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Atomic
Theory
DEMOCRITUS 460 - 370 BC
• The Greek philosopher Democritus
proposed that all matter was made
of small, unbreakable particles he
called atoms which means
unbreakable.
• He believed that atoms were too
small to be seen.
• Philosophers are not scientists. They
do not test their ideas. Instead they
use reasoning to back up their
beliefs.
• To them, human reasoning was
superior to experimentation.
ARISTOTOLE
• The famous philosopher
Aristotle, who also lived at
that time, argued that all
matter was made of only four
elements.
• For the next two thousand
years, Aristotle
overshadowed Democritus.
• Finally, in the early 1800s,
the atomist’s theory was
revived by John Dalton.
John Dalton 1766-1844
• In 1809, Dalton by proposing the
following:
a) All matter was made of atoms.
b) Atoms were solid spheres.
c) Atoms of different elements differed in
mass.
d) Atoms were indivisible and
indestructible.
e) Atoms combine to form compounds.
J.J. THOMSON 1856-1940
• Before you can understand Thomson’s
experiment, 3 properties about electrical
charges:
a) There are two types of electrical charge:
positive and negative.
b) Opposite charges attract.
c) Like charges repel.
• Thomson took Cathod ray tube and added
two plates inside the tube and connected
them with a wire.
• When the plates were not charged, the ray
shot straight.
Thomson’s Experiment
Voltage source
-
+
Vacuum tube
Metal Disks
Thomson’s Experiment
Voltage source
 Passing
+
an electric current makes a
beam appear to move from the
negative to the positive end
Thomson’s Experiment
Voltage source
+
 By
adding an electric field
Thomson’s Experiment
Voltage source
+
 By
adding an electric field he found
that the moving pieces were negative
Cathode Ray Tube Conclusion
• Cathode rays have identical properties regardless of
the element used to produce them. All elements must
contain identically charged electrons.
• Atoms are neutral, so there must be positive particles
in the atom to balance the negative charge of the
electrons
• Electrons have so little mass that atoms must contain
other particles that account for most of the mass
• Thomson’s model was called the
Plum Pudding Model - named
after a popular dessert in
England at that time.
• It was the first model to propose
that smaller charged particles
make up the atom.
• Thomson’s model lasted less than
two decades but it was first to
propose the existence of subatomic
particles.
• In 1911 another scientist who
worked in Thomson’s lab improved
on his atomic model.
ERNEST RUTHERFORD 1871-1937
• One type of radioactivity
is when an atom throws
out a positively charged
particle from the
nucleus.
• This particle was called
an alpha particle (α).
• Rutherford used this
alpha particle to
investigate the structure
Rutherford and Geiger in the Cavendish Lab
Rutherfold’s Gold Foil Experiement
• Uranium is a radioactive element that gives off positive
particles (alpha particles).
• Rutherford used these positive particles to investigate
• Rutherford encased uranium in lead (which absorbs alpha
particles).
• This produced a beam of alpha particles traveling in a straight
line.
• He fired these positive particles
at a thin piece of gold (dense
metal).
• A screen around the gold to
detect where the alpha particles
were traveling.
Rutherfold’s Gold Foil Experiement
• Rutherford shot alpha particles at a thin sheet
of gold to observe what happened when the
positive α particles passes through the gold
atoms.
• If Thompson’s model was correct the alpha
particles should pass through the diffused
positive cloud with ease.
Lead
block
Uranium
Fluorescent
Screen
Gold Foil
What he expected
Because
He thought the mass was evenly
distributed in the atom
Since he thought the
mass was evenly
distributed in the atom
What he got
Rutherfold’s Conclusion
• From his observations Rutherford concluded that
the atom had a dense, positive central nucleus
composed of + charged protons.
• He stated that the electrons orbited the nucleus
like planets orbiting the Sun.
• In 1909 Rutherford proposed his Planetary Model
of the Atom.
• His model created positively charged protons
located in the nucleus and placed electrons in
orbit around the nucleus – like planets around
the sun.
Almost no deflection; few greatly deflected
+
Checking for understanding
Explain Thompson’s
conclusions in 3 points:
1.
2.
3.
Explain Rutherford’s
conclusions in 3 points:
1.
2.
3.
