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Chapter 4
Arrangement of
Electrons in Atoms
4-1 The Development of a New
Atomic Model
Rutherford’s model did not explain where
electrons were – what prevented electrons
from being drawn into nucleus?
 New model arose from experiments
involving absorption and emission of light
by matter

4-1 Properties of Light
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Light can behave as a wave
Visible light is a kind of electromagnetic radiation (energy that
exhibits wavelike behavior as it travels through space)
EM radiation includes X rays, UV and IR light, microwaves,
radiowaves
4-1 Properties of Light

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All EM radiation moves at the same speed in a
vacuum: 3.0 x 108 m/s
Wave motion is repetitive
Wavelength (λ): distance between
corresponding points on adjacent waves (m, cm,
nm)
Frequency (v): number of waves that pass a
given point in a specific time, usually one second
(1/s, Hz)
4-1 Properties of Light
4-1 Properties of Light

Since speed is constant, frequency and
wavelength are related to each other
mathematically
c = λv
Wavelength and frequency are
INVERSELY proportional because their
product is a constant.
4-1 Sample Problem

Determine the frequency of light with
wavelength 550 nm.
 Convert
nm to m
 Use formula c=λν to determine v
4-1 The Photoelectric Effect (Light
as a Particle)
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1900s – an experiment that
cannot be explained by the
wave theory of light
Photoelectric effect – refers to
the emission of electrons from
a metal surface when light
shines on the metal
For a given metal, no electrons
are emitted if the light’s
frequency is below a certain
minimum, regardless of how
intense the light or how long it
is shone on the metal
4-1 The Photoelectric Effect
Wave theory predicts that ANY frequency
of light could supply enough energy to
eject an electron from the metal surface
 Wave theory can’t explain why light must
be of certain minimum frequency

4-1 The Particle Description of
Light

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1900 – Max Planck –
studying emission of
light by hot objects
Proposed matter does
not emit energy
continuously but in
small, specific amounts
called quanta
Idea is called Quantum
Theory. Planck wins
Nobel prize in 1918 for
his work.
4-1 The Particle Description of
Light
Quantum – minimum quantity of energy
that can be lost or gained by an atom
 Energy of a quantum is related to
frequency

E = hv
4-1 The Particle Description of
Light
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1905 – Einstein – light
has a dual nature –
sometimes it acts like a
wave, sometimes it acts
like a particle
Light has wave properties
Light is also like a stream
of particles, each particle
carries a quantum of
energy
Einstein called these
particles photons
4-1 Explanation for the
Photoelectric Effect

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Electrons are bound to the atom with a certain
amount of energy.
Metal surface must be struck by a photon of light
carrying at least this amount of energy to knock
the electron loose.
Energy and frequency are directly proportional.
(E=hν)
Only frequencies equal to or greater than the
threshold frequency will knock an electron off an
atom.
4-1 Sample Problem

Calculate the energy associated with a
photon of light of frequency 4.1 x 1014 Hz.
4-1 Hydrogen-Atom Line-Emission
Spectrum

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Spectrum – a pattern of
energy observed when
matter absorbs and emits
energy
Ground state – lowest
energy state of an atom
or molecule
Excited state –state in
which atom or molecule
has higher PE than
ground state
4-1 Hydrogen-Atom Line-Emission
Spectrum

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Current passed
through vacuum tube
with hydrogen gas
inside
Pink light passed
through prism to
separate into specific
frequencies of light
4-1 Hydrogen-Atom Line-Emission
Spectrum
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Why does hydrogen give
off only specific
frequencies of light?
1913 – Niels Bohr
proposed a model for
hydrogen atom that linked
the atom’s electron with
photon emission
Ties line emission
spectrum to quantum
theory.
4-1 Bohr Model of the Hydrogen
Atom

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Electron can circle nucleus only in allowed
paths, or orbits
Orbit closest to nucleus has lowest energy
(ground state)
Orbits farther from nucleus have higher energy
(excited states)
When electron absorbs energy, it jumps to
higher orbit
When electron emits energy, it drops to lower
orbit
4-1 Bohr Model of the Hydrogen
Atom

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Electron can only
exist in certain
allowed orbits.
Can only absorb and
emit amounts of
energy that
correspond to energy
differences between
orbits.
4-1 Bohr Model of the Hydrogen
Atom
Bohr’s model did not explain the spectra of
atoms with more than one electron
 Bohr’s theory did not explain the chemical
behavior of atoms

4-2 Electrons as Waves
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It was already known
that light can behave
as a particle or a
wave.
1924 – Louis
deBroglie asked if
electrons could also
have dual waveparticle nature
4-2 deBroglie’s Hypothesis
Electrons are particles
but they can act like
waves
 A wave confined to a
space can only have
certain frequencies –
seems to correspond to
Bohr’s quantized electron
orbits
The electron-wave is confined to a certain space – the
region around the nucleus – so electron-waves can only
have certain frequencies, which correspond to certain
energies (E = hv)

