Chapter 6Chapter 6

WavelengthWavelength

LightLight• The study of light led to the The study of light led to the

development of the quantum development of the quantum mechanical model.mechanical model.

• Light is a kind of electromagnetic Light is a kind of electromagnetic radiation.radiation.

• In Wave Model, Light is considered to In Wave Model, Light is considered to consist of electromagnetic waves that consist of electromagnetic waves that travel in a vacuum @ speed of travel in a vacuum @ speed of 3.00 x 103.00 x 1088 m/s m/s

• Electromagnetic radiation includes Electromagnetic radiation includes many kinds of waves many kinds of waves

• All move at 3.00 x 10All move at 3.00 x 1088 m/s ( c) m/s ( c)

ERER

• Electromagnetic Radiation – forms of energy that Electromagnetic Radiation – forms of energy that exhibits wavelight behavior as it travels thru spaceexhibits wavelight behavior as it travels thru space

• Examples of Electromagnetic Radiation:Examples of Electromagnetic Radiation:1.1. Radio WvaesRadio Wvaes2.2. MicrowavesMicrowaves3.3. InfraredInfrared4.4. Visible LightVisible Light5.5. Ultraviolet Ultraviolet 6.6. X-RaysX-Rays7.7. Gamma RaysGamma Rays• ER has measurable wave properties of wavelength and ER has measurable wave properties of wavelength and

frequencyfrequency

Parts of a waveParts of a wave

Wavelength

AmplitudeOrgin

Crest

Trough

Parts of WaveParts of Wave• Orgin - the base line of the energy.Orgin - the base line of the energy.• Crest - high point on a waveCrest - high point on a wave• Trough - Low point on a waveTrough - Low point on a wave• Amplitude - distance from origin to Amplitude - distance from origin to

crestcrest• Wavelength - distance from crest to Wavelength - distance from crest to

crestcrest• Wavelength - is abbreviated Wavelength - is abbreviated Greek Greek

letter lambda.letter lambda.

FrequencyFrequency

• The number of waves that pass a The number of waves that pass a given point per second.given point per second.

• Units are cycles/sec or hertz (hz)Units are cycles/sec or hertz (hz)

• Abbreviated Abbreviated the Greek letter nuthe Greek letter nu

c = c =

Frequency and Frequency and wavelengthwavelength

• Are inversely relatedAre inversely related

• As one goes up the other goes down.As one goes up the other goes down.

• Different frequencies of light is different Different frequencies of light is different colors of light.colors of light.

• There is a wide variety of frequenciesThere is a wide variety of frequencies

• The whole range is called a spectrumThe whole range is called a spectrum

• Frequency and Wavelength are mathematically related, they are Frequency and Wavelength are mathematically related, they are inversely relatedinversely related

• The relationship is shown by the following equation:The relationship is shown by the following equation:

•c = c = • c= speed of lightc= speed of light WavelengthWavelength

• Long WavelengthLong Wavelength

==

Low EnergyLow Energy

Low FrequencyLow Frequency

• Short WavelengthShort Wavelength

==

High EnergyHigh Energy

High FrequencyHigh Frequency

Radiowaves

Microwaves

Infrared .

Ultra-violet

X-Rays

GammaRays

Low energy

High energy

Low Frequency

High Frequency

Long Wavelength

Short WavelengthVisible Light

Calculating LightCalculating Light

• What is the wavelength if light with a What is the wavelength if light with a frequency of 5.89 x 10frequency of 5.89 x 1055 Hz? Hz?

• What is the frequency of blue light What is the frequency of blue light with a wavelength of 484 nm?with a wavelength of 484 nm?

H.W. QuestionsH.W. Questions

1.1. List 5 examples of E.R.List 5 examples of E.R.2.2. What is the speed of all forms of E.R. in a What is the speed of all forms of E.R. in a

vacuumvacuum3.3. Relate Frequency and WavelengthRelate Frequency and Wavelength4.4. The speed of light is 3.00 x 10The speed of light is 3.00 x 1088 m/s and m/s and

the frequency is 7.500 x 10the frequency is 7.500 x 101212 Hz. Hz. Calculate the Wavelength of E.R.Calculate the Wavelength of E.R.

5.5. Determine the frequency of light w/ a Determine the frequency of light w/ a wavelength of 4.257 x 10wavelength of 4.257 x 10-7-7 cm. cm.

