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Chapters 4 & 5
Atomic Theory
Section 4.3
Atomic Number
• The key distinguishing trait between different
elements is the number of protons in the
nucleus.
• The “atomic number” (Z) is the number of
protons in an element
• Consider tin (atomic symbol “Sn”). If a neutral
tin atom contains 50 protons, how many
electrons does it have?
Mass Number
• The total number of protons and neutrons in
an atom is called the “mass number”.
• The atomic number of gold (Au) is 79. If the
mass number for gold is 197, how many
neutrons does a typical gold atom contain?
– a. 197
b. 79
c. 118
d. 122
Chemical Symbols
• The complete symbol for an element on the Periodic Table
includes the atomic symbol, the mass number, and the
atomic number.
Superscript →
Subscript →
Atomic
number
Mass
number
X
• Note: you can also refer to atoms by using the mass
number and the name of the element, i.e. gold-197.
Comprehension Check
• Identify the atomic number and mass number in the
symbol for bromine below. Then, find the number of
protons, neutrons and electrons in a typical bromine atom.
35
80
Br
• Draw the complete chemical symbol for the element that
has the atomic number 19. What is the name of this
element?
• A scientist has a mystery atom with 47 protons and 62
neutrons. What element is this? How is this atom unique?
• Use your Periodic Table to answer these questions.
Isotopes
• Isotopes are atoms that have the same number of
protons but different numbers of neutrons.
– Whose theory of the atom does this contradict?
• Health Science Application: Nuclear Medicine
– Nanoparticles of gold-198 are used in some radiotherapy
cancer treatments (particularly for prostate cancer).
• Fun Fact: The only known stable (non-radioactive) isotope of
gold is gold-197.
• Note: Isotopes of the same element are chemically
alike because they have the same number of protons
and electrons.
• Right now, we’re concerned with chemical reactions. Nuclear
reactions come in Chapter 25!
The Three Known Hydrogen Isotopes
Atomic Mass
• Recall, the number of protons plus the
number of neutrons in an atom is the mass
number.
• The atomic mass of an element is the
weighted average mass of all naturally
occurring isotopes of that element.
» Math Check: What is the difference between a weighted
average and an arithmetic mean?
– The weighted average reflects both the mass and
the percent abundance of the isotopes.
Measuring Atomic Mass
• Scientists do not measure the mass of single
atoms in grams.
– The numbers would always be tiny and complicated
• Mass of 1 proton = 1.673x10-24 grams
• Instead of grams, we use atomic mass units based
on the mass of a carbon-12 atom.
– By definition 1 amu = 1/12 mass of carbon-12 atom.
• Why carbon-12?
– High isotope purity
Isotopes of Carbon
Carbon = 12.011
Calculating a Weighted Average
• Naturally ocurring iron (Fe) has 4 isotopes: iron54 (5.845%), iron-56 (91.754%), iron-57 (2.119%),
and iron-58 (0.282%). Find iron’s atomic mass by
computing the weighted average of these four
isotopes.
• 54 x 5.845% = 3.156
• 56 x 91.754% = 51.382
• 57 x 2.119% = 1.208
• 58 x 0.282% = 0.164
• Total = 55.91 amu
Preview of the Periodic Table
• A periodic table is an arrangement of elements in
which the elements are separated into groups
based on a set of repeating properties.
• The periodic table allows you to easily compare
the properties of one element to another.
• Each horizontal row is called a period.
• Each vertical column is called a group, or family.
– Elements in a group typically have similar physical and
chemical properties
Section 5.1
Atomic Orbitals
• Principal Quantum Number (n) = the
energy level of the electron: 1, 2, 3, etc.
• These are called atomic orbitals (coined by
scientists in 1932) - regions where there is a
high probability of finding an electron.
• Sublevels- like theater seats arranged in
sections: letters s, p, d, and f
Principal Quantum Number
Generally symbolized by “n”, it denotes the shell
(energy level) in which the electron is located.
Maximum number of
electrons that can fit in
an energy level is:
2n2
# of shapes
(orbitals)
s
1
p
3
d
5
f
7
Summary
Maximum
electrons
Starts at energy level
2
1
6
10
2
14
4
3
By Energy Level
•
•
•
•
First Energy Level
Has only s orbital
only 2 electrons
1s2
• Second Energy Level
• Has s and p orbitals
available
• 2 in s, 6 in p
2
6
• 2s 2p
• 8 total electrons
By Energy Level
• Third energy level
• Has s, p, and d
orbitals
• 2 in s, 6 in p, and 10
in d
• 3s23p63d10
• 18 total electrons
• Fourth energy level
• Has s, p, d, and f
orbitals
• 2 in s, 6 in p, 10 in d,
and 14 in f
• 4s24p64d104f14
• 32 total electrons
By Energy Level
Any more than the
• The orbitals do not
fourth and not all
fill up in a neat order.
the orbitals will fill
• The energy levels
up.
overlap
• You simply run out of • Lowest energy fill
electrons
first.
