Chapter 28Chapter 28

Atomic PhysicsAtomic Physics

Importance of Hydrogen Importance of Hydrogen AtomAtom

Hydrogen is the simplest atomHydrogen is the simplest atom The quantum numbers used to The quantum numbers used to

characterize the allowed states of characterize the allowed states of hydrogen can also be used to hydrogen can also be used to describe (approximately) the allowed describe (approximately) the allowed states of more complex atomsstates of more complex atoms This enables us to understand the This enables us to understand the

periodic tableperiodic table

More Reasons the More Reasons the Hydrogen Atom is so Hydrogen Atom is so ImportantImportant

The hydrogen atom is an ideal system The hydrogen atom is an ideal system for performing precise comparisons of for performing precise comparisons of theory and experimenttheory and experiment Also for improving our understanding of Also for improving our understanding of

atomic structureatomic structure Much of what we know about the Much of what we know about the

hydrogen atom can be extended to hydrogen atom can be extended to other single-electron ions other single-electron ions For example, HeFor example, He++ and Li and Li2+2+

Early Models of the AtomEarly Models of the Atom

J.J. Thomson’s model J.J. Thomson’s model of the atomof the atom A volume of positive A volume of positive

chargecharge Electrons embedded Electrons embedded

throughout the volumethroughout the volume A change from A change from

Newton’s model of Newton’s model of the atom as a tiny, the atom as a tiny, hard, indestructible hard, indestructible spheresphere

Early Models of the Atom, Early Models of the Atom, 22

RutherfordRutherford Planetary modelPlanetary model Based on results of Based on results of

thin foil thin foil experimentsexperiments

Positive charge is Positive charge is concentrated in the concentrated in the center of the atom, center of the atom, called the called the nucleusnucleus

Electrons orbit the Electrons orbit the nucleus like planets nucleus like planets orbit the sunorbit the sun

Difficulties with the Difficulties with the Rutherford ModelRutherford Model

Atoms emit certain discrete characteristic Atoms emit certain discrete characteristic frequencies of electromagnetic radiationfrequencies of electromagnetic radiation The Rutherford model is unable to explain this The Rutherford model is unable to explain this

phenomenaphenomena Rutherford’s electrons are undergoing a Rutherford’s electrons are undergoing a

centripetal acceleration and so should radiate centripetal acceleration and so should radiate electromagnetic waves of the same frequencyelectromagnetic waves of the same frequency The radius should steadily decrease as this The radius should steadily decrease as this

radiation is given offradiation is given off The electron should eventually spiral into the The electron should eventually spiral into the

nucleusnucleus It doesn’tIt doesn’t

Emission SpectraEmission Spectra

A gas at low pressure has a voltage A gas at low pressure has a voltage applied to itapplied to it

A gas emits light characteristic of the gasA gas emits light characteristic of the gas When the emitted light is analyzed with a When the emitted light is analyzed with a

spectrometer, a series of discrete bright spectrometer, a series of discrete bright lines is observedlines is observed Each line has a different wavelength and colorEach line has a different wavelength and color This series of lines is called an This series of lines is called an emission emission

spectrumspectrum

Examples of SpectraExamples of Spectra

Emission Spectrum of Emission Spectrum of Hydrogen – Equation Hydrogen – Equation

The wavelengths of hydrogen’s spectral The wavelengths of hydrogen’s spectral lines can be found fromlines can be found from

RRHH is the is the Rydberg constantRydberg constant RRHH = 1.0973732 x 10 = 1.0973732 x 1077 m m-1-1

n is an integer, n = 1, 2, 3, …n is an integer, n = 1, 2, 3, … The spectral lines correspond to different The spectral lines correspond to different

values of nvalues of n

22H n

1

2

1R

1

Spectral Lines of HydrogenSpectral Lines of Hydrogen

The Balmer Series The Balmer Series has lines whose has lines whose wavelengths are wavelengths are given by the given by the preceding equationpreceding equation

Examples of Examples of spectral linesspectral lines n = 3, n = 3, λ = 656.3 nmλ = 656.3 nm n = 4, n = 4, λ = 486.1 nmλ = 486.1 nm

Absorption SpectraAbsorption Spectra An element can also absorb light at An element can also absorb light at

specific wavelengthsspecific wavelengths An absorption spectrum can be obtained An absorption spectrum can be obtained

by passing a continuous radiation by passing a continuous radiation spectrum through a vapor of the gasspectrum through a vapor of the gas

