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Chapter 7Chapter 7

Atomic StructureAtomic Structure

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LightLight Made up of electromagnetic radiationMade up of electromagnetic radiation Waves of electric and magnetic fields Waves of electric and magnetic fields

at right angles to each other.at right angles to each other.

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Parts of a waveParts of a wave

Wavelength

Frequency = number of cycles in one secondMeasured in hertz 1 hertz = 1 cycle/second

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Frequency = Frequency =

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Kinds of EM waves Kinds of EM waves There are many There are many different different and and Radio waves, microwaves, x rays Radio waves, microwaves, x rays

and gamma rays are all examplesand gamma rays are all examples Light is only the part our eyes can Light is only the part our eyes can

detectdetect

GammaRays

Radiowaves

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The speed of lightThe speed of light in a vacuum is 2.998 x 10in a vacuum is 2.998 x 1088 m/s m/s = c= c c = c = What is the wavelength of light with a What is the wavelength of light with a

frequency 5.89 x 10frequency 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?

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In 1900In 1900 Matter and energy were seen as Matter and energy were seen as

different from each other in different from each other in fundamental waysfundamental ways

Matter was particlesMatter was particles Energy could come in waves, with Energy could come in waves, with

any frequency.any frequency. Max Planck found that the cooling of Max Planck found that the cooling of

hot objects couldn’t be explained by hot objects couldn’t be explained by viewing energy as a wave.viewing energy as a wave.

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Energy is QuantizedEnergy is Quantized Planck found Planck found E came in chunks with E came in chunks with

size hsize h E = hE = hνν

– h is Planck’s constant h is Planck’s constant – h = 6.626 x 10h = 6.626 x 10-34-34 J s J s

these packets of hthese packets of hνν are called are called quantumquantum

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Einstein is nextEinstein is next Said electromagnetic radiation is Said electromagnetic radiation is

quantized in particles called photonsquantized in particles called photons Each photon has energy = hEach photon has energy = hνν = hc/ = hc/ Combine this with E = mcCombine this with E = mc22 you get the apparent mass of a you get the apparent mass of a

photonphoton m = h / (m = h / (c)c)

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Which is it?Which is it? Is energy a wave like light, or a Is energy a wave like light, or a

particle?particle? Yes Yes Concept is called the Wave -Particle Concept is called the Wave -Particle

duality.duality. What about the other way, is matter a What about the other way, is matter a

wave? wave? YesYes

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Matter as a waveMatter as a wave Using the velocity v instead of the Using the velocity v instead of the

frequency frequency νν we get we get De Broglie’s equation De Broglie’s equation = h/mv = h/mv can calculate the wavelength of an can calculate the wavelength of an

objectobject

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ExamplesExamples The laser light of a CD is 7.80 x 10The laser light of a CD is 7.80 x 1022 m. m.

What is the frequency of this light?What is the frequency of this light?

What is the energy of a photon of this What is the energy of a photon of this light?light?

What is the apparent mass of a What is the apparent mass of a photon of this light?photon of this light?

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What is the wavelength?What is the wavelength? of an electron with a mass of of an electron with a mass of

9.11 x 109.11 x 10-31-31 kg traveling at kg traveling at 1.0 x 1.0 x

101077 m/s?m/s?

Of a softball with a mass of 0.10 kg Of a softball with a mass of 0.10 kg moving at 125 mi/hr?moving at 125 mi/hr?

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How do they know?How do they know? When light passes through, or When light passes through, or

reflects off, a series of thinly spaced reflects off, a series of thinly spaced lines, it creates a rainbow effect lines, it creates a rainbow effect

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

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A wave moves toward a slit.

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Comes out as a curve

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with two holes

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with two holes Two Curves

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Two Curveswith two holes

Interfere with each other

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Two Curveswith two holes

Interfere with each other

crests add up

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Several waves

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Several wavesSeveral Curves

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Several wavesSeveral waves

Interference Pattern

Several Curves

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What will an electron do?What will an electron do? It has mass, so it is matter.It has mass, so it is matter. A particle can only go through one A particle can only go through one

holehole A wave goes through both holesA wave goes through both holes Light shows Light shows interference patternsinterference patterns

Electron “gun”

Electron as Particle

Electron “gun”

Electron as wave

Which did it do?

It made the diffraction pattern The electron is a wave Led to Schrödingers equation

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What will an electron do?What will an electron do? An electron does go though both, An electron does go though both,

and makes an interference pattern.and makes an interference pattern. It behaves like a wave.It behaves like a wave. Other matter has wavelengths too Other matter has wavelengths too

short to notice.short to notice.

ImageImage

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SpectrumSpectrum The range of frequencies present in The range of frequencies present in

light.light. White light has a continuous White light has a continuous

spectrum.spectrum. All the colors are possible.All the colors are possible. A rainbow.A rainbow.

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Hydrogen spectrumHydrogen spectrum Emission spectrum because these are the Emission spectrum because these are the

colors it gives off or emitscolors it gives off or emits Called a line spectrum.Called a line spectrum. There are just a few discrete lines showingThere are just a few discrete lines showing

410 nm

434 nm

486 nm

656 nm

•Spectrum

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What this meansWhat this means Only certain energies are allowed for Only certain energies are allowed for

the hydrogen atom.the hydrogen atom. Can only give off certain energies.Can only give off certain energies. Use Use E = hE = h= hc / = hc / Energy in the atom is quantized Energy in the atom is quantized

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Niels BohrNiels Bohr Developed the quantum model of the Developed the quantum model of the

hydrogen atom.hydrogen atom. He said the atom was like a solar He said the atom was like a solar

systemsystem The electrons were attracted to the The electrons were attracted to the

nucleus because of opposite nucleus because of opposite charges.charges.