Atomic SpectrumAtomic Spectrum

How color tells us about How color tells us about atomsatoms

SpectrumSpectrum

• Spectrum- Range of wavelengths of E.R., Spectrum- Range of wavelengths of E.R., wavelengths of visible light are separated wavelengths of visible light are separated when a beam of white light passes thru a when a beam of white light passes thru a prismprism

• Example of SpectrumExample of Spectrum

• Rainbow (also a phenomenon)Rainbow (also a phenomenon)

• Each droplet of water acts as a prism to Each droplet of water acts as a prism to produce a spectrumproduce a spectrum

• Each color blends into the next color.Each color blends into the next color.

Colors of the SpectrumColors of the Spectrum

• Colors of the Spectrum:Colors of the Spectrum:1.1. Red (Longest Wavelength & Lowest Frequency)Red (Longest Wavelength & Lowest Frequency)2.2. OrangeOrange3.3. YellowYellow4.4. GreenGreen5.5. Blue Blue 6.6. IndigoIndigo7.7. Violet (Shortest Wavelength & Highest Violet (Shortest Wavelength & Highest

Frequency)Frequency)• These colors are known as the visible part of the These colors are known as the visible part of the

spectrumspectrum

PrismPrism

• White light is White light is made up of all the made up of all the colors of the colors of the visible spectrum.visible spectrum.

• Passing it through Passing it through a prism separates a prism separates it.it.

DiffractionDiffraction

• When light passes through, or When light passes through, or reflects off, a series of thinly spaced reflects off, a series of thinly spaced line, it creates a rainbow effect line, it creates a rainbow effect

• because the waves interfere with because the waves interfere with each other. each other.

A wave moves toward a slit.

Comes out as a curve

with two holes

with two holes Two Curves

Two Curveswith two holes

Interfere with each other

Two Curveswith two holes

Interfere with each other

crests add up

Several waves

Several wavesSeveral Curves

Several wavesSeveral waves

Interference Pattern

Several Curves

Spectroscopic analysis of the visible spectrum…Spectroscopic analysis of the visible spectrum…

…produces all of the colors in a continuous spectrum

If the light is not whiteIf the light is not white

• By heating a gas By heating a gas with electricity we with electricity we can get it to give can get it to give off colors.off colors.

• Passing this light Passing this light through a prism through a prism does something does something different.different.

• More on that LaterMore on that Later

Quantum ConceptQuantum Concept

• Laws of Physics state no limits on Laws of Physics state no limits on how much or how little energy can how much or how little energy can be gained or lost.be gained or lost.

• Classic physics assumed atoms and Classic physics assumed atoms and molecules could emit any arbitrary molecules could emit any arbitrary amount of radiant energy.amount of radiant energy.

• Does not explain the Emission Does not explain the Emission Spectrum of AtomsSpectrum of Atoms

Max PlankMax Plank

• Tried to explain why the body changed Tried to explain why the body changed colors as it heated.colors as it heated.

• He could only explain the change if He could only explain the change if assumed energy of the body changes in assumed energy of the body changes in small discrete units (brick by brick).small discrete units (brick by brick).

• Plank showed mathematically that the Plank showed mathematically that the amount of radiant energy, absorbed or amount of radiant energy, absorbed or emitted by a body is proportional to the emitted by a body is proportional to the frequency of radiationfrequency of radiation

Plank’s Quantum ConceptPlank’s Quantum Concept

• Plank went against classic physicsPlank went against classic physics• Stated: atoms and molecules could emit Stated: atoms and molecules could emit

energy only is discrete quantities, like energy only is discrete quantities, like small packages or bundlessmall packages or bundles

• Quantum- smallest quantity of energy Quantum- smallest quantity of energy that can be emitted in the form of E.R.that can be emitted in the form of E.R.

• The energy of a single quantum is given The energy of a single quantum is given by E = hby E = hνν

Planck’s Quantum Theory Planck’s Quantum Theory Cont.Cont.• According to theory, energy is always According to theory, energy is always

emitted in multiples of hemitted in multiples of hνν..

• Example: 2hv, 3hv, ect…..Example: 2hv, 3hv, ect…..

• Never in 1.67hv and so onNever in 1.67hv and so on

• Could not explain why energies are Could not explain why energies are fixed but explained the emission of fixed but explained the emission of solids over the entire range or solids over the entire range or wavelengths.wavelengths.

Energy and frequencyEnergy and frequency

• E = h x E = h x • E is the energy of the photonE is the energy of the photon

• is the frequencyis the frequency

• h is Planck’s constant h is Planck’s constant

• h = 6.6262 x 10 h = 6.6262 x 10 -34 -34 Joules sec.Joules sec.