The absorption spectrum consists of a The absorption spectrum consists of a series of dark lines superimposed on the series of dark lines superimposed on the otherwise continuous spectrumotherwise continuous spectrum The dark lines of the absorption spectrum The dark lines of the absorption spectrum

coincide with the bright lines of the emission coincide with the bright lines of the emission spectrumspectrum

Applications of Absorption Applications of Absorption SpectrumSpectrum

The continuous spectrum emitted The continuous spectrum emitted by the Sun passes through the by the Sun passes through the cooler gases of the Sun’s cooler gases of the Sun’s atmosphereatmosphere The various absorption lines can be The various absorption lines can be

used to identify elements in the solar used to identify elements in the solar atmosphereatmosphere

Led to the discovery of heliumLed to the discovery of helium

The Bohr Theory of The Bohr Theory of HydrogenHydrogen

In 1913 Bohr provided an In 1913 Bohr provided an explanation of atomic spectra that explanation of atomic spectra that includes some features of the includes some features of the currently accepted theorycurrently accepted theory

His model includes both classical His model includes both classical and non-classical ideasand non-classical ideas

His model included an attempt to His model included an attempt to explain why the atom was stableexplain why the atom was stable

Bohr’s Assumptions for Bohr’s Assumptions for HydrogenHydrogen

The electron The electron moves in circular moves in circular orbits around the orbits around the proton under the proton under the influence of the influence of the Coulomb force of Coulomb force of attractionattraction The Coulomb The Coulomb

force produces the force produces the centripetal centripetal accelerationacceleration

Bohr’s Assumptions, contBohr’s Assumptions, cont

Only certain electron orbits are stableOnly certain electron orbits are stable These are the orbits in which the atom does These are the orbits in which the atom does

not emit energy in the form of not emit energy in the form of electromagnetic radiationelectromagnetic radiation

Therefore, the energy of the atom remains Therefore, the energy of the atom remains constant and classical mechanics can be constant and classical mechanics can be used to describe the electron’s motionused to describe the electron’s motion

Radiation is emitted by the atom when Radiation is emitted by the atom when the electron “jumps” from a more the electron “jumps” from a more energetic initial state to a lower stateenergetic initial state to a lower state The “jump” cannot be treated classicallyThe “jump” cannot be treated classically

Bohr’s Assumptions, finalBohr’s Assumptions, final

The electron’s “jump,” continuedThe electron’s “jump,” continued The frequency emitted in the “jump” is The frequency emitted in the “jump” is

related to the change in the atom’s related to the change in the atom’s energyenergy

It is It is generally not the same as the generally not the same as the frequency of the electron’s orbital motionfrequency of the electron’s orbital motion

The size of the allowed electron orbits The size of the allowed electron orbits is determined by a condition imposed is determined by a condition imposed on the electron’s orbital angular on the electron’s orbital angular momentummomentum

Mathematics of Bohr’s Mathematics of Bohr’s Assumptions and ResultsAssumptions and Results

Electron’s orbital angular Electron’s orbital angular momentummomentum mmee v r = n v r = n ħ where n = 1, 2, 3, …ħ where n = 1, 2, 3, …

The total energy of the atomThe total energy of the atom

The energy can also be expressed The energy can also be expressed asas

r

ekvm

2

1PEKEE

2

e2

e

r2

ekE

2e

Bohr RadiusBohr Radius

The radii of the Bohr orbits are The radii of the Bohr orbits are quantizedquantized

This shows that the This shows that the electron can only electron can only exist in certain allowed orbits exist in certain allowed orbits determined by the integer ndetermined by the integer n

When n = 1, the orbit has the smallest When n = 1, the orbit has the smallest radius, called the radius, called the Bohr radiusBohr radius, a, aoo

aaoo = 0.0529 nm = 0.0529 nm

,3,2,1nekm

nr

2ee

22

n

Radii and Energy of OrbitsRadii and Energy of Orbits

A general A general expression for the expression for the radius of any orbit radius of any orbit in a hydrogen in a hydrogen atom isatom is rrnn = n = n22 a aoo

The energy of any The energy of any orbit isorbit is EEnn = - 13.6 eV/ n = - 13.6 eV/ n22

Specific Energy LevelsSpecific Energy Levels The lowest energy state is called the The lowest energy state is called the ground ground

statestate This corresponds to n = 1This corresponds to n = 1 Energy is –13.6 eVEnergy is –13.6 eV

