1 quantum mechanics chapters 4 & 5. 2 way way back in time... greek philosopher democritus (460-...

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Quantum MechanicsQuantum Mechanics

Chapters 4 & 5Chapters 4 & 5

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WAY WAY BACK IN WAY WAY BACK IN TIME... TIME...

Greek philosopher Greek philosopher Democritus (460-Democritus (460-370 BCE.) 370 BCE.)

substances that substances that comprised nature comprised nature – empty spaceempty space – tiny particlestiny particles

““atoms”atoms”

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Democritus Democritus

different kinds of atoms existed different kinds of atoms existed not able to be broken down by not able to be broken down by

ordinary means ordinary means

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Aristotle Aristotle

More popular More popular a contemporary of Democritus a contemporary of Democritus matter was a continuous matter was a continuous

substance which he called "hyle“substance which he called "hyle“ this idea was accepted without this idea was accepted without

support for nearly two thousand support for nearly two thousand years.years.

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pseudo- science pseudo- science

explained natural phenomena in explained natural phenomena in philosophical ways philosophical ways – without experimentation without experimentation – without logicwithout logic

maggots come from rotting meat maggots come from rotting meat frogs cause warts frogs cause warts

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Isaac Newton, Robert Isaac Newton, Robert Boyle and John Dalton Boyle and John Dalton Questioned natural occurrences Questioned natural occurrences conducted experiments conducted experiments

– controlled variables controlled variables made observations made observations collected data collected data data and observations used to data and observations used to

support hypothesessupport hypotheses

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John Dalton John Dalton

matter is particulate in nature matter is particulate in nature atoms of a single element are atoms of a single element are

identicalidentical atoms of different elements are atoms of different elements are

different from each otherdifferent from each other Dalton's hypothesis explained the Dalton's hypothesis explained the

observationsobservations first modern atomic theoryfirst modern atomic theory

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J.J. ThomsonJ.J. Thomson

Are atoms really the smallest Are atoms really the smallest particles?particles?

Cathode ray tubes Cathode ray tubes Rays originated at the cathode Rays originated at the cathode

(negative electrode) and traveled (negative electrode) and traveled toward the anode (positive electrode). toward the anode (positive electrode).

Produced rays composed of negatively Produced rays composed of negatively charged subatomic particles charged subatomic particles – he called particles electrons (he called particles electrons (ee-). -). – mathematically calculated the electron's mathematically calculated the electron's

mass to charge ratio mass to charge ratio

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Oil Drop ExperimentOil Drop Experiment

Robert Millikan Robert Millikan determined the charge of a single determined the charge of a single

electron (-1) electron (-1) Oil Drop ExperimentOil Drop Experiment

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Thomson AtomThomson Atom

Plum Pudding ModelPlum Pudding Model

ElectronsElectrons

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Atomic ResearchAtomic Research

Ernest Rutherford Ernest Rutherford – Niels BohrNiels Bohr– Hans GeigerHans Geiger– Ernest MarsdenErnest Marsden

Experiment to study structure of Experiment to study structure of atomatom– Gold Foil ExperimentGold Foil Experiment

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Gold Foil ExperimentGold Foil Experiment Ernest Rutherford Ernest Rutherford

positively charged helium nuclei (alpha () particles) positively charged helium nuclei (alpha () particles) propelled at high speed toward a thin sheet (tissue propelled at high speed toward a thin sheet (tissue paper-like) of gold foil surrounded by a fluorescent paper-like) of gold foil surrounded by a fluorescent screenscreen

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Experimental Results:Experimental Results:

1. Most of particles pass straight 1. Most of particles pass straight through foilthrough foil

2. Some particles are slightly 2. Some particles are slightly deflecteddeflected

3. A few particles (1 per 8000) 3. A few particles (1 per 8000) are deflected greatly. Nearly are deflected greatly. Nearly bounce back to origin.bounce back to origin.

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Conclusions based on Conclusions based on experimental data:experimental data: 1. The atom is 1. The atom is mostly space.mostly space.

2. 2. Mild deflectionMild deflection was caused by was caused by repulsion of similarrepulsion of similar electrostatic electrostatic chargecharge. Therefore, the atom has a . Therefore, the atom has a positive region. 'Protons“positive region. 'Protons“

3. The 3. The positive corepositive core is is very smallvery small (1 (1 x 10x 10-12-12 of total atomic volume) and of total atomic volume) and contains contains most of the atom's most of the atom's massmass. . 'Nucleus''Nucleus'

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Rutherford AtomRutherford Atom

The Atom is mostly empty The Atom is mostly empty space…..space…..

