Download Chapter 8 Modern Atomic Theory

Chapter 8
Modern Atomic Theory
Setting the Stage – Emission of
Light


The beautiful color of fireworks comes
from the particular elements used.
The colors are characteristic of the
elements and can be used to understand
their properties.
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Setting a Goal – Part A
The Emission Spectra of the
Elements and Bohr’s Model


You will understand historically how
elemental emission spectra were
used to determine the structure
electrons adopt within an atom.
For more details, see “Special
Topics”
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Objectives for Section 8-1


8-1a Describe the relationships among the
wavelengths of light, energy, and color.
8-1b Describe the relationship between
emission spectra and the electronic
structure of the hydrogen atom as
explained by Bohr’s model.
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Two Atom-Sized Jokes
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

Two Hydrogen atoms sit down at a bar.
One says to the other "I think I've lost an
electron." The other says "Are you sure?",
and he replies, "Yeah, I'm positive."
So a neutron walks into a bar, sits down
and asks for a glass of soda. Finishing his
drink, the neutron asks "How much?" The
bartender says, "For you, no charge."
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8-1 The Emission Spectra of the
Elements and Bohr’s Model
The Nature of Light
 Electromagnetic energy
 Travels at 3.0  1010 cm/s
 White light is a continuous spectrum of
light (all energies represented) and can
be separated.
 Refer to Figure 8-1 in text.
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The Visible Spectrum
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Properties of Light

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Light has intensity, which is termed amplitude.
Light is characterized by its wavelength, which is
given the symbol  (lambda).
Wavelength is the distance between two adjacent
peaks.
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Wavelength and Energy
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Wavelength and energy have an inverse
relationship, as shown below.
h is Planck’s constant (6.626  10-34 J·s)
c is the speed of light
E
1

hc
E =

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Wavelength, frequency and
velocity
The velocity of propagated light waves
in vacuum (c) = 2.998 x 108 m/s
It is the product of the wavelength and wave
frequency:
c = n
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Period and Frequency
The period (t) of the wave is the time
taken for the wave to travel one
complete wavelength.
The frequency (n) is the reciprocal of
the period (n = 1/t)
Energy and frequency are directly
proportional; E = hn (originally from
Planck’s quantum theory)
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Visible Light


Visible light comprises only a small fraction of
the electromagnetic spectrum (400-800 nm).
Ultraviolet and infrared light cannot be seen with
the unaided eye, but are important.
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Energy Range of Light

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Infrared light is of lower energy than
visible light.
Ultraviolet light is of higher energy than
visible light (some of the ultraviolet range
is of high enough energy to damage living
tissue).
X-rays and gamma rays are even higher
energy forms of light (there are special
hazards associated with this type of
radiation).
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Emission Spectra of Atoms


When atoms are excited (like in a flame) they emit
discrete wavelengths of light, not a continuum.
These are called atomic emission (line) spectra
Shown below is the visible light range at the top,
the emission spectrum of Na in the middle and
the emission spectrum of H at the bottom.
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Measuring the Emission Spectrum


The H2 in the gas discharge tube is excited
by electricity.
The light produced is separated by the
prism.
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Atomic Phenomena and Classical
Physics
Classical physics (Newtonian mechanics
and Maxwell’s electromagnetism theory)
could not explain:
 Emission line spectra
 The Rutherford (nuclear) model of the atom
 Black body radiation
 Photoelectric effect
 Electron diffraction
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A Model for the Electrons in the
Atom

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A model is a description or analogy used
to help visualize a phenomenon or entity.
Bohr proposed a model that violated
classical physics, but started a new way of
looking at atomic and molecular structure.
The central concept of this model is that
the properties of atoms and electrons do
not behave in a continuous fashion.
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The Bohr Atom
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Electrons revolve around the nucleus in certain
stable orbits only.
Each stable orbit is quantized
 the electron is a discrete distance from the
nucleus
 the orbit has a discrete energy
These orbits are referred to as energy levels.
The energy levels are characterized by an integral
number called the principle quantum number, n.
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The Bohr Atom (con’t.)

