1 © 2009 Brooks/Cole - Cengage ATOMIC STRUCTURE. 2 © 2009 Brooks/Cole - Cengage Atomic Structure Much of what we know about the very nature of matter

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© 2009 Brooks/Cole - Cengage

ATOMIC ATOMIC STRUCTURESTRUCTURE

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Atomic StructureAtomic StructureAtomic StructureAtomic Structure

• Much of what we know about the very nature of Much of what we know about the very nature of

matter and the universe around us is due to the matter and the universe around us is due to the

work of pioneering chemists, mathematicians and work of pioneering chemists, mathematicians and

physicists in the late 19physicists in the late 19thth and early 20 and early 20thth centuries centuries» No Computers, calculators, Starbucks, cell phones or even No Computers, calculators, Starbucks, cell phones or even

ELECTRICITYELECTRICITY

• This knowledge sprang from studies on lightThis knowledge sprang from studies on light» What is it?What is it?

» How do atoms interact with it?How do atoms interact with it?

» How is it made?How is it made?

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Electromagnetic RadiationElectromagnetic RadiationElectromagnetic RadiationElectromagnetic Radiation• In 1864 In 1864 (what was going on in America at the time?),(what was going on in America at the time?), James Maxwell developed a mathematical James Maxwell developed a mathematical

way to describe radiationway to describe radiation

• He said that radiation is a wave with electric and magnetic He said that radiation is a wave with electric and magnetic

fields at right angles to each other move togetherfields at right angles to each other move together

• Since it is a wave, it has the following characteristics of all Since it is a wave, it has the following characteristics of all

waveswaves– Wavelength: Wavelength: λλ (lambda) = The distance between successive crests of a wave. (lambda) = The distance between successive crests of a wave.

It is measured in units of distance (nanometers, micrometers, meters)It is measured in units of distance (nanometers, micrometers, meters)

– Frequency: Frequency: νν (nu) = The number of waves that pass a given point in some (nu) = The number of waves that pass a given point in some

amount of time (usually per second). It is measured in Hertz (Hz) or samount of time (usually per second). It is measured in Hertz (Hz) or s -1-1

• The speed of an electromagnetic wave is defined as:The speed of an electromagnetic wave is defined as:

c = c = λν λν

where c is the Universal Constant = 3.00 x10where c is the Universal Constant = 3.00 x1088 m/s m/s

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wavelength Visible light

wavelength

Ultraviolet radiation

Amplitude

Node

Electromagnetic RadiationElectromagnetic RadiationElectromagnetic RadiationElectromagnetic Radiation

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Electromagnetic RadiationElectromagnetic Radiation

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Long wavelength Long wavelength ,, small frequency v small frequency v

Short wavelength Short wavelength ,, high frequency v high frequency v

increasing increasing frequencyfrequency

increasing increasing wavelengthwavelength


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Red light has Red light has = 700 nm. Calculate the frequency. = 700 nm. Calculate the frequency.

Freq =

3.00 x 108 m/s

7.00 x 10-7 m= 4.29 x 1014 sec-1

Freq =

3.00 x 108 m/s

7.00 x 10-7 m= 4.29 x 1014 sec-1

700 nm 1 x 10-9 m

1 nm

⎛

⎝⎜⎜

⎞

⎠⎟⎟ = 7.00 x 10-7 m

700 nm 1 x 10-9 m

1 nm

⎛

⎝⎜⎜

⎞

⎠⎟⎟ = 7.00 x 10-7 m


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Long wavelength Long wavelength small frequencysmall frequency

low energylow energy

Short wavelength Short wavelength high frequencyhigh frequency

high energyhigh energy


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ElectroElectromagneticmagnetic SpectrumSpectrum

ElectroElectromagneticmagnetic SpectrumSpectrum

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Let’s look at an object being heatedLet’s look at an object being heatedLet’s look at an object being heatedLet’s look at an object being heated

• The emitted light from a heated object comes from a collection of oscillatorsThe emitted light from a heated object comes from a collection of oscillators– Some at high energy, some at intermediate energy, some at low energySome at high energy, some at intermediate energy, some at low energy

• In 1879, Josef Stefan determined that the total intensity of all radiation emitted from a heated object increases as the fourth power of temperatureIn 1879, Josef Stefan determined that the total intensity of all radiation emitted from a heated object increases as the fourth power of temperature– Intensity=(5.67x10Intensity=(5.67x10-8-8WmWm-2-2KK-4-4) · T) · T44

» 1 Watt (W) = 1J/sec1 Watt (W) = 1J/sec

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Wien’s Law

Wilhelm Wien studied the relationship between temperature and the wavelength of maximum intensity

in a black body emitter.

