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:

λ = v c

Speed of Light

(3.00x108 m/s) Frequency

(hz)

Wavelength

(in meters)

The Sine Wave • What is the wavelength of yellow sodium emission, which

has a frequency of 5.09x1014hz?

c =

λ = unknown

v = 5.09x1014 hz

3.00x108 m/s c = v

=

λ = 5.89 x 10-7 m

λ

3.00x108 m/s (5.09x1014 hz) (λ)

The Sine Wave • What is the frequency of violet light with a wavelength of

4.08x10-9 meters?

c =

λ = 4.08x10-9 m

v = unknown

3.00x108 m/s c = v

=

v = 7.35x1016 hz

λ

3.00x108 m/s (v) (4.08x10-9 m)

Relationship Between Energy

and Frequency • Mathematically, the relationship between

energy and frequency are as follows:

v = h E

Energy (in joules)

Planck’s Constant

(6.626x10-34 Jxs)

Frequency

(in hz)

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 = 6.626x10-34 J x s

v = 4.47x1014 hz

unknown E = h

=

E = 2.96x10-19 J

v

E (4.47x1014 hz) (6.626x10-34 J x s)

Relationship Between Energy

Frequency, and Wavelength • Mathematically, the relationship between

energy and frequency are as follows:

v = h E

c = v λ

You can substitute

frequency between the two

equations!

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.

E =

h = 6.626x10-34 J x s

v = unknown

unknown

c = v

=

v = 4.47x1014 hz

λ

3.0x108 m/s (v)

λ = 6.71x10-7 m

v = h E

c = 3.00x108 m/s

(6.71x10-7 m)

= E (6.626x10-34 J x s) (v)

= E (6.626x10-34 J x s) (4.47x1014 hz)

= E 2.96x10-19 J

Relationship Between Energy

and Frequency • An electromagnetic wave has an energy of 3.15x10-19J.

What is the wavelength of this wave?

E =

h = 6.626x10-34 J x s

v = unknown

3.15x10-19 J

c = v

=

λ = 6.32x10-7 m

λ

3.0x108 m/s (4.75x1014 hz)

λ = unknown

v = h E

c = 3.00x108 m/s

(λ)

= 3.15x10-19 J (6.626x10-34 J x s) (v)

= 3.15x10-19 J (6.626x10-34 J x s) (v)

= v 4.75x1014 hz

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.

Wavelength

(in meters) Mass (in kg) Speed (in m/s)

Planck’s Constant (6.626x10-34 J x 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 = 6.626x10-34 J x s

v = 0.278 m/s

m = 1.00 kg

unknown λ = h

v m

λ = 1.00kg x 0.278 m/s

6.626x10-34 J x s

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 = 6.626x10-34 J x s

v = 2.19x106 m/s

m = 9.11x10-31 kg

unknown λ = h

v m

λ = 9.11x10-31 kg x 2.19x106 m/s

6.626x10-34 J x s

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

You Are Here Planetary Bodies

Start Here