ground-state hydrogen
atom  electron in this
orbital
The 2s orbital is the next
highest in energy, then
the 2p orbitals
Beginning with the third
main energy level, n = 3,
the energies of the
sublevels in different main
energy levels begin to
overlap

The 4s sublevel is lower
in energy than the 3d
sublevel

Therefore, the 4s orbital
is filled before any
electrons enter the 3d
orbitals

(Less energy is required
for two electrons to pair
up in the 4s orbital than
for a single electron to
occupy a 3d orbital)
Pauli Exclusion Principle
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
The second rule reflects
the importance of the spin
quantum number
According to the Pauli
exclusion principle, no
two electrons in the same
atom can have the same set
of four quantum numbers
Hund’s Rule
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The third rule requires placing as many unpaired
electrons as possible in separate orbitals in the same
sublevel
Electron-electron repulsion is minimized  the electron
arrangements have the lowest energy possible
Hund’s rule  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
Orbital Notation
H
C
He
Electron-Configuration Notation

Electron-configuration notation eliminates the lines
and arrows of orbital notation

Instead, the number of electrons in a sublevel is
shown by adding a superscript to the sublevel
designation

The hydrogen configuration is represented by 1s1
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The superscript indicates that one electron is
present in hydrogen’s 1s orbital
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The helium configuration is represented by 1s2

Here the superscript indicates that there are two
electrons in helium’s 1s orbital
Sample Problem
The electron configuration of boron is
1s22s22p1. How many electrons are present in
an atom of boron? What is the atomic
number for boron? Write the orbital notation
for boron.
Practice Problems

The electron configuration of nitrogen is 1s22s22p3.
How many electrons are present in a nitrogen
atom? What is the atomic number of nitrogen?
Write the orbital notation for nitrogen.
Practice Problems
The electron configuration of fluorine is 1s22s22p5. What is
the atomic number of fluorine? How many of its p
orbitals are filled? How many unpaired electrons does a
fluorine atom contain?
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Answer
9
2
1
Elements of the Second Period
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According to Aufbau principle, after 1s orbital is filled, the
next electron occupies the s sublevel in the second main
energy level
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Lithium, Li, has a configuration of 1s22s1

The electron occupying the 2s level of a lithium atom is in
the atom’s highest, or outermost, occupied level

The highest occupied level  the electron-containing
main energy level with the highest principal quantum
number

The two electrons in the 1s sublevel of lithium are no
longer in the outermost main energy level

They have become inner-shell electrons  electrons
that are not in the highest occupied energy level

The fourth electron in an atom of beryllium, Be, must
complete the pair in the 2s sublevel because this sublevel is of
lower energy than the 2p sublevel
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With the 2s sublevel filled, the 2p sublevel, which has three
vacant orbitals of equal energy, can be occupied

One of the three p orbitals is occupied by a single electron in
an atom of boron, B
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Two of the three p orbitals are occupied by unpaired
electrons in an atom of carbon, C

And all three p orbitals are occupied by unpaired electrons in
an atom of nitrogen, N
Elements of Third Period

After the outer octet is filled in neon, the next electron
enters the s sublevel in the n = 3 main energy level

Atoms of sodium, Na, have the configuration 1s22s22p63s1

Once past Neon, can use Noble-gas notation
Noble-Gas Notation


The Group 18 elements (helium, neon, argon, krypton,
xenon, and radon) are called the noble gases
To simplify sodium’s notation, the symbol for neon,
enclosed in square brackets, is used to represent the
complete neon configuration:
[Ne] = 1s22s22p6

This allows us to write sodium’s electron configuration as
[Ne]3s1, which is called sodium’s noble-gas notation
Elements of the Fourth Period

Period begins by filling 4s orbital (empty orbital of lowest
energy)

First element in fourth period is potassium, K
E- configuration [Ar]4s1
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Next element is calcium, Ca
E- configuration [Ar]4s2
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With 4s sublevel filled, 4p
and 3d sublevels are next
available empty orbitals
Diagram shows 3d
sublevel is lower energy
than 4p sublevel
So 3d is filled next

Total of 10 electrons can
fill 3d orbitals

These are filled from
element scandium (Sc) to
zinc (Zn)
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Scandium has e- configuration [Ar]3d14s2
Titanium, Ti, has configuration [Ar]3d24s2
Vanadium,V, has configuration [Ar]3d34s2
Up to this point, 3 e- with same spin added to 3 separate
d orbitals (required by Hund’s rule)

Chromium, Cr, has configuration [Ar]3d54s1


We added one electron to 4th 3d orbital
We also took a 4s electron and added it to 5th 3d orbital
Seems to be against Aufbau principle

In reality, [Ar]3d54s1 is lower energy than [Ar]3d44s2


Having 6 outer orbitals with unpaired electrons in 3d
orbital is more stable than having 4 unpaired electrons in
3d orbitals and forcing 2 electrons to pair in 4s

For tungsten, W, (same group as chromium) having 4 e- in
5d orbitals and 2 e- paired in 6s is most stable
arrangement

No easy explanantion


Manganese, Mn, has configuration [Ar]3d54s2
Added e- goes to 4s orbital, completely filling it and
leaving 3d half-filled

Starting with next element, e- continue to pair in d
orbitals

So iron, Fe, has configuration [Ar]3d64s2
Cobalt, Co, has [Ar]3d74s2
Nickel, Ni, has [Ar]3d84s2
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

With copper, Cu, an electron from 4s moves to pair with
e- in 5th 3d orbital
Configuration: [Ar]3d104s1 (most stable)

For zinc, Zn, 4s sublevel filled to give [Ar]3d104s2

For next elements, 1 e- added to 4p orbitals according to
Hund’s rule

Elements of Fifth Period

In 18 elements of 5th period, sublevels fill in similar way to
4th period elements
BUT they start at 5s level instead of 4s level

Fill 5s, then 4d, and finally 5p

There are exceptions just like in 4th period

Practice Problem
Write both the complete electron-configuration notation
and the noble-gas notation for iron, Fe.
Write both the complete electron configuration notation
and the noble-gas notation for iodine, I. How many innershell electrons does an iodine atom contain?



1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p5
[Kr] 4d10 5s2 5p5
46
How many electron-containing orbitals are in an atom of
iodine? How many of these orbitals are filled? How many
unpaired electrons are there in an atom of iodine?



27
26
1
Write the noble-gas notation for tin, Sn. How many
unpaired electrons are there in an atom of tin?


[Kr] 5s2 4d10 5p2
2
Without consulting the periodic table or a table in this
chapter, write the complete electron configuration for the
element with atomic number 25.

1s2 2s2 2p6 3s2 3p6 3d5 4s2
Elements of 6th and 7th periods



6th period has 32 elements
To build up e- configurations for elements in this period,
e- first added first to 6s orbital in cesium, Cs, and barium,
Ba
Then in lanthanum, La, e- added to 5d orbital

With next element, cerium, Ce, 4f orbitals begin to fill
Ce: [Xe]4f15d16s2

In next 13 elements, 4f orbitals filled

Next 5d orbitals filled

Period finished by filling 6p orbitals

(some exceptions happen)

Practice Problem
Write both the complete electron-configuration notation
and the noble-gas notation for a rubidium atom.


1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s1
[Kr]5s1
Write both the complete electron configuration notation
and the noble-gas notation for a barium atom.


1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
[Xe]6s2