Click Below for the Video Lectures
Atomic Models
History of Atoms
Atomic
Structure
Subatomic Particles
• Over the past century scientist have
discovered that the atom is composed of 3
subatomic particles:
Protons
Neutrons
Electrons
Checking for understanding
Draw this diagram. Label all subatomic particles
and include their charges.
The Proton
1. Symbol = p+
2. Relative Mass =
1 Atomic Mass
Unit (AMU).
3. Actual mass =
1.674 x 10 -24 g
4. Location: Inside
the nucleus
5. Electrical charge: Positive.
6. Importance: The atomic
number which is the
identity of the element.
7. Discovered by: Ernest
Rutherford in 1909
Real World Application - PROTON
• The electron transport chain, which occurs in the membrane of
mitochondria, uses a proton gradient to help produce ATP, a compound
our body uses for energy.
• Most acidic substances have more free protons (hydrogen ions) in them
than hydroxide ions. Vinegar, lemon juice, and hydrochloric acid (HCl) are
examples of acidic liquids.
• pH is a measure of the number of free protons (hydrogen ions) in a
solution. The pH scale ranges from 0-14, with 0 being acidic (more
protons) and 14 being basic (fewer protons). pH measurements are widely
used to determine the acidity of rain, bodies of water, and liquid waste
from factories.
• Proton therapy is also a new treatment for treat cancer. A beam of protons
is directed towards a tumor and damages the tumor cells' DNA so they
cannot reproduce.
The Electron
1. Symbol = e2. Relative Mass = 1 /1836
Atomic Mass Unit.
5. Electrical charge: Negative.
3. Actual mass =
6. Importance: The number of
9.11 x 10 -28 g
electrons
located
in
the
last
4. Location: Energy level
energy level determine the
outside the nucleus
chemical activity of the
element.
7. Discovered by: J.J.Thomson in
1897
Real World Application - Electron
•
•
•
•
•
•
Microscopes can be made by utilizing properties of electrons. One example is the
scanning electron microscope (SEM). By sending a beam of electrons at the surface of
an object, a SEM can make images of the surface with up to 500,000 times
magnification. SEMs are commonly used to make high resolution images of dead cells,
metal surfaces, and fossils.
The electron transport chain, which occurs in the membrane of mitochondria, uses
proteins to catalyze reduction and oxidation reactions (reactions that exchange
electrons between molecules) that produce ATP, a compound our body uses for energy.
Electrons moving through a metal wire produce electric current, or electricity.
All reduction and oxidation (redox) reactions occur by transferring electrons from one
element, ion, or molecule to another. Examples of redox reactions include the
formation of salt from elemental sodium and chlorine gas and the corrosion (rusting) of
a iron nail in air.
Electrochemical cells and batteries produce energy by moving electrons from a cell with
an oxidizing reaction to a cell with a reduction reaction.
Lasers work by pumping electrons into higher energy level orbitals. When the electrons
fall back down into the lower energy orbital, they each release a photon, which we see
as light.
The Neutron
1. Symbol = n
2. Relative Mass = 1 Atomic
Mass Unit (AMU).
3. Actual mass =
5. Electrical charge: Neutral.
1.675 x 10 -24 g
6. Importance: Is responsible for
4. Location: Inside the
isotopes (atoms of the same
nucleus
element with different numbers
of neutrons.
7. Discovered by: James
Chadwick in 1932
Real World Application - Neutron
•
•
•
•
Neutron stars can be formed when stars use up all of their fuel. Protons and electrons
in the star merge to form neutrons and neutrinos. The neutrons form the neutron star,
which is usually around 20 km in diameter, but can be over twice the mass of the sun.
Nuclear fission reactions occur when a free neutron hits an atom's nucleus causing it to
break apart into two different nuclei, thus forming two different atoms. Some
elements, such as uranium-235, not only split into two different atoms when
undergoing fission, but also release more neutrons. This allows for a chain reaction to
occur as these neutrons go on to hit other uranium atoms and cause them to break
apart as well. Nuclear power plants and nuclear weapons work by nuclear fission.
Neutrons are used in isotopic labeling, a process where atoms with a larger number of
neutrons than usual are placed in a system and tracked to understand where they move
in the system. One example of isotopic labeling is labeling atoms in pharmaceuticals to
see where they end up in the body. This is a common use for deuterium, which is
another stable form of hydrogen.
Different isotopes of elements (elements with different numbers of neutrons) are used
to date objects. Carbon dating uses the ratio of carbon-14 to carbon-12 to determine
the age of organic material up to 60,000 years old.