The next energy level has an energy of –3.40 The next energy level has an energy of –3.40 eVeV The energies can be compiled in an The energies can be compiled in an energy level energy level

diagramdiagram The The ionization energyionization energy is the energy needed to is the energy needed to

completely remove the electron from the atomcompletely remove the electron from the atom The ionization energy for hydrogen is 13.6 eVThe ionization energy for hydrogen is 13.6 eV

Energy Level DiagramEnergy Level Diagram

The value of RThe value of RHH from Bohr’s from Bohr’s analysis is in analysis is in excellent excellent agreement with the agreement with the experimental valueexperimental value

A more generalized A more generalized equation can be equation can be used to find the used to find the wavelengths of any wavelengths of any spectral linesspectral lines

Generalized EquationGeneralized Equation

For the Balmer series, nFor the Balmer series, nf f = 2 = 2

For the Lyman series, nFor the Lyman series, nff = 1 = 1

Whenever an transition occurs between a Whenever an transition occurs between a state, nstate, nii to another state, n to another state, nff (where n (where nii > > nnff), a photon ), a photon is emittedis emitted The photon has a frequency f = (Ei – Ef)/h The photon has a frequency f = (Ei – Ef)/h

and wavelength and wavelength λ λ

2i

2f

H n

1

n

1R

1

Bohr’s Correspondence Bohr’s Correspondence PrinciplePrinciple

Bohr’s Bohr’s Correspondence PrincipleCorrespondence Principle states that quantum mechanics is in states that quantum mechanics is in agreement with classical physics agreement with classical physics when the energy differences when the energy differences between quantized levels are very between quantized levels are very smallsmall Similar to having Newtonian Mechanics Similar to having Newtonian Mechanics

be a special case of relativistic be a special case of relativistic mechanics when v << cmechanics when v << c

Successes of the Bohr Successes of the Bohr TheoryTheory

Explained several features of the hydrogen Explained several features of the hydrogen spectrumspectrum Accounts for Balmer and other seriesAccounts for Balmer and other series Predicts a value for RPredicts a value for RHH that agrees with the experimental that agrees with the experimental

valuevalue Gives an expression for the radius of the atomGives an expression for the radius of the atom Predicts energy levels of hydrogenPredicts energy levels of hydrogen Gives a model of what the atom looks like and how it Gives a model of what the atom looks like and how it

behavesbehaves Can be extended to “hydrogen-like” atomsCan be extended to “hydrogen-like” atoms

Those with one electronThose with one electron ZeZe22 needs to be substituted for e needs to be substituted for e22 in equations in equations

Z is the atomic number of the elementZ is the atomic number of the element

Modifications of the Bohr Modifications of the Bohr Theory – Elliptical OrbitsTheory – Elliptical Orbits

Sommerfeld extended the results to Sommerfeld extended the results to include elliptical orbitsinclude elliptical orbits Retained the Retained the principle quantum numberprinciple quantum number, ,

nn Added the Added the orbital quantum numberorbital quantum number, , ℓℓ

ℓ ℓ ranges from 0 to n-1 in integer stepsranges from 0 to n-1 in integer steps All states with the same principle All states with the same principle

quantum number are said to form a quantum number are said to form a shellshell The states with given values of n and ℓ The states with given values of n and ℓ

are said to form a are said to form a subshellsubshell

Modifications of the Bohr Modifications of the Bohr Theory – Zeeman EffectTheory – Zeeman Effect

Another modification was needed to Another modification was needed to account for the account for the Zeeman effectZeeman effect The Zeeman effect is the splitting of spectral The Zeeman effect is the splitting of spectral

lines in a strong magnetic fieldlines in a strong magnetic field This indicates that the energy of an electron is This indicates that the energy of an electron is

slightly modified when the atom is immersed in slightly modified when the atom is immersed in a magnetic fielda magnetic field

A new quantum number, mA new quantum number, m ℓℓ, called the , called the orbital orbital magnetic quantum numbermagnetic quantum number, had to be , had to be introducedintroduced

m m ℓℓ can vary from - ℓ to + ℓ in integer steps can vary from - ℓ to + ℓ in integer steps

Modifications of the Bohr Modifications of the Bohr Theory – Fine StructureTheory – Fine Structure