Didn’t fall in to the nucleus because Didn’t fall in to the nucleus because it was moving aroundit was moving around

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The Bohr Ring AtomThe Bohr Ring Atom He didn’t know why but only certain He didn’t know why but only certain

energies were allowed.energies were allowed. He called these allowed energies He called these allowed energies

energy levels.energy levels. Putting energy into the atom moved Putting energy into the atom moved

the electron away from the nucleusthe electron away from the nucleus From ground state to excited state.From ground state to excited state. When it returns to ground state it When it returns to ground state it

gives off light of a certain energygives off light of a certain energy

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The Bohr Ring AtomThe Bohr Ring Atom

n = 3n = 4

n = 2n = 1

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The Bohr ModelThe Bohr Model n is the energy leveln is the energy level for each energy level the energy isfor each energy level the energy is Z is the nuclear charge, which is +1 Z is the nuclear charge, which is +1

for hydrogen.for hydrogen. E = -2.178 x 10E = -2.178 x 10-18-18 J (ZJ (Z22 / n / n22 ) ) n = 1 is called the ground staten = 1 is called the ground state

when the electron is removed, n = when the electron is removed, n = E = 0E = 0

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We are worried about the change We are worried about the change When the electron moves from one When the electron moves from one

energy level to another.energy 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))

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ExamplesExamples Calculate the energy need to move an Calculate the energy need to move an

electron from its first energy level to electron from its first energy level to the third energy level.the third energy level.

Calculate the energy released when Calculate the energy released when an electron moves from n= 4 to n=2 in an electron moves from n= 4 to n=2 in a hydrogen atom.a hydrogen atom.

Calculate the energy released when Calculate the energy released when an electron moves from n= 5 to n=3 in an electron moves from n= 5 to n=3 in a Hea He+1+1 ion ion

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When is it true?When is it true? Only for hydrogen atoms and other Only for hydrogen atoms and other

monoelectronic species.monoelectronic species. Why the negative sign?Why the negative sign? To increase the energy of the To increase the energy of the

electron you make it further to the electron you make it further to the nucleus.nucleus.

the maximum energy an electron can the maximum energy an electron can have is zero, at an infinite distance. have is zero, at an infinite distance.

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The Bohr ModelThe Bohr Model Doesn’t workDoesn’t work only works for hydrogen atomsonly works for hydrogen atoms electrons don’t move in circleselectrons don’t move in circles the quantization of energy is right, the quantization of energy is right,

but not because they are circling like but not because they are circling like planets.planets.

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The Quantum Mechanical ModelThe Quantum Mechanical Model A totally new approachA totally new approach De Broglie said matter could be like a De Broglie said matter could be like a

wave.wave. De Broglie said they were like De Broglie said they were like

standing waves.standing waves. The vibrations of a stringed The vibrations of a stringed

instrumentinstrument

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What’s possible?What’s possible? You can only have a standing wave if You can only have a standing wave if

you have complete waves.you have complete waves. There are only certain allowed waves.There are only certain allowed waves. In the atom there are certain allowed In the atom there are certain allowed

waves called electrons.waves called electrons. 1925 Erwin Schroedinger described 1925 Erwin Schroedinger described

the wave function of the electronthe wave function of the electron Much math, but what is important are Much math, but what is important are

the solutionsthe solutions

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SchrSchröödinger’s Equationdinger’s Equation The wave function is a F(x, y, z)The wave function is a F(x, y, z) Actually F(r,Actually F(r,θθ,,φφ)) Solutions to the equation are called Solutions to the equation are called

orbitals.orbitals. These are not Bohr orbits.These are not Bohr orbits. Each solution is tied to a certain Each solution is tied to a certain

energy energy These are the energy levelsThese are the energy levels

•AnimationAnimation

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There is a limit to what we can There is a limit to what we can knowknow

We can’t know how the electron is We can’t know how the electron is moving or how it gets from one moving or how it gets from one energy level to another.energy level to another.

The The Heisenberg Uncertainty PrincipleHeisenberg Uncertainty Principle There is a limit to how well we can There is a limit to how well we can

know both the position and the know both the position and the momentum of an object.momentum of an object.

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MathematicallyMathematically x · x · (mv) > h/4(mv) > h/4 x is the uncertainty in the positionx is the uncertainty in the position (mv) is the uncertainty in the (mv) is the uncertainty in the

momentum.momentum. the minimum uncertainty is h/4the minimum uncertainty is h/4

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What does the wave Function What does the wave Function mean?mean?

nothing.nothing. it is not possible to visually map it.it is not possible to visually map it. The square of the function is the The square of the function is the

probability of finding an electron near probability of finding an electron near a particular spot.a particular spot.

best way to visualize it is by mapping best way to visualize it is by mapping the places where the electron is likely the places where the electron is likely to be found.to be found.

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Pro

babi

lity

Distance from nucleus

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Sum

of

all P

roba

bili

ties

Sum

of

all P

roba

bili

ties

Distance from nucleusDistance from nucleus

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Defining the sizeDefining the size The nodal surface.The nodal surface. The size that encloses 90% to the The size that encloses 90% to the

total electron probability.total electron probability. NOT at a certain distance, but a most NOT at a certain distance, but a most

likely distance.likely distance. For the first solution it is a a sphere. For the first solution it is a a sphere.