Atomic
Number
Atomic number
(Z) of an element is
the number of protons
in the nucleus of each
atom of that element.
Element
# of protons Atomic # (Z)
Carbon
6
6
Phosphorus
15
15
Gold
79
79
Mass Number
Mass number is the number of protons
and neutrons in the nucleus of an isotope.
Mass # =
18
Arsenic
Phosphorus
+
p
8
75
16
+
0
n
8
18
33
75
15
31
Isotopes are atoms
of the same element
Isotopes
having different masses due to varying
numbers of neutrons.
Isotope
Protons Electrons Neutrons
Hydrogen–1
1
1
0
(protium)
Hydrogen-2
(deuterium)
1
1
1
Hydrogen-3
(tritium)
1
1
2
Nucleus
Real World Application - ISOTOPES
• Isotopes are used in a multitude of everyday objects. Smoke detectors, for
instance, often contain a small amount of americium-241. One of the
radioactive properties of this material allows for smoke to be detected at an
extremely early stage.
• Another rising use for radioactive isotopes is food irradiation. This is a process
where food is exposed to the radiation of an element, often cobalt-60, though
not in direct contact with it. With the high energy particles that are passing
through the food, bacteria and microorganisms are killed. Cellular processes
that lead to over-ripening and spoiling are also hindered.
• Carbon, the main element in organic materials, has a variety of isotopes that
are present in living organisms. By analyzing the abundances of these carbon
molecules, paleontologists are able to discover the age of organic materials
from bones to clothing.
Atomic
Atomic mass
is theMasses
average of all the
naturally occurring isotopes of that element.
Composition % in nature
of the nucleus
6 protons
98.89%
6 neutrons
Isotope
Symbol
Carbon12
12C
Carbon13
13C
6 protons
7 neutrons
1.11%
Carbon14
14C
6 protons
8 neutrons
<0.01%
Carbon = 12.011
Weight Average Atomic Mass
• The atomic masses given on the periodic table
are WEIGHT-AVERAGED masses.
• This is calculated using both the masses of each
isotope and their percent abundances in nature.
• For the purposes of simplicity, we will round
weight-average mass to the THOUSANDTHS
place.
• The weight-average mass is based on the
abundance of the naturally occurring isotopes of
that element
Weight Average Atomic Mass
• To find the weight-average mass of an
element given the mass of each isotope and
each isotopes percent abundance:
WAM =
(massisotope 1 X % ) + (massisotope 2 X % ) +
(massisotope 3 X % ) + etc…
Atomic Mass Unit (AMU)
• amu = atomic mass unit
– the ratio of the average mass per atom of
the element to 1/12 of the mass of 12C in
its nuclear and electronic ground state.
• An atomic mass unit is actually an
average mass, found by taking the mass
of a C-12 nucleus and dividing it by 12
– Hydrogen = 1amu, 1/12 of C
Carbon has two stable isotopes
Carbon-12 has natural abundance of 98.89% and 12.000 amu
Carbon-13 has natural abundance of 1.11% and 13.003 amu
Calculate the atomic mass
1. Givens
Carbon-12 m=12.000 amu Abundance= 98.89%=0.9889
Carbon-13 m = 13.003 amu Abundance = 1.11%=0.0111
2. Formula
atomic mass of carbon-avg
= (mass C-12 x nat.abund) + (mass C-13 x nat.abund.)
3. Plug in the #s
(12.000amu x 0.9889) + (13.003 amu x 0.0111)
= 12.011 amu
= 12.0 amu
45
4 Types of
Electron
Configuration
of Elements
1. Shell Configuration
• Shows how many
electrons are found in
each shell (principal
energy level).
• This is the configuration
Niels Bohr would have
come up with as the
discoverer of the energy
level!
Shell
Number
(Principle
Electron
Level)
Number of
Electrons to
hold
1
2
2
8
3
8
4
18
5
18
6
32
7
32
Shell Configuration (Bohr Diagrams)
C
1) Draw a nucleus with
the element symbol
inside.
2) Carbon is in the 2nd
period, so it has two
energy levels, or shells.
3) Draw the shells around
the nucleus.
Shell Configuration (Bohr Diagrams)
C
1) Add the
electrons.
2) Carbon has 6
electrons.
3) The first shell can
only hold 2
electrons.