4-2 Wave-Particle Duality of Nature
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Particles can
have wave
properties.
Waves can
have particle
properties.
4-2 Heisenberg Uncertainty
Principle
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If the electron is both a
particle and a wave,
where is it?
Werner Heisenberg,
German physicist, 1927
Electrons are detected by
hitting them with photons,
but hitting them changes
their position
It is impossible to
determine simultaneously
the position and velocity
of an electron
4-2 The Schrodinger Wave
Equation

1926 – Erwin
Schrodinger uses
assumption that
electron behaves
as a wave to
describe
mathematically
the wave
properties of
electrons and
other very small
particles
(Quantum theory)
4-2 What does it mean?
Solutions to the Schrodinger equation are
called wave functions
 Wave functions can give probability of
finding an electron at a particular position
in the space around the nucleus
 An orbital is a 3D region around the
nucleus that indicates the probable
location of an electron

4-2 Atomic Orbitals and Quantum
Numbers
Quantum numbers specify the properties
of atomic orbitals and the properties of
electrons in orbitals.
 Each electron in an atom can be assigned
a set of four quantum numbers.

4-2 The Principal Quantum Number
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Symbolized by n
Indicates the main energy level
occupied by an electron
Values of n are positive
integers (ex. n = 1 is the first
energy level)
Principal quantum number also
gives approximate distance
from nucleus/size of energy
level or shell
Total number of electrons that
can exist in a given energy
level, n, is equal to 2n2.
Energy level, n
Maximum
number of
electrons, 2n2
1
2
3
4
5
6
7
2
8
18
32
50
72
98
4-2 Angular Momentum Quantum
Number
Symbolized by l
 Indicates the shape of the orbital
 “sublevels”
 For each energy level, n, the number of
orbital shapes possible is equal to n
 The first four shapes are given letter
symbols (s, p, d and f)

4-2 Magnetic Quantum Number
Symbolized by m
 Indicates the orientation of an orbital
around the nucleus

s orbital (1
orientation)
p orbital (3
orientations)
d orbitals (5 orientations)
f orbitals (7 orientations)
sublevel
number of orbitals
available
number of electrons
sublevel can hold
s
1
2
p
3
6
d
5
10
f
7
14
4-2 Spin Quantum Numbers
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Electrons in orbitals spin on internal axes.
When charged bodies spin, they induce a
magnetic field.
An electron can spin in one of two possible
directions.
The spin quantum number has two possible
values, + ½ and – ½
A single orbital can hold a total of two electrons,
which MUST have opposite spins.
4-3 Electron Configuration
The arrangement of electrons in an atom
 Assigns an energy level and sublevel to
each electron in an atom.

4-3 Rules Governing Electron
Configurations
The Aufbau Principle – an electron
occupies the lowest-energy orbital
available. (aufbau is German for “building
up”
 Electrons fill low energy orbitals before
filling higher energy orbitals.
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4-3 Electron Configuration
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1s has the lowest
energy.
Energies of sublevels
in different main
energy levels begin to
overlap in n=3
Use orbital filling
diagram to determine
order in which
sublevels are filled.
start
4-3 Rules Governing Electron
Configurations
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Pauli Exclusion Principle –
no two electrons in the same
atom can have the same set
of four quantum numbers
In other words, if two
electrons are going to occupy
the same orbital, they must
have opposite spin.
-let horizontal line
represent orbital
-an up arrow and a
down arrow represent
two electrons of
opposite spin
4-3 Rules Governing Electron
Configurations
Hund’s rule – orbitals of equal energy
(degenerate orbitals) are 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
 Bus seat rule

4-3 Ways to Represent Electron
Configuration Examples:
Na
Electron
Configuration
Notation
 Assigns each
electron to an
energy level and
a sublevel.

P
Br
Rb
K
Ar
4-3 Electron Configuration Sample
Problems

Name the elements indicated by the
following electron configurations:
 1s22s22p63s23p5
 1s22s22p63s23p64s23d5
4-3 Electron Configuration Sample
Problems

Write the electron configuration for an
element that has the following number of
electrons:
7
 14
 19
 33
4-3 Ways to Represent Electron
Configuration
Orbital Notation – uses lines and arrows to
represent orbitals and electrons
 Example: Write the orbital notations for
nitrogen and oxygen.

N
O
4-3 Ways to Represent Electron
Configuration
Noble Gas Notation – to simplify an
element’s electron configuration, use the
preceding noble gas as shorthand to
indicate all the electrons possessed by
that noble gas
 Example – Ne and Na

4-3 Valence Electrons
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Valence electrons are
electrons in the
outermost energy level
of an atom, farthest
from the nucleus
They are important
because they are the
electrons that are
usually involved in
chemical reactions.
How many valence electrons does
sodium have?
Bromine?
Silicon?
4-3 Electron Configurations with
Special Stability
Octet – the outer energy level is
considered filled when the s and p
sublevels are completely filled with 8
electrons
 A filled outer energy level (8 electrons) is a
very stable electron configuration.
 The noble gases have filled outer energy
levels. This is why they are unreactive.

4-3 Electron Configurations with
Special Stability Chromium
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Filled and halffilled sublevels
have special
stability
(especially d).
This fact
sometimes
results in electron
configurations
that deviate from
the Aufbau
principle.
Copper
Molybdenum
Silver
Pig boots!