Atomic Physics

Chapter 28Chapter 28

Atomic Models

Introduction

How do How do neonneon signs work? signs work?

Our main focus will be on the Our main focus will be on the hydrogenhydrogen atom. atom.It is the simplestIt is the simplest

atomic system.atomic system.

Why is it important to study the hydrogen Why is it important to study the hydrogen atom?atom? Studying the quantum numbers for the allowed Studying the quantum numbers for the allowed

states of hydrogen will help us to describe the states of hydrogen will help us to describe the allowed states of allowed states of more complex atomsmore complex atoms. .

The hydrogen atom is an The hydrogen atom is an ideal systemideal system for for relating theory to experimentation.relating theory to experimentation.

Much that we learn about hydrogen can be Much that we learn about hydrogen can be extended to extended to single electron ionssingle electron ions like He and Li. like He and Li.

Early Models Of The Atom

The Greek modelThe Greek model Tiny, hard, indestructible sphereTiny, hard, indestructible sphere

33

The J. J. Thomson modelThe J. J. Thomson model A volume of positive charge is embedded A volume of positive charge is embedded

with negative charges called “electrons”with negative charges called “electrons”

The Rutherford modelThe Rutherford model A positive nucleus orbited by electrons.A positive nucleus orbited by electrons.

The nucleus contains 99.9% of the atom’s The nucleus contains 99.9% of the atom’s massmass

The RutherfordThe Rutherford modelmodel Which force holds the electrons in orbit?Which force holds the electrons in orbit?

The Coulomb forceThe Coulomb force

Problems with the Rutherford Model

There were There were two basic difficultiestwo basic difficulties with with the Rutherford model.the Rutherford model. It could not explain why atoms radiate It could not explain why atoms radiate

discretediscrete frequencies. frequencies. Accelerating electronsAccelerating electrons should radiate should radiate

electromagnetic waves.electromagnetic waves.

Electron Transitions

Using a high voltage to move electrons Using a high voltage to move electrons through a gas causes the gas electrons to through a gas causes the gas electrons to become become excitedexcited and to jump from and to jump from lower lower energy levels to higher energy levelsenergy levels to higher energy levels..

PhotonsPhotons of various wavelengths are of various wavelengths are produced when electrons fall from produced when electrons fall from higher higher energy levels to lower energy levelsenergy levels to lower energy levels..

Emission Spectra

The The emission spectrumemission spectrum of hydrogen of hydrogen Can be produced by applying a high voltage Can be produced by applying a high voltage

across an evacuated glass tube filled with across an evacuated glass tube filled with hydrogen hydrogen

The observed wavelengths are characteristic The observed wavelengths are characteristic only of hydrogenonly of hydrogen

279, 57279, 57

The Balmer Series

In the Balmer SeriesIn the Balmer Series nnff

= 2= 2 There are There are fourfour prominent wavelengths prominent wavelengths

656.3 nm656.3 nm (red)(red)486.1 nm486.1 nm (green)(green)434.1 nm434.1 nm (purple)(purple)410.2 nm410.2 nm (deep violet)(deep violet)

278, 28.7278, 28.7

Balmer Wavelengths

The Balmer Series Wavelength Equation

RRH H is the Rydberg constantis the Rydberg constant

RRH H = 1.0973732 x 10= 1.0973732 x 1077 mm-1-1

€

1

λ= RH

1

22−

1

ni2

⎛

⎝ ⎜

⎞

⎠ ⎟

Two Other Important Series

Lyman seriesLyman series (UV) (UV) nnff

= 1= 1

Paschen seriesPaschen series (IR) (IR) nnff

= 3= 3

7070

Spectral Lines

How many How many differentdifferent spectral lines spectral lines could be produced by an electron in the could be produced by an electron in the n = 3n = 3 state? state?

ThreeThree

How many How many differentdifferent spectral lines spectral lines could be produced by an electron in the could be produced by an electron in the n = 4n = 4 state? state?