Shell Configuration (Bohr Diagrams)
C
1) Since you have 2
electrons already
drawn, you need to
add 4 more.
2) These go in the 2nd
shell.
3) Add one at a time starting on the right
side and going
counter clock-wise.
Shell Configuration (Bohr Diagrams)
C
1) Check your work.
2) You should have 6 total
electrons for Carbon.
3) Only two electrons can
fit in the 1st shell.
4) The 2nd shell can hold up
to 8 electrons.
5) The 3rd shell can hold 18,
but the elements in the
first few periods only
use 8 electrons.
2. Sublevel Electron Configuration
• Principal energy levels are made up of
sublevels, much as a town is made up of
streets.
• The expanded configuration tells you how
many electrons are found in each sublevel of
each PEL.
• Most of the time (and for all of the
configurations you will be responsible for),
one sublevel must fill up completely before
the next one can get any electrons.
Arrangement of Electrons in an Atom
Electrons in atoms are arranged as
SHELLS (n)
SUBSHELLS (l)
ORBITALS (ml)
row #
shell #
possibilities are 1-7
7 rows
subshell
possibilities are
s, p, d, or f
4 subshells
Each orbital
can be
assigned no
more than 2
electrons!
group #
# es subshell : 1 orbital , total 2 ep subshell : 3 orbital, total of 6 ed subshell :5 orbital, total of 10 ef subshell: 7 orbital, total of 14 e-
s , orbital shapes
p orbitals are peanut or
dumbbell shaped.
d orbitals
f orbitals
group # = # valence (outside) e-
1A
1
2A
8A
3A 4A 5A 6A 7A
2
Row 3
=
4
# shells
5
6
3B 4B 5B 6B 7B 8B 8B 8B 1B 2B
s
d
p
7
6
7
f
Subshells d and f are “special”
group # = # valence e-
1A
period # = # e- shells
1
8A
2A
3A 4A 5A 6A 7A
2
3
3B 4B 5B 6B 7B 8B 8B 8B 1B 2B
4
3d
4d
5d
6d
5
6
7
d
6 4f
7 5f
f
Electron Configuration – Spdf notation
HELIUM – 2 electrons
row #
shell #
possibilities are 1-7
7 rows
2
Is
subshell
possibilities are
s, p, d, or f
4 subshells
group #
# valence epossibilities are:
s: 1 or 2
p: 1-6
d: 1-10
f: 1-14
Total e- should equal
Atomic #
3. Orbital Box Diagram
• Shows how many electrons are in each ORBITAL of
each sublevel, and what each electron’s SPIN is.
• Orbitals are all the same size, they can all fit up to
two electrons in them.
• The spin of electrons is indicated by arrows up and
down.
• If the orbital has two electrons in it, the first will
have an up spin, and the second will have a down
spin.
• The number of arrows will equal the number of
electrons in the sublevel.
Guide to Drawing Orbital Diagrams
Drawing Orbital Diagram
Draw the orbital diagram for nitrogen.
Step 1 Draw boxes to represent the occupied
orbitals. Nitrogen has an atomic
number of seven, which means it has
seven electrons. Draw boxes to
represent the 1s, 2s, and 2p orbitals.
Drawing Orbital Diagram
Step 2 Place a pair of electrons in the last
occupied sublevel in separate orbitals.
We place the remaining three electrons
in the 2s orbitals.
Drawing Orbital Diagram
Step 3 Place remaining electrons with
opposite spins in each filled orbital.
First we place a pair of electrons with
opposite spins in the 2p orbitals, with
arrows in the same direction.
Click Below for the Video Lectures
Electron Configuration
HONORS CHEMISTRY ONLY
3a. Quantum Numbers
• Electron energies are addressed in a similar
way to a ZIP code. Many addresses in Ulster
and northern Orange
• county have 125 as the prefix, with the last
two digits signifying the actual postal box.\
• For example, New Paltz is 12561, Wallkill is
12589, Newburgh is 12550, Pine Bush is
12566.
3a. Quantum Numbers
• There are four identifying characteristics of
the energy of a specific electron in an atomic,
each more specific than the last.
• They are:
– n (principal quantum number) = Principal Energy
Level (1, 2, 3, 4, etc.)