High resolution spectrometers show High resolution spectrometers show that spectral lines are, in fact, two that spectral lines are, in fact, two very closely spaced lines, even in very closely spaced lines, even in the absence of a magnetic fieldthe absence of a magnetic field This splitting is called This splitting is called fine structurefine structure Another quantum number, mAnother quantum number, mss, called , called

the the spin magnetic quantum number,spin magnetic quantum number, was introduced to explain the fine was introduced to explain the fine structurestructure

de Broglie Wavesde Broglie Waves

One of Bohr’s postulates was the One of Bohr’s postulates was the angular momentum of the electron is angular momentum of the electron is quantized, but there was no quantized, but there was no explanation why the restriction explanation why the restriction occurredoccurred

de Broglie assumed that the electron de Broglie assumed that the electron orbit would be stable only if it orbit would be stable only if it contained an integral number of contained an integral number of electron wavelengthselectron wavelengths

de Broglie Waves in the de Broglie Waves in the Hydrogen AtomHydrogen Atom

In this example, three In this example, three complete wavelengths complete wavelengths are contained in the are contained in the circumference of the circumference of the orbitorbit

In general, the In general, the circumference must circumference must equal some integer equal some integer number of number of wavelengthswavelengths 2 2 r = n r = n λ n = 1, 2, …λ n = 1, 2, …

de Broglie Waves in the de Broglie Waves in the Hydrogen Atom, contHydrogen Atom, cont

The expression for the de Broglie wavelength The expression for the de Broglie wavelength can be included in the circumference can be included in the circumference calculationcalculation mmee v r = n v r = n This is the same quantization of angular momentum This is the same quantization of angular momentum

that Bohr imposed in his original theorythat Bohr imposed in his original theory This was the first convincing argument that This was the first convincing argument that

the wave nature of matter was at the heart of the wave nature of matter was at the heart of the behavior of atomic systemsthe behavior of atomic systems

SchrSchrödinger’s wave equation was ödinger’s wave equation was subsequently applied to atomic systemssubsequently applied to atomic systems

QUICK QUIZ 28.1In an analysis relating Bohr's theory to the de Broglie wavelength of electrons, when an electron moves from the n = 1 level to the n = 3 level, the circumference of its orbit becomes 9 times greater. This occurs because (a) there are 3 times as many wavelengths in the new orbit, (b) there are 3 times as many wavelengths and each wavelength is 3 times as long, (c) the wavelength of the electron becomes 9 times as long, or (d) the electron is moving 9 times as fast.

QUICK QUIZ 28.1 ANSWER

(b). The circumference of the orbit is n times the de Broglie wavelength (2πr = nλ), so there are three times as many wavelengths in the n = 3 level as in the n = 1 level. Also, by combining Equations 28.4, 28.6 and the defining equation for the de Broglie wavelength (λ = h/mv), one can show that the wavelength in the n = 3 level is three times as long.

Quantum Mechanics and Quantum Mechanics and the Hydrogen Atomthe Hydrogen Atom

One of the first great achievements of One of the first great achievements of quantum mechanics was the solution of quantum mechanics was the solution of the wave equation for the hydrogen atomthe wave equation for the hydrogen atom

The significance of quantum mechanics is The significance of quantum mechanics is that the quantum numbers and the that the quantum numbers and the restrictions placed on their values arise restrictions placed on their values arise directly from the mathematics and not directly from the mathematics and not from any assumptions made to make the from any assumptions made to make the theory agree with experimentstheory agree with experiments

Quantum Number Quantum Number SummarySummary

The values of n can range from 1 The values of n can range from 1 to to in integer steps in integer steps

The values of The values of ℓ can range from 0 to ℓ can range from 0 to n-1 in integer stepsn-1 in integer steps

The values of The values of mm ℓℓ can range from -ℓ can range from -ℓ to ℓ in integer stepsto ℓ in integer steps Also see Table 28.2Also see Table 28.2

QUICK QUIZ 28.2

How many possible orbital states are there for (a) the n = 3 level of hydrogen? (b) the n = 4 level?

QUICK QUIZ 28.2 ANSWER

The quantum numbers associated with orbital states are n, , and m . For a specified value of n, the allowed values of range from 0 to n – 1. For each value of , there are (2 + 1) possible values of m.

(a) If n = 3, then = 0, 1, or 2. The number of possible orbital states is then [2(0) + 1] + [2(1) + 1] + [2(2) + 1] = 1 + 3 + 5 = 9.