SixSix

Photon Energy

The equation for determining the The equation for determining the energyenergy of the emitted photon in any of the emitted photon in any series:series:

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

2i

2f n

1

n

1eV 13.6E

The Absorption Spectrum

An element can absorb the same An element can absorb the same wavelengths that it emits.wavelengths that it emits.

The spectrum consists of a series of dark The spectrum consists of a series of dark lines.lines.

Identifying Elements

The The absorption spectrumabsorption spectrum was used to was used to identify elements in the solar atmosphere identify elements in the solar atmosphere were identified in this way.were identified in this way.

Helium was discovered.Helium was discovered.

Thermal vs. Atomic Spectra

How could you tell if the light from a How could you tell if the light from a candle flame is candle flame is thermalthermal or or atomicatomic in in origin?origin?

If the spectrum is If the spectrum is continuouscontinuous, the , the source must besource must be thermalthermal..

Auroras

What is the origin of the colors in the What is the origin of the colors in the aurora borealisaurora borealis??

High speed particlesHigh speed particles from space from space interact with the earth’s magnetic field.interact with the earth’s magnetic field.

The Bohr Theory Of Hydrogen

At the beginning of the 20At the beginning of the 20thth century, century, scientists wondered why atoms only scientists wondered why atoms only radiated radiated certain wavelengthscertain wavelengths.. Bohr provided an explanation.Bohr provided an explanation.

Four Assumptions of The Bohr Theory

1) 1) The electron orbits the proton due to theThe electron orbits the proton due to the

Coulomb forceCoulomb force which produces centripetal which produces centripetal

acceleration.acceleration.

2) Only certain electron orbits are 2) Only certain electron orbits are stablestable

and do not radiate energy.and do not radiate energy.

3) 3) RadiationRadiation is only emitted when an is only emitted when an

electron electron dropsdrops from a more energetic from a more energetic

state to a lower state.state to a lower state.

hfEE fi =−

4) 4) The The radiusradius of the electron’s orbit is of the electron’s orbit is

determined by the electron’s determined by the electron’s orbitalorbital

angular momentumangular momentum. .

28.628.6

€

rn = nh

2π mev

⎛

⎝ ⎜

⎞

⎠ ⎟ n = 1, 2, 3, ...

Total Energy of the Hydrogen Atom

The The total energytotal energy of the hydrogen of the hydrogen atom can be determined by using atom can be determined by using this equation.this equation.

€

ET = −k ee

2

2r

The Bohr Radius

An electron can exist only in An electron can exist only in certain certain allowed orbitsallowed orbits determined by the determined by the integer n.integer n.When n = 1, we have what is known When n = 1, we have what is known

as the as the Bohr radiusBohr radius ( (aaoo).).

aaoo = 0.0529 nm = 0.0529 nm

Orbital Radii

A general equation for finding the A general equation for finding the radiusradius of any orbit: of any orbit:

( )Z

2

n

nnm 0.0529r =

Energy States

The The energyenergy for various energy states for various energy states can be found by using:can be found by using:

n= 1 is the ground staten= 1 is the ground state

2

2

n n

ZeV 13.6E −=

Ionization Energy

The minimum energy required to The minimum energy required to ionize the atom is called the ionize the atom is called the ionization energyionization energy..An electron is completely removed An electron is completely removed

from the atom.from the atom.

The Hydrogen Spectrum

The general expression for The general expression for determining wavelengths of the determining wavelengths of the various series in the hydrogen various series in the hydrogen spectrumspectrum

€

1

λ= RH

1

n f2 −

1

ni2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

Bohr’s Correspondence Principle

Quantum mechanicsQuantum mechanics is in agreement is in agreement with with classical physicsclassical physics when the energy when the energy differences between quantized levels differences between quantized levels are very small.are very small.

Successes of the Bohr Theory

It accounted for theIt accounted for the Balmer seriesBalmer series and other and other series.series.