Section 5.2
Electron Arrangement in Atoms
• OBJECTIVES:
•Describe how to write the
electron configuration for an
atom.
7p
7s
6s
6p
5p
6d
5f
5d
4f
4d
Increasing energy
5s
4p
3d
4s
3p
3s
2p
2s
aufbau diagram - page 133
1s
Aufbau is German for “building up”
Electron Configurations…
•
…are the way electrons are arranged in
various orbitals around the nuclei of
atoms. Three rules tell us how:
1) Aufbau principle - electrons enter the
lowest energy first.
•
This causes difficulties because of the overlap
of orbitals of different energies – follow the
diagram!
2) Pauli Exclusion Principle - at most 2
electrons per orbital - different spins
Pauli Exclusion Principle
No two electrons in an atom
can have the same four
quantum numbers.
To show the different direction of spin, a pair in
the same orbital is written as:
Wolfgang Pauli
Electron Configurations
3) Hund’s Rule- When electrons occupy
orbitals of equal energy, they don’t
pair up until they have to.
• Let’s write the electron configuration
for Phosphorus
 We need to account for all 15
electrons in phosphorus
7p
7s
6s
6p
5p
6d
5f
5d
4f
4d
Increasing energy
5s
4p
3d
4s
3p
3s
2p
2s
1s
• The first two electrons
go into the 1s orbital
Notice the opposite
direction of the spins
• only 13 more to go...
7p
7s
6s
6p
5p
6d
5f
5d
4f
4d
Increasing energy
5s
4p
3d
4s
3p
3s
2p
2s
1s
• The next electrons go
into the 2s orbital
• only 11 more...
7p
7s
6s
6p
5p
6d
5f
5d
4f
4d
Increasing energy
5s
4p
3d
4s
3p
3s
2p
2s
1s
• The next electrons go
into the 2p orbital
• only 5 more...
7p
7s
6s
6p
5p
6d
5f
5d
4f
4d
Increasing energy
5s
4p
3d
4s
3p
3s
2p
2s
1s
• The next electrons go
into the 3s orbital
• only 3 more...
7p
7s
6s
6p
5p
6d
5f
5d
4f
4d
Increasing energy
5s
4p
3d
4s
3p
3s
2p
2s
1s
Orbital
notation
• The last three electrons go
into the 3p orbitals.
They each go into separate
shapes (Hund’s)
• 3 unpaired electrons
= 1s22s22p63s23p3
Orbitals fill in an order
• Lowest energy to higher energy.
• Adding electrons can change the
energy of the orbital. Full orbitals
are the absolute best situation.
• However, half filled orbitals have a
lower energy, and are next best
•Makes them more stable.
•Changes the filling order
Section 5.3
Physics and the Quantum
Mechanical Model
• OBJECTIVES:
•Describe the relationship
between the wavelength
and frequency of light.
Section 5.3
Physics and the Quantum
Mechanical Model
• OBJECTIVES:
•Identify the source of
atomic emission spectra.
Section 5.3
Physics and the Quantum
Mechanical Model
• OBJECTIVES:
•Explain how the frequencies
of emitted light are related to
changes in electron energies.
Light
• The study of light led to the development of
the quantum mechanical model.
• Light is a kind of electromagnetic radiation.
• Electromagnetic radiation includes many
types: gamma rays, x-rays, radio waves…
• Speed of light = 2.998 x 108 m/s, and is
abbreviated “c”
• All electromagnetic radiation travels at this
same rate when measured in a vacuum
- Page 139
“R O Y G B I V”
Frequency Increases
Wavelength Longer
Parts of a wave
Crest
Wavelength
Amplitude
Origin
Trough
Electromagnetic radiation propagates through space as
a wave moving at the speed of light.
Equation:
c =
c = speed of light, a constant (2.998 x 108 m/s)
 (lambda) = wavelength, in meters
 (nu) = frequency, in units of hertz (hz or sec-1)
Wavelength and Frequency
• Are inversely related
• As one goes up the other goes down.
• Different frequencies of light are different
colors of light.
• There is a wide variety of frequencies
• The whole range is called a spectrum
- Page 140
Use Equation: c =
Low Energy
Radiowave
s
High Energy
Microwave
s
Infrared .