• joule is the metric unit of Energyjoule is the metric unit of Energy

ExamplesExamples

•What is the wavelength of blue What is the wavelength of blue light with a frequency of 8.3 x 10light with a frequency of 8.3 x 101515 hz?hz?

•What is the frequency of red light What is the frequency of red light with a wavelength of 4.2 x 10with a wavelength of 4.2 x 10-5 -5 m?m?

•What is the energy of a photon of What is the energy of a photon of each of the above?each of the above?

Solving for photonsSolving for photons

• Calculate the energy of:Calculate the energy of:

• A) photon with a wavelength 5.00 x A) photon with a wavelength 5.00 x 101044 nm (infrared region) nm (infrared region)

• B) photon with a wavelength of 5.00 B) photon with a wavelength of 5.00 x 10x 1022 nm (X ray region) nm (X ray region)

Einstein and Photoelectric Einstein and Photoelectric EffectEffect• 5 years later Einstein used Planck’s 5 years later Einstein used Planck’s

theory to derive the Photoelectric Effecttheory to derive the Photoelectric Effect

• Photoelectric Effect- a phenomenon in Photoelectric Effect- a phenomenon in which electrons are ejected from the which electrons are ejected from the surface of certain metals exposed to surface of certain metals exposed to light of at least a certain minimum light of at least a certain minimum frequencyfrequency

• Threshold FrequencyThreshold Frequency

Photoelectric EffectPhotoelectric Effect

• Number of electrons ejected was Number of electrons ejected was proportional to the intensity (brightness) proportional to the intensity (brightness) of the light, but the energies of the of the light, but the energies of the electrons were not.electrons were not.

• Below the threshold frequency no Below the threshold frequency no electrons were ejected no matter how electrons were ejected no matter how intense the light.intense the light.

• Could not be explained by the wave theory Could not be explained by the wave theory of light.of light.

Photoelectric cont.Photoelectric cont.

• Einstein proposed: Einstein proposed: • That a beam of light is really a stream of That a beam of light is really a stream of

particles.particles.• Particles of light are now called Photons.Particles of light are now called Photons.• Used Planck’s equation to determine:Used Planck’s equation to determine:• Electrons are held in a metal surface by Electrons are held in a metal surface by

attractive forces, and removing them from attractive forces, and removing them from the metal requires light of a sufficiently the metal requires light of a sufficiently high frequency ( which corresponds to high frequency ( which corresponds to sufficiently high energy) to break them sufficiently high energy) to break them free.free.

• Shining a beam of light onto a metal Shining a beam of light onto a metal surface can be though as shooting a surface can be though as shooting a beam of particles/photons at the beam of particles/photons at the metal atoms.metal atoms.

• Frequency of photons = binding Frequency of photons = binding energy, then light will have just energy, then light will have just enough energy to knock them freeenough energy to knock them free

• What if the frequency is higher?What if the frequency is higher?

Photoelectric cont.Photoelectric cont.

• If frequency is stronger they will If frequency is stronger they will acquire some K.E. and be knocked acquire some K.E. and be knocked loose.loose.

• KE = hv – BEKE = hv – BE

• Shows more energetic the photon, Shows more energetic the photon, greater the K.E. of the ejected greater the K.E. of the ejected electron.electron.

Wave-Particle DualityWave-Particle DualityJJ Thomson won the Nobel prize for describing the electron as a particle.

His son, George Thomson won the Nobel prize for describing the wave-like nature of the electron.

The electron is a particle!

The electron is an energy

wave!

Light is a ParticleLight is a Particle

• Energy is quantized.Energy is quantized.

• Light is energyLight is energy

• Light must be quantizedLight must be quantized

• These smallest pieces of light are These smallest pieces of light are called photons.called photons.

• Energy and frequency are directly Energy and frequency are directly related. related.

Energy ChangeEnergy Change

• The size of an emitted or absorbed The size of an emitted or absorbed Quantum depends on the size of the Quantum depends on the size of the energy change.energy change.

• Ex.Ex.A.A.Small energy change involves emission Small energy change involves emission

or absorption of low frequency radiation.or absorption of low frequency radiation.B.B.Large energy change involves emission Large energy change involves emission

or absorption of high frequency or absorption of high frequency radiation.radiation.

The Math in Chapter 12The Math in Chapter 12

• Only 2 equationsOnly 2 equations

• c = c = • E = hE = h• Plug and chug.Plug and chug.