It predicted a value for theIt predicted a value for the Rydberg Rydberg constantconstant that agreed strongly with the that agreed strongly with the experimental value.experimental value.

It gave an expression for theIt gave an expression for the radiusradius of the of the hydrogen atom.hydrogen atom.

It predicted theIt predicted the energy levelsenergy levels of hydrogen.of hydrogen.

It also works with hydrogen-like It also works with hydrogen-like (one (one electron)electron) atoms. atoms. Singly ionized heliumSingly ionized helium

It also works with hydrogen-like It also works with hydrogen-like (one (one electron)electron) atoms. atoms. Doubly ionized lithiumDoubly ionized lithium

It also works with hydrogen-like It also works with hydrogen-like (one (one electron)electron) atoms. atoms. Triply ionized berylliumTriply ionized beryllium

Four Quantum Numbers

The state of an electron is specified byThe state of an electron is specified by fourfour quantum numbers. quantum numbers. These numbers describe These numbers describe allall possible possible

electron states.electron states. The The totaltotal number of electrons in a number of electrons in a

particular energy level is given by:particular energy level is given by:

€

# = 2n2

Principle Quantum Number

The principal quantum numberThe principal quantum number (n) (n) wherewhere n = 1, 2, 3, …n = 1, 2, 3, … Determines the Determines the energyenergy of the allowed of the allowed

states of hydrogenstates of hydrogen States with the same principal quantum States with the same principal quantum

number are said to form a number are said to form a shellshellK, L, M, … (n = 1, 2, 3, …)K, L, M, … (n = 1, 2, 3, …)

Orbital Quantum Number The orbital quantum numberThe orbital quantum number ((ll)) where where ll

ranges from ranges from 00 to to (n – 1)(n – 1) in integral steps in integral steps Allows Allows multiple orbitsmultiple orbits within the same within the same

energy levelenergy level Determines the Determines the shapeshape of the orbits of the orbits States with given values of States with given values of nn and and ll are are

called called subshellssubshellsss ((ll = 0) = 0),, pp ((ll = 1) = 1),, dd ((ll = 2) = 2),, ff ((ll = 3) = 3),, etc… etc…

Electron Subshells

Generally, the electrons in the Generally, the electrons in the ss subshell are subshell are at the lowest energy level and those in the at the lowest energy level and those in the ff subshell in the highest shell occupy the subshell in the highest shell occupy the highest energy level.highest energy level.

As the shell number As the shell number (n)(n) increases the increases the energy difference between the shells energy difference between the shells diminishes, as shown by the decreasing diminishes, as shown by the decreasing distance between each successive shell.distance between each successive shell.

Electron Subshells

Magnetic Quantum Number

The magnetic quantum numberThe magnetic quantum number (m(mll))

wherewhere mmll ranges fromranges from - - ll toto + + ll in in

integral stepsintegral steps Explains why strong magnetic fields can Explains why strong magnetic fields can

cause single cause single spectral linesspectral lines to to splitsplit into into several closely spaced linesseveral closely spaced linesCalled the Zeeman effectCalled the Zeeman effect

Spin Magnetic Quantum Number

The spin magnetic quantum numberThe spin magnetic quantum number (m(mss))

where where mmss can only be can only be + 0.5+ 0.5 or or – 0.5– 0.5 Accounts for the Accounts for the fine structurefine structure of “single” of “single”

spectral lines in the absence of a magnetic fieldspectral lines in the absence of a magnetic field

Hydrogen Like Atoms

Two important equations for Two important equations for hydrogen-likehydrogen-like atoms: atoms: Orbital energyOrbital energy

Orbital radiusOrbital radius

( )eV

n

13.6)ZE

2

2

n −=

€

rn = (0.0529 nm)n2

Z

Angular Momentum

Physicists agreed that angular momentum Physicists agreed that angular momentum was was quantizedquantized but no one was able to but no one was able to explain why.explain why.