(b) If n = 4, one additional value of is allowed ( = 3) so the number of possible orbital states is now 9 + [2(3) + 1] = 9 + 7 = 16

QUICK QUIZ 28.3

When the principal quantum number is n = 5, how many different values of (a) and (b) m are possible?

QUICK QUIZ 28.3 ANSWER(a) For n = 5, there are 5 allowed

values of , namely = 0, 1, 2, 3, and 4.

(b) Since m ranges from – to + in integer steps, the largest allowed value of ( = 4 in this case) permits the greatest range of values for m. For n = 5, there are 9 possible values for m: -4, -3, -2, –1, 0, +1, +2, +3, and +4.

Spin Magnetic Quantum Spin Magnetic Quantum NumberNumber

It is convenient to think It is convenient to think of the electron as of the electron as spinning on its axisspinning on its axis The electron is The electron is notnot

physically spinningphysically spinning There are two directions There are two directions

for the spinfor the spin Spin up, mSpin up, mss = = ½½ Spin down, mSpin down, mss = - = -½½

There is a slight energy There is a slight energy difference between the difference between the two spins and this two spins and this accounts for the Zeeman accounts for the Zeeman effecteffect

Electron CloudsElectron Clouds The graph shows the The graph shows the

solution to the wave solution to the wave equation for hydrogen equation for hydrogen in the ground statein the ground state The curve peaks at the The curve peaks at the

Bohr radiusBohr radius The electron is not The electron is not

confined to a particular confined to a particular orbital distance from the orbital distance from the nucleusnucleus

The The probabilityprobability of of finding the electron at finding the electron at the Bohr radius is a the Bohr radius is a maximummaximum

Electron Clouds, contElectron Clouds, cont The wave function for The wave function for

hydrogen in the ground hydrogen in the ground state is symmetricstate is symmetric The electron can be The electron can be

found in a spherical found in a spherical region surrounding the region surrounding the nucleusnucleus

The result is interpreted The result is interpreted by viewing the electron by viewing the electron as a cloud surrounding as a cloud surrounding the nucleusthe nucleus The densest regions of The densest regions of

the cloud represent the the cloud represent the highest probability for highest probability for finding the electronfinding the electron

The Pauli Exclusion The Pauli Exclusion PrinciplePrinciple

No two electrons in an atom can No two electrons in an atom can ever be in the same quantum stateever be in the same quantum state In other words, no two electrons in In other words, no two electrons in

the same atom can have exactly the the same atom can have exactly the same values for n, same values for n, ℓ, ℓ, mm ℓℓ, and m, and mss

This explains the electronic This explains the electronic structure of complex atoms as a structure of complex atoms as a succession of filled energy levels succession of filled energy levels with different quantum numberswith different quantum numbers

The Periodic TableThe Periodic Table

The outermost electrons are primarily The outermost electrons are primarily responsible for the chemical properties of responsible for the chemical properties of the atomthe atom

Mendeleev arranged the elements Mendeleev arranged the elements according to their atomic masses and according to their atomic masses and chemical similaritieschemical similarities

The electronic configuration of the The electronic configuration of the elements explained by quantum numbers elements explained by quantum numbers and Pauli’s Exclusion Principle explains the and Pauli’s Exclusion Principle explains the configurationconfiguration

QUICK QUIZ 28.4

Krypton (atomic number 36) has how many electrons in its next to outer shell (n = 3)?

(a) 2 (b) 4(c) 8 (d) 18

QUICK QUIZ 28.4 ANSWER

(d). Krypton has a closed configuration consisting of filled n=1, n=2, and n=3 shells as well as filled 4s and 4p subshells. The filled n=3 shell (the next to outer shell in Krypton) has a total of 18 electrons, 2 in the 3s subshell, 6 in the 3p subshell and 10 in the 3d subshell.