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n has discrete values of 1, 2, 3,…
The quantum number n arose from Bohr’s idea of
imposing quantization (from Planck’s Hypothesis,
1901) on the angular momentum of the electron.
Otherwise Bohr’s description of the hydrogen
atom uses classical physics.
Light is absorbed (giving an absorption line) or
emitted (an emission line) only when an electron
changes its stable orbit (excitation or relaxation)
– see next slide
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Balmer Emission Series of Hydrogen
Explained by Bohr Theory
Each energy
level is
associated
with a
particular
Bohr orbit
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Quantized Energy Levels


Quantized energy levels are like the steps of a
staircase.
An electron can have one energy or another, but
not an energy in between (can you stand between
two steps?)
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States of the Atom

Ground state

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the lowest energy state
Excited state


all states that have higher energies
atoms and molecules have many
excited states but only one ground state
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Objectives for Section 8-2
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8-2a Differentiate between a shell, a
subshell, and an orbital.
8-2b Identify an s, p, or d-type orbital
from its shape.
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8-2 Modern Atomic Theory: A
Closer Look at Energy Levels
•Bohr’s model of the hydrogen atom
explained the emission spectra of
hydrogen – a great success
• However, even after several
modifications, it was generally
unsuccessful when applied to other
atomic phenomena and failed totally to
describe the helium atom
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Modern Atomic Theory - Wave
Mechanics


Modern atomic theory involves complex
mathematical descriptions.
It takes into account that atomic-sized things
behave more like waves than particles.
The Schrödinger equation for a hydrogen atom
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Wave Mechanics

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We treat electrons as waves, since we cannot
precisely determine the location of the electrons.
The idea was originally put forward by de Broglie:
all matter has some wave character
Schrödinger was the first person to apply de
Broglie’s idea; he considered the electron in a
hydrogen atom as a standing wave
Electrons are said to be described by orbitals,
which are regions in space where there is a
significant probability of finding the electron.
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Extra Details Revealed
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Wave mechanics reveals that the energy
levels (sometimes called shells) have
sublevels.
The sublevels are designated by letters:
s, p, d, f
The sublevels increase in energy as
s<p<d<f
Each sublevel has one or more orbitals.
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Some Heroes of Modern Atomic Theory
E. Rutherford
N. Bohr
L. de Broglie
W. Heisenberg
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E. Schrödinger
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Orbitals
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The orbital is best thought of as an electron
cloud.
The picture below is the density diagram for an s
orbital.
It indicates the probability of an electron being
located in a particular location near the nucleus.
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Representing Orbitals


We often represent orbitals as spherical volumes
of probability (volume in which the electron is
found 90% of the time).
The orbitals of the s sublevel are shown below,
for n = 1 and n = 2.
1s
2s
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p-Orbitals
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There are three orbitals in the p sublevel (starting
at n = 2).
One is aligned along each of the Cartesian axes
around the nucleus.
Orientation is indicated by subscript x, y or z.
This is the set of 2p orbitals:
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d-Orbitals
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
There are five orbitals in the d-sublevel, starting
at n = 3.
They are important to understanding the behavior
of the transition metals and elements in period 3
and beyond.
This is the set of 3d orbitals:
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Shell Designation
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The shell is indicated by the principle
quantum number n.
The subshell is indicated by the letter (s,
p, d, f).
The number of electrons in the subshell is
indicated by a right superscript.
For example, 4p3 (4th shell, p subshell,
three electrons).
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Electronic Configurations



The electrons in the atom are indicated by
an electron configuration.
We use only as many subshells and shells
as are needed for the number of electrons.
The number of available subshells
depends on the shell that is being filled.