28.1028.10

Electron Standing Waves

de Broglie stated that an electron orbit de Broglie stated that an electron orbit would be stable if it contained anwould be stable if it contained an integral numberintegral number of electron of electron wavelengths.wavelengths.

Analogous to Analogous to standing wavesstanding waves in a string in a string

Wave Properties

It became generally agreed upon that It became generally agreed upon that wave propertieswave properties were involved in the were involved in the behavior of atomic systems.behavior of atomic systems.

Quantum Mechanics And The Hydrogen Atom

A review of the various A review of the various quantum number quantum number rangesranges which are used to determine which are used to determine allowable statesallowable states nn can range from can range from 1 1 toto infinity infinity in integral stepsin integral stepsll can range from can range from 0 0 toto (n - 1) (n - 1) in integral stepsin integral steps mmll can range fromcan range from – – ll toto + + ll in integral stepsin integral steps

mmss can only be can only be + ½+ ½ or or – ½– ½

The Spin Magnetic Quantum Number

The spin magnetic quantum number The spin magnetic quantum number explains the explains the splittingsplitting of each energy of each energy level into two level into two (the Zeeman Effect)(the Zeeman Effect).. It explains how two very closely spaced It explains how two very closely spaced

lines may be formed in the spectra of lines may be formed in the spectra of certain gases.certain gases.Electron spin (spin-up and spin-down)Electron spin (spin-up and spin-down)

Questions

2, 8, 122, 8, 12

Pg. 910Pg. 910

Electron Clouds

The electron may be found at various The electron may be found at various distances from the nucleus but the distances from the nucleus but the probability probability of finding it at a distance of finding it at a distance corresponding to the first Bohr orbit is a corresponding to the first Bohr orbit is a maximum.maximum. It can be found in a spherical region known as It can be found in a spherical region known as

thethe ““electron cloudelectron cloud”.”.

281, 282281, 282

The State of an Electron

The The statestate of an electron is specified by of an electron is specified by fourfour quantum numbers. quantum numbers. These numbers describe These numbers describe allall possible possible

electron states.electron states. The The total number of electronstotal number of electrons in a in a

particular energy level is given by:particular energy level is given by:

22n #=

The Pauli Exclusion Principle

Two electrons in an atom can Two electrons in an atom can never never have the same set of quantum numbers.have the same set of quantum numbers. Because of this, the elements all have Because of this, the elements all have

different chemical propertiesdifferent chemical properties.. The The n = 1n = 1 energy level is filled with energy level is filled with

electrons electrons firstfirst..

The Pauli Exclusion Principle And The Periodic Table

MendeleevMendeleev arranged the elements in a arranged the elements in a periodic tableperiodic table according to their atomic according to their atomic masses and chemical similarities.masses and chemical similarities. He left He left gapsgaps which were filled in within the which were filled in within the

next 20 years.next 20 years. Vertical columns have Vertical columns have similar chemical similar chemical

propertiesproperties..

1515

The Periodic Table

Special Groups Within the Periodic Table

Noble gasesNoble gases The outer shell is The outer shell is filledfilled..

Alkali metalsAlkali metals The outer shell has The outer shell has only one electrononly one electron..

HalogensHalogens The outer shell The outer shell needs one electronneeds one electron..

The Dow Corning Periodic Table

X-Rays

X-rays are X-rays are emittedemitted when a metal target is when a metal target is bombardedbombarded with high-energy electrons to with high-energy electrons to produce:produce: A broad continuous bandA broad continuous band

BremsstrahlungBremsstrahlung Characteristic x-raysCharacteristic x-rays

KK and Kand K

284, 285284, 285

X-Ray Photons

What can the incoming electron from an electron What can the incoming electron from an electron gun do to a gun do to a K-shell electronK-shell electron in a tungsten target in a tungsten target atom?atom? It can knock a It can knock a K-shell electronK-shell electron out of its energy out of its energy

level. Then, an electron from a higher energy level. Then, an electron from a higher energy level can fall into the level can fall into the K-shellK-shell (n = 1).(n = 1).