Characteristic X-RaysCharacteristic X-Rays When a metal target When a metal target

is bombarded by high-is bombarded by high-energy electrons, x-energy electrons, x-rays are emittedrays are emitted

The x-ray spectrum The x-ray spectrum typically consists of a typically consists of a broad continuous broad continuous spectrum and a series spectrum and a series of sharp linesof sharp lines The lines are The lines are

dependent on the metaldependent on the metal The lines are called The lines are called

characteristic x-rayscharacteristic x-rays

Explanation of Explanation of Characteristic X-RaysCharacteristic X-Rays

The details of atomic structure can be used The details of atomic structure can be used to explain characteristic x-raysto explain characteristic x-rays A bombarding electron collides with an electron A bombarding electron collides with an electron

in the target metal that is in an inner shellin the target metal that is in an inner shell If there is sufficient energy, the electron is If there is sufficient energy, the electron is

removed from the target atomremoved from the target atom The vacancy created by the lost electron is filled The vacancy created by the lost electron is filled

by an electron falling to the vacancy from a by an electron falling to the vacancy from a higher energy levelhigher energy level

The transition is accompanied by the emission The transition is accompanied by the emission of a photon whose energy is equal to the of a photon whose energy is equal to the difference between the two levelsdifference between the two levels

Moseley PlotMoseley Plot λ is the wavelength of the λ is the wavelength of the

KK line line KK is the line that is is the line that is

produced by an electron produced by an electron falling from the L shell to falling from the L shell to the K shellthe K shell

From this plot, Moseley From this plot, Moseley was able to determine was able to determine the Z values of other the Z values of other elements and produce a elements and produce a periodic chart in excellent periodic chart in excellent agreement with the agreement with the known chemical known chemical properties of the properties of the elementselements

Atomic Transitions – Atomic Transitions – Energy LevelsEnergy Levels

An atom may have An atom may have many possible energy many possible energy levelslevels

At ordinary At ordinary temperatures, most of temperatures, most of the atoms in a sample the atoms in a sample are in the ground stateare in the ground state

Only photons with Only photons with energies energies corresponding to corresponding to differences between differences between energy levels can be energy levels can be absorbedabsorbed

Atomic Transitions – Atomic Transitions – Stimulated AbsorptionStimulated Absorption

The blue dots The blue dots represent electronsrepresent electrons

When a photon with When a photon with energy energy ΔE is ΔE is absorbed, one absorbed, one electron jumps to a electron jumps to a higher energy levelhigher energy level These higher levels are These higher levels are

called called excited statesexcited states ΔE = hƒ = EΔE = hƒ = E22 – E – E11

In general, ΔE can be In general, ΔE can be the difference between the difference between any two energy levelsany two energy levels

Atomic Transitions – Atomic Transitions – Spontaneous EmissionSpontaneous Emission

Once an atom is in Once an atom is in an excited state, an excited state, there is a constant there is a constant probability that it probability that it will jump back to a will jump back to a lower state by lower state by emitting a photonemitting a photon

This process is This process is called called spontaneous spontaneous emissionemission

Atomic Transitions – Atomic Transitions – Stimulated EmissionStimulated Emission

An atom is in an excited An atom is in an excited stated and a photon is stated and a photon is incident on itincident on it

The incoming photon The incoming photon increases the probability increases the probability that the excited atom that the excited atom will return to the ground will return to the ground statestate

There are two emitted There are two emitted photons, the incident photons, the incident one and the emitted oneone and the emitted one The emitted photon is in The emitted photon is in

exactly in phase with exactly in phase with the incident photonthe incident photon

Population InversionPopulation Inversion

When light is incident on a system of When light is incident on a system of atoms, both stimulated absorption and atoms, both stimulated absorption and stimulated emission are equally probablestimulated emission are equally probable

Generally, a net absorption occurs since Generally, a net absorption occurs since most atoms are in the ground statemost atoms are in the ground state

If you can cause more atoms to be in If you can cause more atoms to be in excited states, a net emission of photons excited states, a net emission of photons can resultcan result This situation is called a This situation is called a population inversionpopulation inversion

LasersLasers To achieve laser action, three conditions To achieve laser action, three conditions

must be metmust be met The system must be in a state of population The system must be in a state of population

inversioninversion The excited state of the system must be a The excited state of the system must be a

metastable statemetastable state Its lifetime must be long compared to the normal Its lifetime must be long compared to the normal

lifetime of an excited statelifetime of an excited state The emitted photons must be confined in the The emitted photons must be confined in the

system long enough to allow them to stimulate system long enough to allow them to stimulate further emission from other excited atomsfurther emission from other excited atoms

This is achieved by using reflecting mirrorsThis is achieved by using reflecting mirrors

Production of a Laser Production of a Laser BeamBeam

Laser Beam – He Ne Laser Beam – He Ne ExampleExample

The energy level diagram The energy level diagram for Nefor Ne

The mixture of helium and The mixture of helium and neon is confined to a neon is confined to a glass tube sealed at the glass tube sealed at the ends by mirrorsends by mirrors

