Waves

Wave-Particle DualityThe electron was previously describe by J.J.

Thompson as a particle.He won a Nobel prize for his research

His son, George Thompson described the electron as having a wave-like natureHe won a Nobel prize for his research

Who was correct?????Both! To better understand the current model

of the atom we will investigate how the electron acts as a wave but also acts as a particle.

Part 1: WavesWe will begin our Journey by discussing how

an electron propagates through space as an energy wave…..

WavesWaves transmit energy through a mediumIf you throw a stone into the middle of a pond

with a smooth surface, it creates a “ripple” on the surface of the water. Ripples = waves

The energy from the stone is being transferred through the medium, water, in the form of waves.

WavesIf a glass bottle is floating on the surface of

the water, the waves will move the bottle vertically (up and down) but will not carry the bottle in the direction of the wave.

Movement of bottle

Direction of wave

Properties of WavesWaves can be represented using drawings and

mathematical equations. An imaginary line may be drawn horizontally at an

equal distance from both the crest and the trough of a wave.

The crest of a wave is the top peak of the wave. The wave’s trough is the bottom of the wave.

Picture 1

Wave

Crest

trough

AmplitudeThe amplitude of a wave is the distance from

the imaginary line to the crest or trough of a wave.

Picture 2

Amplitude Amplitud

e

Frequency The frequency of a wave is the number of

waves which pass a given point in a specified unit of time.

Picture 3 Frequency

Low frequency (ex: 1 wave in 1 sec)

High frequency

(ex: 3 waves in 1 sec)

Frequency The symbol for frequency is the Greek

letter nu. Nu =

The unit for frequency is a hertz, which is abbreviated Hz. One hertz is equal to one cycle per second or sec-1

ν

WavelengthWavelength is the distance between similar

sets of a wave, such as from crest to crest or trough to trough.

Picture 4Wavelength

wavelength

wavelength

WavelengthThe symbol for wavelength is the Greek letter

lambda.Lambda =

The most common unit used when expressing wavelength is the meter; however, the unit Angstrom is sometimes used.

Angstrom = _____ 1 Angstrom = 1 x 10-8 cm (exactly)

λ

Speed of WaveThe speed of any wave equals wavelength

times frequency.Speed of wave formula:Speed = wavelength * frequencys = λ * ν

Wave-Speed calculations 1. A water wave has a frequency of 4.75 x 10-2

Hz and a wavelength of 1.50 x 101 m.

Speed =

Wave-Speed calculations 2. The speed of a wave is 4.75 m/s and its

frequency is 8.35 Hz. Calculate its wavelength.

Speed = Rearrange for wavelength

Sound vs. RadioSound Waves Radio Waves

A sound wave needs a medium to allow it to spread (air, water, solids etc).

Radio Waves can travel through the air or the vacuum of space so they do not need a medium

Electromagnetic RadiationRadio waves are considered to be

Electromagnetic Radiation (energy), where as sound waves are not.

Electromagnetic Radiation is energy that can travel through a vacuum, in the form of waves and at the speed of light.

Electromagnetic energy has no mass.

Lets take a closer look at Electromagnetic Radiation….

Electromagnetic RadiationFrequencies and wavelength of

electromagnetic radiation are related by the speed of light --- all electromagnetic radiation travels at the speed of light, including radio waves.

Note: Assume EM waves travel at the speed of light regardless of being in vacuum

Speed of light (c) = 3.00 x 108 m/s

Speed formulaThe speed of any wave is equal to the

product of its wavelength and frequency (recall: speed = λ*ν)

We can use this information for electromagnetic waves as well. Formula can be adjusted slightly….Speed of light (c) = λ*ν

c = λ*ν

Formula: c = λ*νWhenever you are solving problems using the

formula given above make certain that all measurements for wavelength are expressed in meters.