– l (levarotary) = Sublevel (s, p, d, f)
– m (magnetic) = Orbital
– s (spin) = Spin (+ 1/2, - 1/2)
3a. Quantum Numbers
• n , principal quantum number
–based on Bohr’s observations of line
spectra for different elements
–‘n’ relates to the main energy of an
electron
–allowable values: n = 1, 2, 3, 4, …
–electrons with higher ‘n’ values have
more energy
3a. Quantum Numbers
• l , The Secondary Quantum Number
– based on the observation that lines on line spectra
are actually groups of multiple, thin lines
– ‘l ’ relates to the shape of the electrons’ orbits
– allowable values: l = 0 to l = n - 1
• i.e. for n = 4:
l = 0, 1, 2, or 3
– the ‘l ’ values 0, 1, 2, and 3 correspond to the
shapes we will call s, p, d and f, respectively
3a. Quantum Numbers
• ml , the Magnetic Quantum Number
– based on the observation that single lines on line
spectra split into new lines near a strong magnet
– ‘ml ’ relates to the direction/orientation of the
electrons’ orbits
– allowable values: ml = - l to + l
• i.e. for l = 2:
ml = -2, -1, 0, 1, or 2
– electrons with the same l value but different ml
values have the same energy but different
orientations
3a. Quantum Numbers
• ms , The Spin Quantum Number
– based on the observation that magnets could
further split lines in line spectra, and that some
elements exhibit paramagnetism
– ‘ms ’ relates to the ‘spin’ of an electron
– allowable values: ms = - ½ or + ½
• i.e. for any possible set of n, l, and ml
values, there are two possible ms values
– when two electrons of opposite spin are paired,
there is no magnetism observed; an unparied
electron is weakly magnetic
ms , The Spin Quantum Number
HONORS ONLY ENDS HERE
Click Below for the Video Lectures
Quantum Mechanical Model
4. Electron (Lewis) Dot Diagram
• VALENCE ELECTRONS
– the electrons in the outermost shell (furthest
energy level from the nucleus), which is also
called the valence shell.
– The number of valence electrons that an atom
has can be determined by the last number in
the basic electron configuration.
The number of valence electrons that an atom
has determines its physical and chemical
properties
Group 1 (alkali metals) have 1
valence electron
Group 2 (alkaline earth metals)
have 2 valence electrons
Group 13 elements have 3
valence electrons
Group 14 elements have 4
valence electrons
Group 15 elements have 5
valence electrons
Group 16 elements have 6
valence electrons
Group 17 (halogens) have 7
valence electrons
Group 18 (Noble gases) have 8
valence electrons, except
helium, which has only 2
Transition metals (“d” block)
have 1 or 2 valence electrons
Lanthanides and actinides
(“f” block) have 1 or 2 valence
electrons
Lewis Dot Diagram
• using dots in groups of 2 around the symbol of
the atom to represent the valence electrons.
• For every atom, the valence electrons will
occupy only s and p orbitals.
• The s electrons fill up first, then the p
electrons fill, up electrons first, followed by
the downs, just like in the box diagram.
The Electron Dot diagram for
Nitrogen
Nitrogen has 5 valence
electrons.
 First we write the symbol.

Then
add 1 electron at a
time to each side.
Until
they are forced to pair up.
N
Checking for understanding
Draw orbital Draw Lewis
diagrams
dot diagrams
Carbon
Helium
Fluorine
Electrons
Atomic theory Overview
1) The Humble Beginnings
Democritus (460-370 BC)
and Leucippus (~500 BC)
• The atom is an indestructible thing, it is the
smallest piece that any substance can be
broken in to.
• It is indivisible, that is, it cannot be broken
down any further.
2) Thousands of years passed:
John Dalton (1808)
• Atoms are the smallest part that any sample
of element can be broken into.
• Atoms of the same element have the same
atomic mass, atoms of different elements
have different atomic mass.
3) Not so much time passed: a Crookes Tube in
J. J. Thomson (1897)
• The atom is a sphere made of a diffuse (thin)
positive charge, in which negatively charged
electrons are embedded (stuck).
• He called his model the “plum pudding”
model, but who eats plum pudding anymore?
It’s more like a “chocolate chip cookie dough”
model, where the atom is a positively charged
cookie dough ball with negative chocolate
chip electrons stuck in it.
4) But then Ernest Rutherford discovered the
alpha particle and HAD to play with it! (1911)
• The atom is made of a small, dense, positively
charged nucleus with electrons orbiting
outside the nucleus at a distance with empty
space making up the rest of the atom.
