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Light as a Wave OBJECTIVES: Describe the relationship between the wavelength and frequency of light.

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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.

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**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.

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**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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- Page 139 “R O Y G B I V”

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**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

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Parts of a wave Crest Wavelength Amplitude Origin Trough

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**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

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**As frequency decreases, wavelength increases.**

As frequency increases, the wavelength decreases.

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**Different frequencies of light are different colors of light.**

There is a wide variety of frequencies The whole range is called a spectrum

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**EM Spectrum HIGH ENERGY LOW ENERGY R O Y G. B I V red orange yellow**

green blue indigo violet

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The energy (E ) of electromagnetic radiation is directly proportional to the frequency () of the radiation. Equation: E = hf E = Energy, in units of Joules (kg·m2/s2) (Joule is the metric unit of energy) h = Planck’s constant (6.626 x J·s) f = frequency, in units of hertz (hz, sec-1)

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**Low ENERGY Waves = Long Wavelength Low Frequency High ENERGY Waves =**

Wavelength Table High ENERGY Waves = Short Wavelength High Frequency

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Low Energy High Energy Radiowaves Microwaves Infrared . Ultra-violet X-Rays GammaRays Low Frequency High Frequency Long Wavelength Short Wavelength Visible Light

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**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.

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

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**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

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**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

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**Destructive interference—occurs when a crest meets a trough**

For light waves, you see darkness with destructive interference.

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**Calculating Wavelength of an EM Wave**

Electrons in Atoms: Basic Concepts Topic 9 Calculating Wavelength of an EM Wave Microwaves are used to transmit information. 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).

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**Calculating Wavelength of an EM Wave**

Electrons in Atoms: Basic Concepts Topic 9 Calculating Wavelength of an EM Wave Substitute c and the microwave’s frequency, n, into the equation. Note that hertz is equivalent to 1/s or s–1.

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**Examples c = λf or f = c/λ f = 3.0 x 108m/s 4.2 x 10-5 m**

2) 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 = x 108m/s 4.2 x 10-5 m = 7.1 x 1012 sec-1 E = hf E = (6.626 x J sec) (7.1 x 1012 sec-1) E = 4.73 x Joules

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