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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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 Crest Wavelength Amplitude Origin 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 HIGH ENERGY LOW ENERGY R O Y G. B I V red orange yellow green blue indigo violet

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 10-34 J·s) f = frequency, in units of hertz (hz, sec-1)

Low ENERGY Waves = Long Wavelength Low Frequency High ENERGY Waves = Wavelength Table High ENERGY Waves = Short Wavelength High Frequency

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

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.

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).

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.

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 = 3.0 x 108m/s 4.2 x 10-5 m = 7.1 x 1012 sec-1 E = hf E = (6.626 x 10-34 J sec) (7.1 x 1012 sec-1) E = 4.73 x 10-21 Joules