He found that as Temperature INCREASES, the wavelength of maximum emission DECREASES

We can summarize this in Wien’s Law:

Tmax = Constant = 2.9 K•mm

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Quantization of Energy Quantization of Energy (Planck and Einstein)(Planck and Einstein)

Quantization of Energy Quantization of Energy (Planck and Einstein)(Planck and Einstein)

• For centuries people have observed that as you heat an object, it goes from red to orange-yellow to whiteFor centuries people have observed that as you heat an object, it goes from red to orange-yellow to white– The phrase “white hot” comes from thisThe phrase “white hot” comes from this

• What are we actually observing?What are we actually observing?• This emitted light is an indicator of the heat given off by the objectThis emitted light is an indicator of the heat given off by the object• The problem scientists in the 1800’s had was that it was theorized that the more heat you put into an object, the higher the intensity of radiation that would be emitted at decreasing wavelengthThe problem scientists in the 1800’s had was that it was theorized that the more heat you put into an object, the higher the intensity of radiation that would be emitted at decreasing wavelength

““The Ultraviolet Catastrophe”The Ultraviolet Catastrophe”

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The Ultraviolet Catastrophe

• According to Classical Physics at the time, having a cookout should turn into a nightmare.

• The grill should be emitting x-ray and gamma ray radiation

• But we know this doesn’t happen.

• Max Planck studied this and found…

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Quantization of EnergyQuantization of Energy

See Chem & Chem Reactivity, Figure 6.3See Chem & Chem Reactivity, Figure 6.3

•Planck deduced that Planck deduced that energy would be energy would be quantized and this quantized and this explained the explained the “Catastrophe”“Catastrophe”

•With quantization, only With quantization, only radiation of certain radiation of certain energies would be energies would be emittedemitted

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E = h · E = h · E = h · E = h ·

Quantization of EnergyQuantization of EnergyQuantization of EnergyQuantization of Energy

Energy of radiation is proportional to frequencyEnergy of radiation is proportional to frequency

h = Planck’s constant = 6.6262 x 10h = Planck’s constant = 6.6262 x 10-34-34 J·s J·s

An object can gain or lose energy by absorbing or An object can gain or lose energy by absorbing or emitting radiant energy in emitting radiant energy in QUANTAQUANTA..

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Light with a short Light with a short (large (large ) has a large E.) has a large E.Light with a short Light with a short (large (large ) has a large E.) has a large E.

Light with large Light with large (small (small ) has a small E.) has a small E.Light with large Light with large (small (small ) has a small E.) has a small E.

E = h · E = h · E = h · E = h ·

Quantization of Quantization of EnergyEnergy

Quantization of Quantization of EnergyEnergy

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Let’s look at an object being heatedLet’s look at an object being heatedLet’s look at an object being heatedLet’s look at an object being heated

• As we heat a metal bar, the atoms in the bar vibrate fasterAs we heat a metal bar, the atoms in the bar vibrate faster

• The atoms are called oscillatorsThe atoms are called oscillators

• As they drop back down to a lower vibrational state they emit some radiationAs they drop back down to a lower vibrational state they emit some radiation

• Each oscillator has a fundamental frequency and the energy of the emitted radiation is a multiple of this frequency (this is where Each oscillator has a fundamental frequency and the energy of the emitted radiation is a multiple of this frequency (this is where nn comes into play) comes into play)

• For a single energy level change, the equation becomes:For a single energy level change, the equation becomes:E=hE=hνν (Planck’s Equation)(Planck’s Equation)

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Energy of RadiationEnergy of RadiationEnergy of 1.00 mol of photons of Energy of 1.00 mol of photons of red lightred light..

E = hE = h··

= (6.63 x 10= (6.63 x 10-34-34 J J··s)(4.29 x 10s)(4.29 x 101414 s s-1-1))

= 2.85 x 10= 2.85 x 10-19-19 J per photon J per photon

E per mol = E per mol =

(2.85 x 10(2.85 x 10-19-19 J/ph)(6.02 x 10 J/ph)(6.02 x 102323 ph/mol) ph/mol)

= 172 kJ/mol= 172 kJ/mol

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Photoelectric EffectPhotoelectric EffectPhotoelectric EffectPhotoelectric Effect

Experiment demonstrates the particle nature of light.Experiment demonstrates the particle nature of light.Experiment demonstrates the particle nature of light.Experiment demonstrates the particle nature of light.