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

n = 1 only has an s subshell
n = 2 has s and p subshells
n = 3 has s, p, and d subshells
n = 4 has s, p, d, and f subshells
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The n = 3 Shell
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Dorm Room Analogy
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
We can think of the
levels as dorm
rooms.
A student will
choose the dorm
that is closest to
the campus and a
room on the lowest
floor.
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Dorm Room Analogy, con’t


The dorms correspond to the shells
The floors correspond to the subshells
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Setting a Goal – Part B
The Periodic Table and Electron
Configuration

You will have a detailed
understanding of the structure of
electrons in atoms, and how this
affects that element’s properties.
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Objective for Section 8-3

Using the periodic table, write the
outer electron configuration of a
specific element.
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8-3 Electron Configurations of the
Elements
The Aufbau Principle
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The electrons are added to the atom
beginning with the lowest energy level.
As the sublevels and levels are filled,
electrons are added to the next highest
energy level.
Each orbital can hold two electrons, so
each sublevel can hold twice as many
electrons as there are orbitals.
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The Aufbau Principle
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Electrons occupy the available orbitals in
the subshells of lowest energy.
The electronic configuration of an element
is the assignment of all of the electrons of
the atom into shells and subshells.
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Assignment of Electrons into
Shells and Subshells
Nomenclature or symbolism
for electron configuration
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Ground States of the First Few
Elements

Using the Aufbau Principle, the electron
configurations for the first 10 elements are:
H
He
Li
Be
B
C
N
O
F
Ne
1s1
1s2
1s22s1
1s22s2
1s22s22p1
1s22s22p2
1s22s22p3
1s22s22p4
1s22s22p5
1s22s22p6
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Abbreviated Electron
Configurations
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We develop a shorthand for the electron
configuration by noting that the core is
really the same as the electron
configuration for the noble gas that
occurs earlier in the periodic table.
Example: for S (1s22s22p63s23p4), the core
is 1s22s22p6 which is the same as the
electron configuration for Ne.
So the abbreviated form is [Ne]3s23p4
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Electron Configuration Shorthand
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We note that the valence shell electron
configuration has the same pattern for
elements in the same group.
All elements in the same column as
oxygen or sulfur (group VIA) have the
valence electron configuration
[core]ns2np4.
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Periodic Nature of the Filling
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We find that at the end of a period, the
pattern of electron filling repeats with
higher values of n.
F [He]2s22p5
Cl [Ne]3s23p5
Br [Core]4s24p5
The noble gas in parentheses indicates
the inner electrons.
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Electronic Configurations
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The levels increase
in energy.
Within the levels,
the sublevels also
increase (recall
s<p<d<f).
Recall that the
electrons go into
the lowest orbital
first (1s, then 2s,
etc.).
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Shell, Subshell and Orbitals
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Core and Valence Shells
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Chemically, we find that the electrons in
the shell with the highest value of n are
the ones involved in chemical reactions.
This shell is termed the valence shell.
Electrons in shells with lower n values are
chemically unreactive because they are of
such low energy.
These shells are grouped together as the
core.
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Order of Filling of Atomic Orbitals
The diagram
opposite is a
useful pictorial
description of
atomic orbital
energy order
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Exceptions to the Filling Order
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They occur in atoms where the d or f
orbitals are being filled.
E.g. the ground state electron
configuration of Cr (Z = 24) is [Ar]4s13d5,
and not [Ar]4s23d4, as expected from the
Aufbau Principle.
Generally, it is not important or necessary
to know them all.
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Representative Elements
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Representative elements have the
general electron configuration
[NG]nsxnpy (NG represents noble gas
or core configuration).
Each representative element has one
more electron in the valence shell
than the previous element.
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Representative Elements
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[NG]ns1 - alkali metals
[NG]ns2 - alkaline earths
[NG]ns2np1
[NG]ns2np2
[NG]ns2np3
[NG]ns2np4 - chalcogens
[NG]ns2np5 - halogens
[NG]ns2np6 - noble gases
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Transition Elements
[NG]ns2(n-1)dy or [NG] (n-1)dyns2
- Transition elements
NG is Ar, Kr, Xe or Rn
 [NG]ns2(n-1)dy(n-2)fz or [NG] (n-2)fz(n-1)dy
ns2
- Inner transition elements
NG is Xe or Rn

