Waves
Wave-Particle Duality
 The electron was previously describe by J.J.
Thompson as a particle.
 He won a Nobel prize for his research
 His son, George Thompson described the electron
as having a wave-like nature
 He won a Nobel prize for his research
 Who was correct?????
 Both! To better understand the current model of
the atom we will investigate how the electron acts
as a wave but also acts as a particle.
Part 1: Waves
 We will begin our Journey by discussing how an
electron propagates through space as an energy
wave…..
Waves
 Waves transmit energy through a medium
 If you throw a stone into the middle of a pond
with a smooth surface, it creates a “ripple” on the
surface of the water. Ripples = waves
 The energy from the stone is being transferred
through the medium, water, in the form of waves.
Waves
 If a glass bottle is floating on the surface of the
water, the waves will move the bottle vertically
(up and down) but will not carry the bottle in the
direction of the wave.
Movement
of bottle
Direction
of wave
Properties of Waves
 Waves can be represented using drawings and
mathematical equations.
 An imaginary line may be drawn horizontally at an equal
distance from both the crest and the trough of a wave.
 The crest of a wave is the top peak of the wave. The
wave’s trough is the bottom of the wave.
Crest
 Picture 1
Wave
trough
Amplitude
 The amplitude of a wave is the distance from the
imaginary line to the crest or trough of a wave.
 Picture 2
Amplitude
Amplitude
Frequency
 The frequency of a wave is the number of waves
which pass a given point in a specified unit of
time.
 Picture 3
Frequency
Low
frequency
(ex: 1 wave in 1 sec)
High
frequency
(ex: 3 waves in 1 sec)
Frequency
 The symbol for frequency is the Greek letter
nu.
 Nu =
ν
 The unit for frequency is a hertz, which is
abbreviated Hz. One hertz is equal to one
cycle per second or sec-1
Wavelength
 Wavelength is the distance between similar sets
of a wave, such as from crest to crest or trough
to trough.
 Picture 4
Wavelength
wavelength
wavelength
Wavelength
 The symbol for wavelength is the Greek letter
lambda.
 Lambda =
λ
 The most common unit used when expressing
wavelength is the meter; however, the unit
Angstrom is sometimes used.
 Angstrom = _____
 1 Angstrom = 1 x 10-8 cm (exactly)
Speed of Wave
 The speed of any wave equals wavelength times
frequency.
 Speed of wave formula:
Speed = wavelength * frequency
s= λ*ν
Wave-Speed calculations
 1. A water wave has a frequency of 4.75 x 10-2 Hz
and a wavelength of 1.50 x 101 m.
 Speed =
Wave-Speed calculations
 2. The speed of a wave is 4.75 m/s and its
frequency is 8.35 Hz. Calculate its wavelength.
 Speed =
 Rearrange for wavelength
Sound vs. Radio
Sound Waves
A sound wave needs a
medium to allow it to
spread (air, water, solids
etc).
Radio Waves
Radio Waves can travel
through the air or the
vacuum of space so they do
not need a medium
Electromagnetic Radiation
 Radio waves are considered to be Electromagnetic
Radiation (energy), where as sound waves are not.
 Electromagnetic Radiation is energy that can
travel through a vacuum, in the form of waves and
at the speed of light.
 Electromagnetic energy has no mass.
 Lets take a closer look at Electromagnetic
Radiation….
Electromagnetic Radiation
 Frequencies and wavelength of electromagnetic
radiation are related by the speed of light --- all
electromagnetic radiation travels at the speed of
light, including radio waves.
 Note: Assume EM waves travel at the speed of
light regardless of being in vacuum
 Speed of light (c) =
3.00 x 108 m/s
Speed formula
 The speed of any wave is equal to the product
of its wavelength and frequency
 (recall: speed = λ*ν)
 We can use this information for
electromagnetic waves as well. Formula can be
adjusted slightly….
 Speed of light (c) = λ*ν

c = λ*ν
Formula:
c = λ*ν
 Whenever you are solving problems using the
formula given above make certain that all
measurements for wavelength are expressed in
meters.
 If the wavelength is given in Angstroms, convert
Angstroms to meters than apply the formula
 1 Angstrom = 1 x 10-8 cm = 1 x 10-10 m
 Wavelength is inversely proportional to frequency.