The energy lost by the falling electron shows The energy lost by the falling electron shows up as an emitted up as an emitted x-ray photonx-ray photon..

Characteristic X-Rays

K-shell emissionK-shell emission produces higher-intensity produces higher-intensity x-rays than Bremsstrahlung.x-rays than Bremsstrahlung.

The x-ray photon comes out at a single The x-ray photon comes out at a single (characteristic)(characteristic) wavelength. wavelength. KK or Kor K

K X-Rays

When an incoming electron forces an When an incoming electron forces an electron out of the K shell electron out of the K shell an electron can an electron can drop down from the drop down from the n = 2n = 2 level and a level and a KK

x-ray photon is emitted.x-ray photon is emitted.

K X-Rays

When an incoming electron forces an When an incoming electron forces an electron out of the K shell electron out of the K shell an electron an electron can drop down from the can drop down from the n = 3n = 3 level and a level and aKK x-ray photon is emitted.x-ray photon is emitted.

Which x-ray photon has the highest energy?Which x-ray photon has the highest energy?

K X-Ray Wavelengths

The wavelength of the emitted The wavelength of the emitted KK

x-ray photon is given by:x-ray photon is given by:

€

1

λ= RH Z −1( )

2 1

12−

1

22

⎛

⎝ ⎜

⎞

⎠ ⎟

Electron Shielding

One electron in the K shell One electron in the K shell partially partially shieldsshields the other from the charge of the the other from the charge of the nucleus. nucleus. Because of this, we use Because of this, we use ZZeffeff = = (Z - 1)(Z - 1)

in the in the KK equation. equation.

K X-Ray Wavelengths

The wavelength of the emitted The wavelength of the emitted KK x- x-

ray photon is given by:ray photon is given by:

€

1

λ= RH Z − 9( )

2 1

12−

1

32

⎛

⎝ ⎜

⎞

⎠ ⎟

Electron Shielding

One electron in the K shell and eight One electron in the K shell and eight electrons in the L shell electrons in the L shell partially shieldpartially shield the M-shell electrons from the charge the M-shell electrons from the charge of the nucleus. of the nucleus. Because of this, we use Because of this, we use ZZeffeff = = (Z - 9)(Z - 9)

in the in the KK equation. equation.

Atomic Transitions

Atoms will only emit or absorb EM Atoms will only emit or absorb EM radiation at certain frequencies radiation at certain frequencies corresponding to corresponding to transitionstransitions involving involving the various energy states.the various energy states.

Stimulated Absorption

In the In the stimulated absorptionstimulated absorption process, process, light may be used to light may be used to stimulate stimulate electronselectrons to higher excited states. to higher excited states. Only certain frequencies will do this.Only certain frequencies will do this.

28.1728.17

Spontaneous Emission

When the electrons When the electrons randomlyrandomly fall back fall back to their original orbits we call this to their original orbits we call this spontaneous emissionspontaneous emission..

286286

Spontaneous Emission

Stimulated Emission

In In stimulated emissionstimulated emission, all of the , all of the electrons can be made to fall back electrons can be made to fall back at at the same timethe same time and thus produce bright, and thus produce bright, coherent light.coherent light. This is the basis for the operation of This is the basis for the operation of

LASERSLASERS..

Stimulated Emission

Lasers

LASERLASER - - LLightight AAmplification bymplification by SStimulatedtimulated EEmission ofmission of RRadiationadiation

Population Inversion

In a laser, electrons are stimulated so In a laser, electrons are stimulated so that there arethat there are more electrons in the more electrons in the excited stateexcited state than in the ground state.than in the ground state. This is called a This is called a population inversionpopulation inversion..