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Example 1
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Consider the atom of sulfur (Z = 16)
Sulfur has 16 electrons
Electronic configuration is therefore
1s22s22p63s23p4 = [Ne] 3s23p4
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Example 2
d and f subshells are used for heavier
elements
• Consider the atom of vanadium (Z = 23)
 Vanadium has 23 electrons
 Electronic configuration is therefore
1s22s22p63s23p63d34s2 = [Ar]3d34s2
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Objective for Section 8-4

Using orbital diagrams, determine
the distribution of electrons in an
atom.
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8-4 Orbital Diagrams of the
Elements
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
Electrons act as if they are little magnets
due to a property called spin, and they can
have a spin up () or spin down ().
The Pauli Exclusion Principle - two
electrons can occupy the same orbital
only if they have different spins.
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Orbital Diagrams of the Elements,
Cont’d

Hund’s Rule - when filling a subshell,
electrons will avoid entering an orbital that
already has an electron in it until there is
no other alternative.
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Orbital Diagrams

Represent the
orbitals of the
subshells as boxes
and electrons as
arrows.
For second row
representative
elements
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Objective for Section 8-5

Using the periodic table, predict
trends in atomic and ionic radii,
ionization energy, and electron
affinity.
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8-5 Periodic Trends

Atomic radius is the distance from the
nucleus to the outermost electrons.
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

Atomic radii decrease across a period
Atomic radii increase down a group
The decrease from left to right in a period
results from adding electrons to the same
outer shell while protons are being added
to the nucleus.
All of the outer electrons are drawn closer
to the nucleus.
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Atomic Radii (in pm)
For metals,
the numbers
refer to
single bond
covalent
radii
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Ionization Energy

The energy required to remove an electron from a
gaseous atom to form a gaseous ion
is the 1st ionization energy (IE1)
M(g)



M+(g) + e-
First ionization energies increase across a period.
First ionization energies decrease down a group.
Smaller atoms have higher first ionization
energies (small atoms hold their electrons more
tightly).
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Ionization Energies
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Metals are characterized by the relative
ease that electrons are removed from
them (low IE).
Atoms can lose more than one electron:
M+(g)  M2+(g) + e- IE2 (2nd ionization
energy).
Successive ionization energies increase.
Note that IE2 for Na, IE3 for Mg, and IE4 for
Al are all very large compared to the
preceding IE; see next slide and Table 8-2.
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Ionization Energies for the First Twenty
Elements
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Ionization Energies
The abnormally high ionization energies correspond
to removing an electron from a completely filled shell
E.g. from ns2np6 or ns2
These shells, corresponding to electron configurations
of noble gases, can be considered to be especially
stable.
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Electron Affinity (EA)
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
Electron attachment energy (EAE) is that
associated with the reaction
X(g) + e- → X-(g); EAE
It is negative if the anion is stable.
Electron affinity is the energy needed to remove
an electron from an anion to produce a neutral
atom (all in the gas phase): the reverse of above
X-(g) → X(g) + e-; EA
While some electron affinities are zero or
negative (for unstable anions), many are positive
- in contrast to ionization energies.
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Ion Sizes
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
When atoms lose electrons, the remaining
electrons are more strongly attracted to the
nucleus, hence cations are smaller than the atom.
Anions hold the electrons less tightly, so they are
larger.
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Core vs. Valence Electrons
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Removing an electron from an inner shell
is energetically very costly.
Removing electrons from the valence shell
requires quite a bit less energy.
This will have consequences for the
formation of compounds.
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