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Eugene Goldstein Eugene Goldstein

showed that protons created rays in a showed that protons created rays in a cathode ray tube just as the electrons cathode ray tube just as the electrons had donehad done

traveled in the opposite direction. traveled in the opposite direction. (anode to cathode) (anode to cathode)

concluded that a proton is equal but concluded that a proton is equal but opposite in charge to the electron, or opposite in charge to the electron, or 1+, and approximately 1836 times 1+, and approximately 1836 times more massive more massive

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Thomson's observation Thomson's observation

Atoms that areAtoms that are– chemically identical can have chemically identical can have

variable massvariable mass

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James Chadwick James Chadwick

credited with the discovery of the credited with the discovery of the neutral subatomic particle - the neutral subatomic particle - the neutronneutron

Walter Bothe obtained initial evidence Walter Bothe obtained initial evidence nearly two years before Chadwick's nearly two years before Chadwick's experiments experiments

Neutrons have a mass nearly identical Neutrons have a mass nearly identical to that of the proton, but no electrical to that of the proton, but no electrical charge. charge.

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Explanation lies with Explanation lies with the neutrons the neutrons

IsotopesIsotopes– Atoms of the same element containing Atoms of the same element containing

different numbers of neutrons.different numbers of neutrons. NuclideNuclide

– a particular isotope a particular isotope Each isotope acts the same in Each isotope acts the same in

chemical reactionchemical reaction Each nuclide will produce a product of Each nuclide will produce a product of

different mass. different mass.

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Hydrogen isotopesHydrogen isotopes

Proton + Neutron Electron -

Protium 1 proton, 1 electron

Deuterium 1 proton, 1 electron, 1 neutron

Tritium 1 proton, 1 electron, 2 neutrons

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TO SUMMARIZE... TO SUMMARIZE...

The atom is the smallest particle of The atom is the smallest particle of matter that cannot be chemically matter that cannot be chemically subdivided. subdivided.

Composed of two Composed of two regionsregions and three and three primary primary subatomic particlessubatomic particles. . – Nucleus Nucleus

very small very small positively chargedpositively charged dense. dense.

– Protons Protons – NeutronsNeutrons

Electron Cloud Electron Cloud – ElectronsElectrons

orbit the nucleus. orbit the nucleus. Small point-like negative chargesSmall point-like negative charges

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IN PERFECT BALANCE IN PERFECT BALANCE

The atom is electrically neutralThe atom is electrically neutral contain equal number of:contain equal number of:

– protons (positive charges) and protons (positive charges) and – electrons (negative charges).electrons (negative charges).

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Remind you of Remind you of anything?anything?

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Niels BohrNiels Bohr

1913 1913

Introduced ‘Planetary Model’Introduced ‘Planetary Model’

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Planetary ModelPlanetary Model

Gravity and InertiaGravity and Inertia

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Solar SystemSolar System AtomAtom

Attractive force:Attractive force:– GravityGravity– Pulls planet Pulls planet

toward suntoward sun Repulsive force:Repulsive force:

– InertiaInertia– Pushes planet in Pushes planet in

a straight line a straight line away from sunaway from sun

Attractive force:Attractive force:+ / - charges+ / - charges– + nucleus pulls + nucleus pulls

– electrons – electrons toward ittoward it

Repulsive force:Repulsive force:

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It Ought to Go SPLAT!It Ought to Go SPLAT!

“A charged particle constrained to move in curved path … radiates energy according to Maxwell equations.”

Some basic principles of synchrotron radiation.(document prepared by Antonio Juarez-Reyes, AMLM group, 2001)

Electrons – constant orbit Energy drain

and the atom goes SPLAT!SPLAT!

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Electromagnetic Electromagnetic RadiationRadiation

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Electromagnetic Electromagnetic RadiationRadiation c = 3.0 X 10c = 3.0 X 108 8 m/sm/s

Wavelength = λ Frequency = f (υ)

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Electromagnetic Electromagnetic RadiationRadiation Louis de Louis de

BroglieBroglie Dual Nature Dual Nature

ofof LightLight

Wave NatureWave Nature– Travels through space Travels through space

in wavesin waves– Travels at speed of Travels at speed of

light (c)light (c)

Particle NatureParticle Nature– Interacts with matter Interacts with matter

as a particleas a particle– Quanta (unit of Quanta (unit of

energy) transferred energy) transferred to matter in packets to matter in packets of light (photons)of light (photons)