Low Frequency
Ultraviolet
X-Rays
GammaRays
High Frequency
Long Wavelength
Short Wavelength
Visible Light
Long
Wavelength
=
Low Frequency
=
Low ENERGY
Short
Wavelength
=
High Frequency
=
High ENERGY
Wavelength Table
Atomic Spectra
• White light is
made up of all
the colors of the
visible spectrum.
• Passing it
through a prism
separates it.
If the light is not white
• By heating a gas with
electricity we can
get it to give off
colors.
• Passing this light
through a prism
does something
different.
Atomic Spectrum
• Each element gives
off its own
characteristic
colors.
• Can be used to
identify the atom.
• This is how we
know what stars
are made of.
• These are called the
atomic emission
spectrum
• Unique to each
element, like
fingerprints!
• Very useful for
identifying
elements
Light is a Particle?
•
•
•
•
Energy is quantized.
Light is a form of energy.
Therefore, light must be quantized
These smallest pieces of light are called
photons.
• Energy & frequency: directly related.
The energy (E ) of electromagnetic
radiation is directly proportional to the
frequency () of the radiation.
Equation:
E = h
E = Energy, in units of Joules (kg·m2/s2)
(Joule is the metric unit of energy)
h = Planck’s constant (6.626 x 10-34 J·s)
 = frequency, in units of hertz (hz, sec-1)
The Math in Chapter 5
•
There are 2
equations:
1) c = 
2) E = h
Know these!
Explanation of atomic spectra
• When we write electron configurations,
we are writing the lowest energy.
• The energy level, and where the electron
starts from, is called it’s ground state the lowest energy level.
Changing the energy
• Let’s look at a hydrogen atom, with only
one electron, and in the first energy
level.
Changing the energy
• Heat, electricity, or light can move the
electron up to different energy levels. The
electron is now said to be “excited”
Changing the energy
• As the electron falls back to the ground
state, it gives the energy back as light
Changing the energy
• They may fall down in specific steps
• Each step has a different energy
What is light?
• Light is a particle – it contains discrete
photons (it comes in chunks)
• Light is a wave - we can measure its
wavelength and it behaves as a wave
• If we combine E=mc2 , c=, E = 1/2 mv2
and E = h, then we can get:
 = h/mv
(from Louis de Broglie)
• called de Broglie’s equation
• Calculates the wavelength of a particle.
The physics of the very small
• Quantum mechanics explains how
very small particles behave
•Quantum mechanics is an
explanation for subatomic
particles and atoms as waves
• Classical mechanics describes the
motions of bodies much larger than
atoms
Wave-Particle Duality
J.J. Thomson won the Nobel prize for describing the electron as a
particle.
His son, George Thomson won the Nobel prize for describing the
wave-like nature of the electron.
The electron
is a particle!
The electron is
an energy
wave!
First paradox!
• Light exists and acts as both a particle and a
wave
• Each nature of light can be measured and
observed
• Light is both at the same time!!!
Heisenberg Uncertainty Principle
• It is impossible to know exactly the location
and velocity of a particle simultaneously.
• The better we know one, the less we know
the other.
• Measuring changes the properties.
• True in quantum mechanics, but not
classical mechanics
Heisenberg Uncertainty Principle
“One cannot simultaneously
determine both the position and
momentum of an electron.”
You can find out where the electron
is, but not where it is going.
Werner Heisenberg
OR…
You can find out where the electron
is going, but not where it is!
It is more obvious with the very
small objects
• To measure where a electron is,
we use light.
• But the light energy moves the
electron
• And hitting the electron changes
the frequency of the light.
After
Before
Photon wavelength
changes
Photon
Moving Electron
Electron
velocity changes
Fig. 5.16, p. 145
Second Paradox!!!
• It is impossible to measure both the velocity
and position of an electron at the same time.
• It is only possible to measure or observe one
or the other
• Heisenberg Uncertainty Principle
• Science is cray!!!
Erwin Schrödinger and his cat
• Austrian Physicist
(1887-1961)
• Challenged the paradox
of the particle/wave
duality
• Created famous
thought experiment
about a cat in a box
Schrödinger’s Cat
Your assignment!!
• Work within your table groups
• Develop a model that could be used to explain the
Heisenberg Uncertainty Principle to a student who is
unfamiliar with quantum physics.
• Assume the student is familiar with atomic structure
• You can include objects that we don’t actually have
(like ping pong balls or string or… BE CREATIVE!!)
• You will describe the activity, including the materials
needed
• You will explain how the activity demonstrates the
Heisenberg Uncertainty Principle, as well as a summary
of the principle itself.