An explanation of Atomic An explanation of Atomic SpectraSpectra

Atomic SpectrumAtomic Spectrum

• Each element Each element gives off its own gives off its own characteristic characteristic colors.colors.

• Can be used to Can be used to identify the atom.identify the atom.

• How we know How we know what stars are what stars are made of.made of.

Atomic Emission SpectrumAtomic Emission Spectrum

• Atomic Emission Spectrum- it passes light emitted by an Atomic Emission Spectrum- it passes light emitted by an element thru a prismelement thru a prism

• Atoms first absorb energy and then lose energy as they emit Atoms first absorb energy and then lose energy as they emit lightlight

• Each line in the emission spectrum corresponds to one exact Each line in the emission spectrum corresponds to one exact frequency of light being given off or emitted by an atom.frequency of light being given off or emitted by an atom.

• The light emitted by an electron moving from a higher to The light emitted by an electron moving from a higher to lower energy level has a frequency directly proportional to lower energy level has a frequency directly proportional to the energy change of the electronthe energy change of the electron

• Therefore each line corresponds to one exact amount of Therefore each line corresponds to one exact amount of energy being emitted.energy being emitted.

• Emission Spectrum of each element is unique to that Emission Spectrum of each element is unique to that element.element.

• The emission spectrum is obtained by an instrument called The emission spectrum is obtained by an instrument called Emission SpectrographEmission Spectrograph

• These are called discontinuous spectra

• Or line spectra

• unique to each element.

• These are emission spectra

• The light is emitted given off.

Where the electron startsWhere the electron starts• When we write electron configurations we are When we write electron configurations we are

writing the lowest energy.writing the lowest energy.• The energy level and electron starts from is called The energy level and electron starts from is called

its ground state.its ground state.• If the energy levels are quantized, it takes If the energy levels are quantized, it takes

Quantum Energy (Quantum Energy (E = hE = hto raise an electron from to raise an electron from ground state to excited state.ground state to excited state.

• Same amount of energy is emitted as a photon when the Same amount of energy is emitted as a photon when the electron drops from the excited state to the ground state.electron drops from the excited state to the ground state.

• Only electrons in transition from higher to lower Only electrons in transition from higher to lower energy levels lose energy and emit light.energy levels lose energy and emit light.

• Electron transitions Electron transitions involve jumps of involve jumps of definite amounts of definite amounts of energy.energy.

• This produces This produces bands of light with bands of light with definite definite wavelenghtswavelenghts

Emission Spectrum of Emission Spectrum of HydrogenHydrogen• Transition Wavelength l Transition Wavelength l

(nm) (nm) • n = ¥ to n = 2 361n = ¥ to n = 2 361

n = 7 to n = 2 396 n = 7 to n = 2 396 n = 6 to n = 2 409n = 6 to n = 2 409n = 5 to n = 2 433 n = 5 to n = 2 433

• n = 4 to n = 2 485n = 4 to n = 2 485n = 3 to n = 2 655n = 3 to n = 2 655

Changing the energyChanging the energy

•Let’s look at a hydrogen atomLet’s look at a hydrogen atom

Changing the energy• Heat or electricity or light can move the Heat or electricity or light can move the

electron up energy levelselectron up energy levels

Changing the energy• As the electron falls back to ground As the electron falls back to ground

state it gives the energy back as lightstate it gives the energy back as light

• May fall down in stepsMay fall down in steps

• Each with a different energyEach with a different energy

Changing the energy

{{{

• Further they fall, more energy, higher Further they fall, more energy, higher frequency.frequency.

• This is simplifiedThis is simplified

• the orbitals also have different the orbitals also have different energies inside energy levelsenergies inside energy levels

• All the electrons can move around.All the electrons can move around.

Ultraviolet Visible Infrared

We are worried about the We are worried about the change change

• When the electron moves from one energy When the electron moves from one energy level to another.level to another.

E = EE = Efinal final - E- Einitialinitial

E = -2.178 x 10E = -2.178 x 10-18-18 J ZJ Z22 (1/ n (1/ nff22 - 1/ n - 1/ nii

22))

• Rydberg’s constant and it allowed the Rydberg’s constant and it allowed the calculation of the wavelengths of all the calculation of the wavelengths of all the spectral lines of hydrogen.spectral lines of hydrogen.