287287

Laser Requirements

There are There are three conditionsthree conditions for laser for laser action to occur.action to occur. A population inversionA population inversion The excited state must be a metastable The excited state must be a metastable

(long lifetime)(long lifetime) state. state. The photons must be confined long The photons must be confined long

enough to stimulate further emissions.enough to stimulate further emissions.

He-Ne Lasers

The operation of a The operation of a He-NeHe-Ne laser laser An oscillator is used to sweep electrons through An oscillator is used to sweep electrons through

a thin glass tube containing a a thin glass tube containing a He-Ne mixtureHe-Ne mixture.. The neon atoms are raised to a The neon atoms are raised to a metastablemetastable state state

by collisions with excited helium atoms.by collisions with excited helium atoms. Electrons simultaneously returning to a lower Electrons simultaneously returning to a lower

energy state emit energy state emit coherent photonscoherent photons of a of a particular wavelength. particular wavelength. (632.8 nm)(632.8 nm)

28.22a, 71, 28828.22a, 71, 288

Laser Frequencies

Frequency ranges of lasersFrequency ranges of lasers InfraredInfrared (CO (CO22)) VisibleVisible ( (redred, , greengreen, , blueblue)) UltravioletUltraviolet

Laser Applications

MedicalMedical ““Welding” detached retinasWelding” detached retinas Laser surgeryLaser surgery Laser vision correction (Lasik)Laser vision correction (Lasik)

Lasik Surgery

An ultra-thin flap is created on the eye's surface An ultra-thin flap is created on the eye's surface during LASIK corrective eye surgery. After laser during LASIK corrective eye surgery. After laser energy is applied to reshape the eye, the flap is energy is applied to reshape the eye, the flap is replaced to serve as a type of natural bandage.replaced to serve as a type of natural bandage.

Surveying and distance measurementSurveying and distance measurement

Cutting and drilling metals in industryCutting and drilling metals in industry

Fiber optic communicationsFiber optic communications

Holography

Used in the production of Used in the production of three-dimensional three-dimensional imagesimages

Interference patternsInterference patterns are placed on film. are placed on film. Used to protect Used to protect credit cardscredit cards

283, 284283, 284

Making Holograms

CDs and DVDs

Information is stored in Information is stored in binarybinary form. form. Pits and land areas (ones and zeros)Pits and land areas (ones and zeros)

The laser beam follows a The laser beam follows a spiral pathspiral path.. A A diffraction gratingdiffraction grating is used to provide is used to provide

tracking.tracking. 40+ second memory40+ second memory for music CDs for music CDs

Infrared Remote Control

A different A different infraredinfrared wavelength is assigned to wavelength is assigned to each number or function.each number or function. TV and stereo remote controls use IR.TV and stereo remote controls use IR. Some computers and calculators use IR. Some computers and calculators use IR. My MAC PowerPoint remote uses RF.My MAC PowerPoint remote uses RF.

Don’t confuse Don’t confuse IRIR with with RFRF controls. controls. MAC Photo Booth DemoMAC Photo Booth Demo

Semiconductor Devices

DopingDoping Donor atomsDonor atoms N-type semiconductorN-type semiconductor Acceptor atomsAcceptor atoms P-type semiconductorsP-type semiconductors

Semiconductor Devices

P-N junctionsP-N junctions DiodesDiodes

Forward biasForward biasReverse biasReverse bias

Half-wave rectifiersHalf-wave rectifiers Full-wave rectifiersFull-wave rectifiers TransistorsTransistors

Transistors

Junction transistorsJunction transistors TypesTypes

npn npn pnppnp

Parts of a transistorParts of a transistorEmitterEmitterBaseBaseCollectorCollector

227227

Semiconductor Devices

Integrated circuitsIntegrated circuits What are they?What are they? Where are they used?Where are they used? What are the advantages of integrated What are the advantages of integrated

circuits?circuits?

Computer Memory

Questions

7, 9 - 11, 157, 9 - 11, 15

Pg. 910Pg. 910