 If frequency increases wavelength must decrease
Electromagnetic Spectrum
 Electromagnetic waves are produced by a
combination of electrical and magnetic fields
 The electromagnetic waves are organized in an
electromagnetic spectrum
Each type of
 The spectrum includes
 Radio waves
 Microwaves
 Infrared Radiation
 Visible light
 Ultraviolet rays
 X-rays
 Gamma rays
electromagnetic
radiation is
associated with a
range of
wavelengths and
frequencies.
Electromagnetic spectrum
low energy
High energy
Visible Light
 Visible light makes up a small portion of the
electromagnetic spectrum
 Visible light consists of seven different colors
 ROYGBIV
(red, orange, yellow, green, blue, indigo, violet)
 If red light has the lowest frequency, it must
have the greatest wavelength compared to the
other colors of the visible spectrum
1nm = 1.0 x 10-9 m
1m = 1,000,000,000 nm
Visible Light
 There are no precise boundaries between the
different types of waves that compose the
electromagnetic spectrum. However, the following
frequencies are associated with the following
colors:
Wave
Frequency in Hz
Red light
4.3 x 1014
Yellow light
5.2 x 1014
Blue light
6.4 x 1014
Violet light
7.5 x 1014
Radio Waves
 Radio stations send out radio waves on a specific
frequency. Depending upon the strength of their
broadcasting antenna – the listening area may be large
or small.
 No two broadcasting signals may be the same in
overlapping areas
 We go from 88 to 108 FM band. (frequency
modulation) These frequencies are in kilohertz which is
103 Hz.
 The individual frequencies have associated wavelengths
– which may be determined and calculated.
Wave-Speed calculations
 1. A gamma ray has a frequency of 3.75x 1023 Hz.
What is the wavelength?
2. What radio station sends out a signal with a
wavelength of 3.25m?
ROYGBIV
 The greater the frequency the greater the
energy
 Visible light is made up of ROYGBIV. Each color
associates with a different frequency. A light
bulb emits all of these frequencies at once and
the light appears white.
 When atoms of an individual element absorb and
release energy, scientists assumed the atoms
would emit a continuous spectrum, but instead
they observed bright lines of colors at specific
wavelengths (or frequencies)
 Why do we see these
bright line spectrums
instead of a continuous
spectrum?
Photons
 Thus far we have seen that
Electromagnetic radiation
displays
characteristics
If a beam
of light isof
waves, but EM radiation also
up of these
hasmade
some properties
of
particles. small
packets/photons
 Just
as water waves transmit
energy,
why electromagnetic
don’t we see waves
also transmit
energy
them?
 Light energy (EM radiation)
comes in tiny packets called
photons
Energy Levels
 When an atom absorbs energy, its electrons make
transitions from lower energy levels to higher
energy levels.
 The energy absorbed can be in the form of heat
(as in a flame) or electrical energy
 However, when electrons subsequently return
from higher energy levels to lower energy levels,
energy is released in the form of electromagnetic
radiation (light).
 The same reason why we do not see individual
water molecules when you turn on the faucet
 These packets are traveling at the speed of light.
They are moving too fast for our eyes to see the
photons and the photons are extremely small.
Energy
 The energy of a photon is proportional to the
frequency of the electromagnetic radiation. So, as
the frequency of an electromagnetic wave
increases, the energy of the photons from that
wave will also increase.
 E increases as ν increases
 Each frequency has a specific energy. The
relationship between energy of a photon and
frequency can be expressed by the following
mathematical relationship….
Energy of a photon = Plank’s constant * frequency
 Formula:
E=h*ν
 Symbol for energy is E
 Unit for energy is Joules abbreviated J
 A joule is kgm2
s2
 The symbol for plank’s constant is h
 Plank’s constant is equal to 6.6262x10-34 J*s
 If the frequency of electromagnetic radiation is
directly proportional to the energy of a photon,
then the energy of the photon must be inversely
related to the wavelength. Recall that the
frequency is inversely proportional to wavelength.
So as wavelength increases, frequency decreases
and so does energy.
 c= λ*ν
 E=h*ν
 What is the connection between these two
formulas?
De Broglie’s Equation
E= hc

λ
 The spacing between energy levels in an atom
determines the size of the transitions that occur,
and thus the energy and wavelengths of the
collection of photons emitted.
 When electrons return from higher energy levels
more energy is released than when electrons
return from lower energy levels.
 The colors in a bright line spectrum indicate the
energy levels from which electrons are returning .
Colors with lower frequency (red) indicate less
energy which indicates the return from lower
energy levels.