If the wavelength is given in Angstroms, convert Angstroms to meters than apply the formula1 Angstrom = 1 x 10-8 cm = 1 x 10-10 m

Wavelength is inversely proportional to frequency. If frequency increases wavelength must decrease

Electromagnetic SpectrumElectromagnetic waves are produced by a

combination of electrical and magnetic fieldsThe electromagnetic waves are organized in an

electromagnetic spectrumThe spectrum includes

Radio wavesMicrowaves Infrared RadiationVisible lightUltraviolet raysX-raysGamma rays

Each type of electromagnetic

radiation is associated with a

range of wavelengths and

frequencies.

Electromagnetic spectrum

High energylow energy

Visible LightVisible light makes up a small portion of the

electromagnetic spectrumVisible light consists of seven different colors

ROYGBIV(red, orange, yellow, green, blue, indigo, violet)

If red light has the lowest frequency, it must have the greatest wavelength compared to the other colors of the visible spectrum

1nm = 1.0 x 10-9

m1m = 1,000,000,000

nm

Visible LightThere are no precise boundaries between the

different types of waves that compose the electromagnetic spectrum. However, the following frequencies are associated with the following colors:

Wave Frequency in HzRed light 4.3 x 1014

Yellow light 5.2 x 1014

Blue light 6.4 x 1014

Violet light 7.5 x 1014

Radio WavesRadio stations send out radio waves on a specific

frequency. Depending upon the strength of their broadcasting antenna – the listening area may be large or small.

No two broadcasting signals may be the same in overlapping areas

We go from 88 to 108 FM band. (frequency modulation) These frequencies are in kilohertz which is 103 Hz.

The individual frequencies have associated wavelengths – which may be determined and calculated.

Wave-Speed calculations 1. A gamma ray has a frequency of 3.75x 1023

Hz. What is the wavelength?

2. What radio station sends out a signal with a wavelength of 3.25m?

ROYGBIVThe greater the frequency the greater the

energyVisible light is made up of ROYGBIV. Each color

associates with a different frequency. A light bulb emits all of these frequencies at once and the light appears white.

When atoms of an individual element absorb and release energy, scientists assumed the atoms would emit a continuous spectrum, but instead they observed bright lines of colors at specific wavelengths (or frequencies)

Why do we see these bright line spectrums instead of a continuous spectrum?

PhotonsThus far we have seen that

Electromagnetic radiation displays characteristics of waves, but EM radiation also has some properties of particles.

Just as water waves transmit energy, electromagnetic waves also transmit energy

Light energy (EM radiation) comes in tiny packets called photons

If a beam of light is made up of these small

packets/photons why don’t we see

them?

Energy Levels

When an atom absorbs energy, its electrons make transitions from lower energy levels to higher energy levels.

The energy absorbed can be in the form of heat (as in a flame) or electrical energy

However, when electrons subsequently return from higher energy levels to lower energy levels, energy is released in the form of electromagnetic radiation (light).

The same reason why we do not see individual water molecules when you turn on the faucet

These packets are traveling at the speed of light. They are moving too fast for our eyes to see the photons and the photons are extremely small.

Energy The energy of a photon is proportional to the

frequency of the electromagnetic radiation. So, as the frequency of an electromagnetic wave increases, the energy of the photons from that wave will also increase.E increases as ν increases

Each frequency has a specific energy. The relationship between energy of a photon and frequency can be expressed by the following mathematical relationship….

Energy of a photon = Plank’s constant * frequencyFormula:

Symbol for energy is EUnit for energy is Joules abbreviated JA joule is kgm2

s2

The symbol for plank’s constant is hPlank’s constant is equal to 6.6262x10-34 J*s

E = h * ν

If the frequency of electromagnetic radiation is directly proportional to the energy of a photon, then the energy of the photon must be inversely related to the wavelength. Recall that the frequency is inversely proportional to wavelength. So as wavelength increases, frequency decreases and so does energy.

c = λ * νE = h * ν

What is the connection between these two formulas?

De Broglie’s Equation

E= hc λ

The spacing between energy levels in an atom determines the size of the transitions that occur, and thus the energy and wavelengths of the collection of photons emitted.

When electrons return from higher energy levels more energy is released than when electrons return from lower energy levels.

The colors in a bright line spectrum indicate the energy levels from which electrons are returning . Colors with lower frequency (red) indicate less energy which indicates the return from lower energy levels.