The Sine Wave
• Mathematically, a function
that represents a smooth
oscillation
• For example, if we drew the
motion of how the weight
bobs on the spring to the
weight we would draw out a
sine wave.
The Sine Wave
• You commonly see waves
in the environment
– Light
– Sound
– Electricity
– Ocean “waves”
The Sine Wave
• The wavelength of a wave refers to the
distance between two crests of troughs.
• Units of wavelength are based off the meter.
The Sine Wave
• The frequency of a wave represents the
number of wavelengths that pass a fixed
point in a second
• Units of frequency are in hertz (hz)
Electromagnetic Waves
• Electromagnetic
waves consist of
two components, an
electric and a
magnetic wave.
• Both are at right
angles (90 degrees)
from each other.
Electromagnetic Waves
• Electromagnetic waves
travel at 3.00x108 meters
per second.
• This is also known as the
speed of light.
• At this speed, an
electromagnetic wave
can go around the Earth
8 times in one second.
Electromagnetic Waves
• This does not mean
you can’t slow an
electromagnetic wave
down.
• In a vacuum,
electromagnetic waves
travel at the speed of
light.
• They slow down
considerably if they are
passing through a
medium.
Electromagnetic Spectrum
Note that radio waves have the lowest frequencies while gamma-rays
have the highest frequency.
The Sine Wave
• Mathematically, the relationship between
wavelength and frequency are as follows:
c
Speed of Light
(3.00x108 m/s)
=
Frequency
(hz)
v
λ
Wavelength
(in meters)
The Sine Wave
• What is the wavelength of yellow sodium emission, which
has a frequency of 5.09x1014hz?
c =
λ =
v =
3.00x108 m/s
c =
unknown
3.00x108 m/s = (5.09x1014 hz) (λ)
5.09x1014 hz
λ =
vλ
5.89 x 10-7 m
The Sine Wave
• What is the frequency of violet light with a wavelength of
4.08x10-9 meters?
c =
λ =
v =
3.00x108 m/s
c =
4.08x10-9 m
3.00x108 m/s = (v) (4.08x10-9 m)
unknown
v=
vλ
7.35x1016 hz
Relationship Between Energy
and Frequency
• Mathematically, the relationship between
energy and frequency are as follows:
E
=
h
v
Energy (in joules)
Frequency
(in hz)
Planck’s Constant
(6.626x10-34 Jxs)
Relationship Between Energy
and Frequency
• A red spectral line has a frequency of 4.47x1014 hz.
Calculate the energy of one photon of this light.
E=
h =
v =
unknown
6.626x10-34 J x s
4.47x1014 hz
E = hv
E =(6.626x10-34 J x s) (4.47x1014 hz)
E = 2.96x10-19 J
Relationship Between Energy
Frequency, and Wavelength
• Mathematically, the relationship between
energy and frequency are as follows:
E
=
h
v
You can substitute
frequency between the two
equations!
c =
vλ
Relationship Between Energy
and Frequency
• A red spectral line has a wavelength of 6.71x10-7 meters.
Calculate the energy of one photon of this light.
c =
3.0x108 m/s
E=
h =
v =
unknown
vλ
= (v) (6.71x10-7 m)
v =
4.47x1014 hz
6.626x10-34 J x s
unknown
λ
=
6.71x10-7 m
c
=
3.00x108
m/s
E
=
E
= (6.626x10-34 J x s)(v)
E
= (6.626x10-34 J x s)(4.47x1014 hz)
= 2.96x10-19 J
E
h
v
Relationship Between Energy
and Frequency
• An electromagnetic wave has an energy of 3.15x10-19J.
What is the wavelength of this wave?
c =
3.0x108 m/s
E=
h =
v =
3.15x10-19 J
vλ
= (4.75x1014
λ =
hz) (λ)
6.32x10-7 m
6.626x10-34 J x s
E
unknown
λ
=
unknown
c
=
3.00x108
m/s
=
h
v
3.15x10-19 J
= (6.626x10-34 J x s)(v)
3.15x10-19 J
= (6.626x10-34 J x s)(v)
= 4.75x1014 hz
v
Electrons and Light
• Think back to electron orbitals. Electrons found in orbitals have a
particular energy level.
• However, if energy (namely in the form of photons of light) strike an
electron, it can “jump” to a higher energy level
• Think of this like throwing a ball straight upwards. The more energy
you use to throw a ball, the higher it can go.
Electrons and Light
• However, an electron can not
permanently stay in its excited
state.
• The electron will return back to
the ground state after emitting a
photon of energy.
• If this photon of energy is within
the wavelength and frequency
of our vision, we see the
emission of photon as a form of
light
Lasers
• We use this principle of electrons to invent lasers (which is
an acronym for light amplification by stimulated emission of
radiation)
• However in lasers, we selectively choose which frequency
and wavelength of light we want emitted
De Broglie’s Equation
• The scientist Louis de Broglie discovered the relationship
between wavelength, frequency, and mass.
Planck’s Constant (6.626x10-34 J x s)
Wavelength
(in meters)
Mass (in kg)
Speed (in m/s)
De Broglie’s Equation
• We can use De Broglie’s equation to determine the
wavelength, mass, or frequency for matter assuming we
have two of the three variables.
• For example, calculate the wavelength of a wave
associated with a 1.00kg mass moving at 0.278m/s
λ =
h =
v =
m=
unknown
λ =
6.626x10-34 J x s
0.278 m/s
λ =
h
mv
6.626x10-34 J x s
1.00kg x 0.278 m/s
1.00 kg
λ =
2.38 x 10-33 m
De Broglie’s Equation
• Calculate the wavelength associated with an electron
traveling at a speed of 2.19x106 m/s with a mass of
9.11x10-31 kg.
λ =
h =
v =
m=
unknown
λ =
6.626x10-34 J x s
2.19x106 m/s
λ =
h
mv
6.626x10-34 J x s
9.11x10-31 kg x 2.19x106 m/s
9.11x10-31 kg
λ =
3.32 x 10-10 m
The Visual Spectra
Visible Light
Visible light represents the colors
that we are able to see with our
eyes. The color with the shortest
wavelength and the highest
frequency is violet while the color
with the longest wavelength and the
lowest frequency is red.
And the order of colors, from longest
wavelength to shortest, is red,
orange, yellow, green, blue, indigo,
and violet.
Atomic Spectra
• Photon emissions
generated by
electrons in the
excited state
ultimately give each
element a specific
atomic spectra
• In a sense, each
element has a
unique visual
fingerprint
Prisms
And if you have a prism, you can force light into its component colors.
The Doppler Shift
Planetary Bodies
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