Calculating Energy Calculating Energy ProblemsProblems

• What is the energy of the photon What is the energy of the photon emitted when the electron in a emitted when the electron in a hydrogen atom drops from the hydrogen atom drops from the energy level n=5 to following:energy level n=5 to following:

• A) n=2A) n=2

• B) n=3B) n=3

More Energy ProblemsMore Energy Problems

• How much energy must a hydrogen How much energy must a hydrogen atom absorb to raise its electron atom absorb to raise its electron from the energy level n=1 to the from the energy level n=1 to the following:following:

• A) n=2A) n=2

• B) n=4B) n=4

Positive or NegativePositive or Negative

• When raising an electron the amount When raising an electron the amount of energy is always positive. Why?of energy is always positive. Why?

• When an electron drops the amount When an electron drops the amount of energy is always negative. Why?of energy is always negative. Why?

Calculating Wavelength of Calculating Wavelength of PhotonPhoton

• First determine First determine ∆E∆E

• Then plug into:Then plug into:

• λλ= c h / ∆E= c h / ∆E

• What is the wavelength (in nm) of a What is the wavelength (in nm) of a photon emitted during a transition photon emitted during a transition from nfrom ni i = 6 to n= 6 to nff = 4 = 4

What is lightWhat is light

• Light is a particle - it comes in chunks.Light is a particle - it comes in chunks.

• Light is a wave- we can measure its Light is a wave- we can measure its wave length and it behaves as a wavewave length and it behaves as a wave

• If we combine E=mcIf we combine E=mc22 , c= , c=, E = 1/2 , E = 1/2 mvmv2 2 and E = hand E = h

• We can get We can get = h/mv = h/mv

• The wavelength of a particle. The wavelength of a particle.

Matter is a WaveMatter is a Wave• Does not apply to large objectsDoes not apply to large objects

• Things bigger that an atomThings bigger that an atom

• A baseball has a wavelength of about A baseball has a wavelength of about

1010--32 32 m when moving 30 m/s m when moving 30 m/s

• An electron at the same speed has a An electron at the same speed has a

wavelength of 10wavelength of 10--3 3 cmcm

• Big enough to measure. Big enough to measure.

Calculating Wavelength of a Calculating Wavelength of a ParticleParticle

• 1) Calculate the wavelength of a 1) Calculate the wavelength of a particle in:particle in:

• A) The fastest serve in tennis is A) The fastest serve in tennis is about 140 miles per hour, or 63 m/s. about 140 miles per hour, or 63 m/s. Calculate the wavelength associated Calculate the wavelength associated with a 6.0 x 10with a 6.0 x 10-2-2 kg tennis ball kg tennis ball traveling at this speed. What color traveling at this speed. What color would be produced?would be produced?

• B) Calculate the wavelength B) Calculate the wavelength associated with an electron (9.1094 x associated with an electron (9.1094 x 1010-31-31 kg) moving at 63 m/s kg) moving at 63 m/s

• Which color would be produced?Which color would be produced?

The Wave-like ElectronThe Wave-like Electron

Louis deBroglie

The electron propagates through space as an

energy wave. To understand the atom, one

must understand the behavior of

electromagnetic waves.

The physics of the very The physics of the very smallsmall

• Quantum mechanics explains how Quantum mechanics explains how the very small behaves.the very small behaves.

• Classic physics is what you get when Classic physics is what you get when you add up the effects of millions of you add up the effects of millions of packages.packages.

• Quantum mechanics is based on Quantum mechanics is based on probability becauseprobability because

More obvious with the More obvious with the very smallvery small

• To measure where a electron is, we use light.To measure where a electron is, we use light.• But the light moves the electronBut the light moves the electron• And hitting the electron changes the frequency And hitting the electron changes the frequency

of the light.of the light.

Moving Electron

Photon

Before

ElectronChanges velocity

Photon changes wavelength

After

• ““One cannot One cannot simultaneously simultaneously determine both the determine both the position and position and momentum of an momentum of an electron.”electron.”

• ““One cannot One cannot simultaneously simultaneously determine both the determine both the position and position and momentum of an momentum of an electron.”electron.”

Heisenberg Uncertainty Heisenberg Uncertainty PrinciplePrinciple

• It is impossible to know exactly the position It is impossible to know exactly the position and velocity (momentum) of a particle.and velocity (momentum) of a particle.

• The better we know one, the less we know The better we know one, the less we know the other.the other.

• The act of measuring changes the The act of measuring changes the properties.properties.

• More precisely the velocity is measured, More precisely the velocity is measured, less precise is the position (vice versa). less precise is the position (vice versa).