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Photoelectric EffectPhotoelectric Effect

Classical theory said that E of ejected Classical theory said that E of ejected electron should increase with electron should increase with increase in light intensity—not increase in light intensity—not observed!observed!

• No eNo e-- observed until light of a certain observed until light of a certain minimum E minimum E (or frequency, remember Placnk’s equation?) (or frequency, remember Placnk’s equation?) is is used.used.

– Once this value is reached, electrons are Once this value is reached, electrons are immediately ejectedimmediately ejected

• Number of eNumber of e-- ejected depends on ejected depends on light intensity.light intensity.

• The kinetic energy of the ejected The kinetic energy of the ejected electrons increases with the electrons increases with the frequency of the incident radiationfrequency of the incident radiation

A. Einstein (1879-A. Einstein (1879-1955)1955)

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Understand experimental observations Understand experimental observations if light consists of particles called if light consists of particles called PHOTONSPHOTONS of discrete energy.of discrete energy.

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• Einstein explained the observations of Einstein explained the observations of photo-electric experiments by combining photo-electric experiments by combining Planck’s equation with a new conceptPlanck’s equation with a new concept

– Light has particle-like propertiesLight has particle-like properties– Massless packets of energy are called Massless packets of energy are called PHOTONSPHOTONS (hv) (hv)

and the energy of the packets is proportional to their and the energy of the packets is proportional to their frequencyfrequency

• No electrons are ejected by the metal if the No electrons are ejected by the metal if the incident photons do not have a high incident photons do not have a high enough energyenough energy

• If the frequency is high enough, the energy If the frequency is high enough, the energy is high enough and an electron is knocked is high enough and an electron is knocked offoff

A. Einstein (1879-A. Einstein (1879-1955)1955)

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Photoelectric EffectLet’s look at this in more detail:

If we have a stream of photons colliding with a metal object, some of those photons are going to collide with the electrons in the metal

The photons have an energy associated with them (hv) but this value must be above a certain minimum to eject an electron from the metal.

Different metals do not release electrons with the exact same incident photons

The metals want to hold onto the electrons and have a characteristic energy value associated with them called a WORK FUNCTION,

If the energy of the incident photons is greater than , then the metal releases electrons

1/2mev2 = hv -

Ek of ejected electron

Work function of metal

Energy of incident photon

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Atomic Line Emission Atomic Line Emission Spectra and Niels BohrSpectra and Niels BohrAtomic Line Emission Atomic Line Emission

Spectra and Niels BohrSpectra and Niels Bohr• It has long been known that applying high voltage It has long been known that applying high voltage

to a tube containing a gas would result in the gas to a tube containing a gas would result in the gas giving off lightgiving off light

• However, if we split the light into its component However, if we split the light into its component wavelengths with a prism, we’ll see a small wavelengths with a prism, we’ll see a small number of lines at specific colors (wavelengths)number of lines at specific colors (wavelengths)

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Line Emission Spectra Line Emission Spectra of Excited Atomsof Excited Atoms


• Excited atoms emit light of only certain wavelengths

• The wavelengths of emitted light depend on the element.

QuickTime™ and aGraphics decompressor

are needed to see this picture.

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Visible lines in H atom spectrum are Visible lines in H atom spectrum are called the called the BALMERBALMER series. series.

High EHigh EShort Short High High

Low ELow ELong Long Low Low



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Line Spectra of Other Line Spectra of Other ElementsElements

Why do elements emit at certain characteristic wavelengths?Why do elements emit at certain characteristic wavelengths?Balmer and Rydberg developed an explanation for the line emission Balmer and Rydberg developed an explanation for the line emission behaviour (Rydberg Formula)behaviour (Rydberg Formula)

€

=R1

n12 −

1

n22

⎛

⎝ ⎜

⎞

⎠ ⎟ R = Rydberg Constant = R = Rydberg Constant =

1.0974x101.0974x10-3-3 m m-1-1

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Line Spectra

€

=R1

n12 −

1

n22

⎛

⎝ ⎜

⎞

⎠ ⎟ R = Rydberg Constant = R = Rydberg Constant =

1.0974x101.0974x10-3-3 m m-1-1

When n1=2 (and n2=2, 3, 4…) You can calculate the Balmer Series of lines

When n1=1 (and n2=2, 3, 4…) You can calculate the Lyman Series of lines

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What do Line Spectra Tell Us?