• The majority of an atom’s volume is empty
space, and the majority of the atom’s mass is
in the nucleus.
5) He saw the light! Broken up into bright lines though a
spectroscope!
Neils Bohr! (1913)
• Bohr observed the light given off when several elements are
heated and give off light. Different elements gave off different
colors of light.
• When this light was passed through a prism, the light was
broken up into lines of color. Each element’s lines were different.
• Bohr figured that electrons falling from high energy levels to low
energy levels were causing the light.
• Each element’s spectrum of colored lines was different,
meaning that the energy levels of different elements have a
different amount of energy.
• This process, called spectroscopy, is useful for identifying
element samples.
6) Werner Heisenberg may have slept here: we’re uncertain!
The Quantum-Mechanical Model
• The atom contains a small, dense positive nucleus
surrounded by electrons that travel in a wave-like motion
around the nucleus.
• This motion is modified by mass and charge interactions
between electrons and the nucleus.
• The interactions and the fast speed of the electron make it
impossible to know with any certainty both where an
electron is and where it is going in any particular instant.
• All we can know is the general area of space in which the
electron might be found. They very from the most general
location to the most specific.
• Electrons travel in principal energy levels, which are made
up of sublevels, which are made up of orbitals that contain
up to two electrons each. If two electrons are in the same
orbital, they will spin in opposite directions.
1) Electrons (charged –1 each, with a mass of
1/1836 amu each) surround the nucleus of
the atom in distinct energy levels.
Electrons occupy the lowest possible energy
levels when the atom is in the ground state.
2) When electrons are given energy (in the form of
light, heat or electricity), electrons will rise in
energy level by the same amount of energy that
the electrons were given.
The more energy electrons absorb, the higher they
rise. This is called the excited state.
This is in accordance with the Law of Conservation
of Energy, which states that energy cannot be
created or destroyed by physical or chemical
change.
3) Since electrons are negatively charged, and
therefore attracted to the positively charged
nucleus, they will eventually fall back to the
ground state.
As the electrons fall back to the ground state,
they release the energy that caused them to
rise in the first place.
4) The energy is released in the form of
photons.
They travel at the fastest theoretical speed
possible, 3.00 X 108 m/sec, otherwise known as
the speed of light.
Photons are, in fact, particles of light.
5) The color of the light is determined by the
amount of energy lost by the electron when it
dropped back to the ground state.
Light particles travel in a wave pattern.
The length of each wave is called, strangely
enough, a wavelength. The more energy a
photon has, the shorter its wavelength is.
An excited lithium atom emitting a
photon of red light to drop to a
lower energy state.
An excited H atom returns to a
lower energy level.
Click Below for the Video Lectures
Light and Matter
Electromagnetic
Spectrum
The Nature of Light
• The electromagnetic spectrum includes
many different types of radiation.
• Visible light accounts for only a small part
of the spectrum
• Other familiar forms include: radio waves,
microwaves, X rays
• All forms of light travel in waves
Copyright McGraw-Hill 2009
110
Electromagnetic Spectrum
Figure 06.01Figure 06.01
Copyright McGraw-Hill 2009
111
Wave Characteristics
• Wavelength:  (lambda) distance between
identical points on successive waves…peaks
or troughs
• Frequency:  (nu) number of waves that
pass a particular point in one second
• Amplitude: the vertical distance from the
midline of waves to the top of the peak or
the bottom of the trough
Copyright McGraw-Hill 2009
112
Copyright McGraw-Hill 2009
113
Wave Characteristics
• Wave properties are mathematically related
as:
c = 
where
c = 2.99792458 x 108 m/s (speed of light)
 = wavelength (in meters, m)
 = frequency (reciprocal seconds, s1)
Copyright McGraw-Hill 2009
114
Wave Calculation
• The wavelength of a laser pointer is reported to be
663 nm. What is the frequency of this light?
c = 

c

9
10 m
7
  663 nm 
 6.63  10 m
nm
3.00 108 m/s
14 1


4.52

10
s
7
6.63 10 m
Copyright McGraw-Hill 2009
115
• Calculate the wavelength of light, in nm,
of light with a frequency of 3.52 x 1014 s-1.
c = 
c


3.00  10 m/s
7

 8.52  10 m
14 1
3.52 10 s
8
9
10
nm
7
  8.52 10 m 
 852 nm
m
Copyright McGraw-Hill 2009
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