Light as a Wave OBJECTIVES:

• Describe the relationship between the wavelength and frequency of light.

Electrons and Light After Bohr’s model, the mystery of the

atom was the nature of the electron cloud.

The study of light – particularly the wave nature of light – played a critical role in probing the nature of the electron cloud.

Light and Energy are Linked Energy travels through space as light

waves. These Light waves are known as

Electromagnetic Radiation (EMR) EMR – defined as a form of energy

that exhibits wavelike behavior as it travels trough space.

Types of EMR Visible Light is one type of EMR Others include x-rays, microwaves,

radiowaves, gamma rays, ultraviolet waves, infrared waves.

All electromagnetic radiation travels at this same rate.

This rate is the speed of light (c) c = 3.0 x 108 m/sec

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“R O Y G B I V”

Basic Properties of Waves Wavelength (λ- lambda) – distance

between two crests of a wave. Units are usually meters.

Frequency (f or (nu) )- the number of wave cycles that pass a given point per unit time (usually seconds) Units are sec-1 = Hertz

Parts of a wave

Wavelength

AmplitudeOrigin

Crest

Trough

Wavelength and Frequency Are inversely related

• As one goes up the other goes down.

• c = or c = f

c = speed of light = 3.0 x 108m/s

As frequency decreases, wavelength increases.

As frequency increases, the wavelength decreases.

Different frequencies of light are different colors of light.

There is a wide variety of frequencies

The whole range is called a spectrum

EM Spectrum

LOW

ENERGY

HIGH

ENERGY

R O Y G. B I V

red orange yellow green blue indigo violet

Equation: E = hf

EE = Energy, in units of Joules (kg·m = Energy, in units of Joules (kg·m22/s/s22)) (Joule is the metric unit of energy)(Joule is the metric unit of energy)

hh = Planck’s constant (6.626 x 10 = Planck’s constant (6.626 x 10-34-34 J·s) J·s)

f f = frequency, in units of hertz (hz, sec= frequency, in units of hertz (hz, sec-1-1))

The energy (E ) of electromagnetic radiation is directly proportional to the frequency () of the radiation.

Low ENERGYWaves

=Long

Wavelength=

Low Frequency

High ENERGYWaves

=Short

Wavelength=

High Frequency

Wavelength Table

Radiowaves

Microwaves

Infrared .

Ultra-violet

X-Rays

GammaRays

Low Frequency

High Frequency

Long Wavelength

Short WavelengthVisible Light

Low Energy

High Energy

Behavior of Light That Supports Wave Theory

Reflection — Waves rebound from a collision with an even substance at the same angle which they approached it.

Refraction — Waves change speed when they enter a new medium (from air to water).

Refraction explains how a prism separates the colors that make up white light.

Each color will refract (or bend) to different degrees based on its characteristic wavelength

Diffraction — Waves can interfere with other waves

They create diffraction patterns Constructive interference—occurs

when a crest meets a crest or a trough meets a trough

Destructive interference—occurs when a crest meets a trough

For light waves, you see darkness with destructive interference.

• Microwaves are used to transmit information.

Calculating Wavelength of an EM Wave

• What is the wavelength of a microwave having a frequency of 3.44 x 109 Hz?

• Solve the equation relating the speed, frequency, and wavelength of an electromagnetic wave for wavelength (λ).

Electrons in Atoms: Basic ConceptsElectrons in Atoms: Basic ConceptsElectrons in Atoms: Basic ConceptsElectrons in Atoms: Basic ConceptsTopic 9Topic 9

• Substitute c and the microwave’s frequency, , into the equation. Note that hertz is equivalent to 1/s or s–1.

Calculating Wavelength of an EM Wave

Electrons in Atoms: Basic ConceptsElectrons in Atoms: Basic ConceptsElectrons in Atoms: Basic ConceptsElectrons in Atoms: Basic ConceptsTopic 9Topic 9

Examples2) What is the frequency of red light with a

wavelength of 4.2 x 10-5 m?

3) What is the energy of the photon above?

c = λf or f = c/λ

f = 3.0 x 108m/s

4.2 x 10-5 m= 7.1 x 1012 sec-1

E = hfE = (6.626 x 10-34 J sec) (7.1 x 1012 sec-1)

E = 4.73 x 10-21 Joules