The characteristic line spectra of each element tells us that electrons can only

have certain SPECIFIC energies (that’s what those n values mean, but more on that in a minute)

Each element has a unique configuration of electrons as evidenced by their unique

line spectra

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Atomic Spectra and Atomic Spectra and BohrBohr


1.1. Any orbit should be possible Any orbit should be possible and so is any energy.and so is any energy.

2.2. But a charged particle moving But a charged particle moving in an electric field should emit in an electric field should emit energy. energy.

End result should be destruction!End result should be destruction!

+Electronorbit

One view of atomic structure in early 20th One view of atomic structure in early 20th century was that an electron (e-) traveled century was that an electron (e-) traveled about the nucleus in an orbit.about the nucleus in an orbit.

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Bohr said classical view is wrong. Bohr said classical view is wrong.

Need a new theory — now called Need a new theory — now called QUANTUMQUANTUM or or WAVE MECHANICSWAVE MECHANICS..

e- can only exist in certain discrete orbits — e- can only exist in certain discrete orbits — called called stationary statesstationary states. .

e- is restricted to e- is restricted to QUANTIZEDQUANTIZED energy states. energy states.

Energy of state = - Rhc/nEnergy of state = - Rhc/n22

where n = quantum no. = 1, 2, 3, 4, ....where n = quantum no. = 1, 2, 3, 4, ....

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• Only orbits where n = some positive integer Only orbits where n = some positive integer are permitted.are permitted.

• The energy of an electron in an orbit has a The energy of an electron in an orbit has a negative valuenegative value

• An atom with its electrons in the lowest An atom with its electrons in the lowest possible energy level is at possible energy level is at GROUND STATEGROUND STATE

Energy of quantized state = - Rhc/nEnergy of quantized state = - Rhc/n22

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If e-’s are in quantized energy If e-’s are in quantized energy states, then ∆E of states can have states, then ∆E of states can have only certain values. This explain only certain values. This explain sharp line spectra.sharp line spectra.

n = 1

n = 2E = -C (1/2 2)

E = -C (1/1 2)n = 1

n = 2E = -C (1/2 2)

E = -C (1/1 2) PLAY MOVIE

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Energy Adsorption/Emission

Energy Adsorption/Emission

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Origin of Line SpectraOrigin of Line Spectra

Balmer seriesBalmer series

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Atomic Line Spectra and Atomic Line Spectra and Niels BohrNiels Bohr

Atomic Line Spectra and Atomic Line Spectra and Niels BohrNiels Bohr

Bohr’s theory was a great Bohr’s theory was a great accomplishment.accomplishment.

Rec’d Nobel Prize, 1922Rec’d Nobel Prize, 1922

Problems with theory —Problems with theory —

• theory only successful for H.theory only successful for H.

• introduced quantum idea artificially.introduced quantum idea artificially.

• So, we go on to So, we go on to QUANTUMQUANTUM or or WAVE WAVE MECHANICSMECHANICS

Niels BohrNiels Bohr

(1885-1962)(1885-1962)

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Wave-Particle DualityWave-Particle DualityWave-Particle DualityWave-Particle Duality

de Broglie (1924) proposed de Broglie (1924) proposed that all moving objects have that all moving objects have wave properties. wave properties.

For light: E = mcFor light: E = mc22

E = hE = h = hc / = hc / Therefore, mc = h / Therefore, mc = h / and for particlesand for particles

(mass)(velocity) = h / (mass)(velocity) = h /

de Broglie (1924) proposed de Broglie (1924) proposed that all moving objects have that all moving objects have wave properties. wave properties.

For light: E = mcFor light: E = mc22

E = hE = h = hc / = hc / Therefore, mc = h / Therefore, mc = h / and for particlesand for particles

(mass)(velocity) = h / (mass)(velocity) = h /

L. de BroglieL. de Broglie(1892-1987)(1892-1987)

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Baseball (115 g) at Baseball (115 g) at 100 mph100 mph

= 1.3 x 10= 1.3 x 10-32-32 cm cm

e- with velocity = e- with velocity =

1.9 x 101.9 x 1088 cm/sec cm/sec

= 0.388 nm= 0.388 nmExperimental proof of waveExperimental proof of waveproperties of electronsproperties of electrons

Wave-Particle DualityWave-Particle DualityWave-Particle DualityWave-Particle Duality

•The mass times the velocity of the ball is very large, so the wavelength is very The mass times the velocity of the ball is very large, so the wavelength is very small for the baseballsmall for the baseball•The deBroglie equation is only useful for particles of very small massThe deBroglie equation is only useful for particles of very small mass

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1 © 2009 Brooks/Cole - Cengage ATOMIC STRUCTURE. 2 © 2009 Brooks/Cole - Cengage Atomic Structure Much of what we know about the very nature of matter