A high voltage applied A high voltage applied causes electrons to sweep causes electrons to sweep through the tube, through the tube, producing excited statesproducing excited states

When the electron falls to When the electron falls to EE22 in Ne, a 632.8 nm in Ne, a 632.8 nm photon is emittedphoton is emitted

HolographyHolography Holography is the Holography is the

production of three-production of three-dimensional images of dimensional images of an objectan object

Light from a laser is Light from a laser is split at Bsplit at B

One beam reflects off One beam reflects off the object and onto a the object and onto a photographic platephotographic plate

The other beam is The other beam is diverged by Lens 2 and diverged by Lens 2 and reflected by the mirrors reflected by the mirrors before striking the filmbefore striking the film

Holography, contHolography, cont The two beams form a complex The two beams form a complex

interference pattern on the photographic interference pattern on the photographic filmfilm It can be produced only if the phase It can be produced only if the phase

relationship of the two waves remains constantrelationship of the two waves remains constant This is accomplished by using a laserThis is accomplished by using a laser

The hologram records the intensity of the The hologram records the intensity of the light and the phase difference between the light and the phase difference between the reference beam and the scattered beamreference beam and the scattered beam

The image formed has a three-dimensional The image formed has a three-dimensional perspectiveperspective

Energy Bands in SolidsEnergy Bands in Solids

In solids, the discrete energy levels In solids, the discrete energy levels of isolated atoms broaden into of isolated atoms broaden into allowed energy bands separated allowed energy bands separated by forbidden gapsby forbidden gaps

The separation and the electron The separation and the electron population of the highest bands population of the highest bands determine whether the solid is a determine whether the solid is a conductor, an insulator, or a conductor, an insulator, or a semiconductorsemiconductor

Energy Bands, DetailEnergy Bands, Detail Sodium exampleSodium example Blue represents energy bands Blue represents energy bands

occupied by the sodium occupied by the sodium electrons when the atoms are electrons when the atoms are in their ground statesin their ground states

Gold represents energy bands Gold represents energy bands that are emptythat are empty

White represents energy gapsWhite represents energy gaps Electrons can have any energy Electrons can have any energy

within the allowed bandswithin the allowed bands Electrons cannot have energies Electrons cannot have energies

in the gapsin the gaps

Energy Level DefinitionsEnergy Level Definitions

The The valence bandvalence band is the highest is the highest filled bandfilled band

The The conduction bandconduction band is the next is the next higher empty bandhigher empty band

The energy gap has an energy, EThe energy gap has an energy, Egg, , equal to the difference in energy equal to the difference in energy between the top of the valence between the top of the valence band and the bottom of the band and the bottom of the conduction bandconduction band

ConductorsConductors When a voltage is applied When a voltage is applied

to a conductor, the to a conductor, the electrons accelerate and electrons accelerate and gain energygain energy

In quantum terms, In quantum terms, electron energies electron energies increase if there are a increase if there are a high number of high number of unoccupied energy levels unoccupied energy levels for the electron to jump tofor the electron to jump to

For example, it takes very For example, it takes very little energy for electrons little energy for electrons to jump from the partially to jump from the partially filled to one of the nearby filled to one of the nearby empty statesempty states

InsulatorsInsulators The valence band is The valence band is

completely full of completely full of electronselectrons

A large band gap A large band gap separates the valence separates the valence and conduction bandsand conduction bands

A large amount of A large amount of energy is needed for an energy is needed for an electron to be able to electron to be able to jump from the valence jump from the valence to the conduction bandto the conduction band The minimum required The minimum required

energy is Eenergy is Egg

SemiconductorsSemiconductors A semiconductor has a A semiconductor has a

small energy gapsmall energy gap Thermally excited Thermally excited

electrons have enough electrons have enough energy to cross the band energy to cross the band gapgap

The resistivity of The resistivity of semiconductors semiconductors decreases with increases decreases with increases in temperaturein temperature

The white area in the The white area in the valence band represents valence band represents holesholes

Semiconductors, contSemiconductors, cont HolesHoles are empty states in the valence band are empty states in the valence band

created by electrons that have jumped to created by electrons that have jumped to the conduction bandthe conduction band

Some electrons in the valence band move to Some electrons in the valence band move to fill the holes and therefore also carry currentfill the holes and therefore also carry current

The valence electrons that fill the holes The valence electrons that fill the holes leave behind other holesleave behind other holes It is common to view the conduction process in It is common to view the conduction process in

the valence band as a flow of positive holes the valence band as a flow of positive holes toward the negative electrode applied to the toward the negative electrode applied to the semiconductorsemiconductor

Current Process in Current Process in SemiconductorsSemiconductors

An external voltage is An external voltage is suppliedsupplied

Electrons move Electrons move toward the positive toward the positive electrodeelectrode

Holes move toward Holes move toward the negative the negative electrodeelectrode

There is a There is a symmetrical current symmetrical current process in a process in a semiconductorsemiconductor

Doping in SemiconductorsDoping in Semiconductors

DopingDoping is the adding of impurities is the adding of impurities to a semiconductorto a semiconductor Generally about 1 impurity atom per Generally about 1 impurity atom per

101077 semiconductor atoms semiconductor atoms Doping results in both the band Doping results in both the band

structure and the resistivity being structure and the resistivity being changedchanged

n-type Semiconductorsn-type Semiconductors

Donor atomsDonor atoms are doping materials that are doping materials that contain one more electron than the contain one more electron than the semiconductor materialsemiconductor material This creates an essentially free electron This creates an essentially free electron

with an energy level in the energy gap, with an energy level in the energy gap, just below the conduction bandjust below the conduction band

Only a small amount of thermal Only a small amount of thermal energy is needed to cause this energy is needed to cause this electron to move into the conduction electron to move into the conduction bandband

p-type Semiconductorsp-type Semiconductors Acceptor atomsAcceptor atoms are doping materials that are doping materials that

contain one less electron than the contain one less electron than the semiconductor materialsemiconductor material A hole is left where the missing electron would A hole is left where the missing electron would

bebe The energy level of the hole lies in the The energy level of the hole lies in the

energy gap, just above the valence bandenergy gap, just above the valence band An electron from the valence band has An electron from the valence band has

enough thermal energy to fill this impurity enough thermal energy to fill this impurity level, leaving behind a hole in the valence level, leaving behind a hole in the valence bandband

A p-n JunctionA p-n Junction

A p-n junction is A p-n junction is formed when a p-formed when a p-type semiconductor type semiconductor is joined to an n-typeis joined to an n-type

Three distinct Three distinct regions existregions exist A p regionA p region An n regionAn n region A depletion regionA depletion region

The Depletion RegionThe Depletion Region Mobile donor electrons from the n side Mobile donor electrons from the n side

nearest the junction diffuse to the p side, nearest the junction diffuse to the p side, leaving behind immobile positive ionsleaving behind immobile positive ions

At the same time, holes from the p side At the same time, holes from the p side nearest the junction diffuse to the n side and nearest the junction diffuse to the n side and leave behind a region of fixed negative ionsleave behind a region of fixed negative ions

The resulting The resulting depletion regiondepletion region is depleted of is depleted of mobile charge carriersmobile charge carriers There is also an electric field in this region that There is also an electric field in this region that

sweeps out mobile charge carriers to keep the sweeps out mobile charge carriers to keep the region truly depletedregion truly depleted

Diode ActionDiode Action The p-n junction has the The p-n junction has the

ability to pass current in ability to pass current in only one directiononly one direction

When the p-side is When the p-side is connected to a positive connected to a positive terminal, the device is terminal, the device is forward biasedforward biased and and current flowscurrent flows

When the n-side is When the n-side is connected to the positive connected to the positive terminal, the device is terminal, the device is reverse biasedreverse biased and a and a very small reverse very small reverse current resultscurrent results

Applications of Applications of Semiconductor DiodesSemiconductor Diodes

RectifiersRectifiers Change AC voltage to DC voltageChange AC voltage to DC voltage A A half-wave rectifierhalf-wave rectifier allows current to flow during allows current to flow during

half the AC cyclehalf the AC cycle A A full-wave rectifierfull-wave rectifier rectifies both halves of the AC rectifies both halves of the AC

cyclecycle TransistorsTransistors

May be used to amplify small signalsMay be used to amplify small signals Integrated circuitIntegrated circuit

A collection of interconnected transistors, diodes, A collection of interconnected transistors, diodes, resistors and capacitors fabricated on a single piece resistors and capacitors fabricated on a single piece of siliconof silicon