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Light Light →→

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Light Light → → ExcitedExcited atomic atomic

statestate

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ee-- jumps to jumps to

Higher EnergyHigher Energy

levellevel

Light → Light → ExcitedExcited atomic atomic

statestate

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ee-- jumps to jumps to e- jumps to

Higher EnergyHigher Energy Lower EnergyLower Energy

levellevel levellevel

Light → Light → ExcitedExcited atomic atomic →→→→→→→→→→→→

statestate

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ee-- jumps to jumps to e- jumps to



Light → Light → ExcitedExcited atomic atomic →→→→→→→→→→→→

statestate

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Electromagnetic Electromagnetic RadiationRadiation ee-- jumps to jumps to e- jumps to



Light Light →→ExcitedExcited atomic atomic →→→→→→ Atom in Ground State→→→→→→ Atom in Ground State

statestate

photon releasedphoton released

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Electromagnetic Electromagnetic RadiationRadiation ee-- jumps to jumps to e- jumps to



Light Light →→ExcitedExcited atomic atomic →→→→→→ Atom in Ground State→→→→→→ Atom in Ground State

statestate

photon releasedphoton released

Bright-line SpectrumBright-line Spectrum

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Electromagnetic Electromagnetic RadiationRadiation Speed of waveSpeed of wave

c=fc=fλλ solving for frequencysolving for frequency

cc=f =f

λλ

cc==

λλ

ch=ch=

E=

Energy of photon Energy of photon

E=hfE=hfsolving for frequencysolving for frequency

EE=f=f

hh

EE

hh

EEλλ

chch

λλ

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Electromagnetic Electromagnetic RadiationRadiation Irwin SchrodingerIrwin Schrodinger Developed the ‘Wave Developed the ‘Wave

Equation’ Equation’ to support de Broglie’s idea to support de Broglie’s idea

of the dual nature of lightof the dual nature of light

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Quantum LeapQuantum Leap

Bohr’s Planetary Model is used to Bohr’s Planetary Model is used to explain the spectral lines explain the spectral lines produced by atoms.produced by atoms.

Quantum leap animationQuantum leap animation

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Quantum LeapQuantum Leap

TheThe color color of light indicates its of light indicates its wavelengthwavelength

A particular wavelength has a A particular wavelength has a definite definite frequencyfrequency

A particular wavelength has a A particular wavelength has a definite definite amount ofamount of energyenergy

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Riding the Wave Riding the Wave (Equation(Equation))

The Wave Equation The Wave Equation – confirmed Bohr’s theory of confirmed Bohr’s theory of

quantized energy levels.quantized energy levels. Treating electrons as waves, Treating electrons as waves,

explains why the tiny negative explains why the tiny negative electrons are not drawn into the electrons are not drawn into the more massive and positive more massive and positive nucleusnucleus

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Riding the WaveRiding the Wave

“A charged particle constrained to move in curved path … radiates energy according to Maxwell equations.”

Some basic principles of synchrotron radiation.(document prepared by Antonio Juarez-Reyes, AMLM group, 2001)

As the e- approach the As the e- approach the nucleus, their wavelengths nucleus, their wavelengths become shorter.become shorter. E = E = chch λλ

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Solar SystemSolar System AtomAtom

Attractive force:Attractive force:– GravityGravity– Pulls planet Pulls planet

toward suntoward sun

Repulsive force:Repulsive force:– InertiaInertia– Pushes planet in Pushes planet in

a straight line a straight line away from sunaway from sun

Attractive force:Attractive force:+ / - charges+ / - charges– + nucleus pulls + nucleus pulls

– electrons – electrons toward ittoward it

Repulsive force:Repulsive force:– Energy produced Energy produced

form the shorter form the shorter λλ pushes the e pushes the e-- away from the away from the nucleusnucleus

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QUANTUM MECHANICSQUANTUM MECHANICS

Electrons do not obey the laws of Electrons do not obey the laws of classical or Newtonian physicsclassical or Newtonian physics

A new science to describe the A new science to describe the laws of small particles was laws of small particles was established established

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LOOK! IT ISN'T THERE!LOOK! IT ISN'T THERE!Uncertainty principleNot possible to locate an electron's exact position Position and momentum cannot be determined at the same time

to determine one you effect a change in the other

Electrons - only "seen” when they jump from a higher to lower energy level.

once electron is "seen," its direction and speed are different from what they were prior to observation.

Determining position changes its momentum. Applies to electron when it is considered a particle

Werner Heisenberg

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WAVE REVIEWS!WAVE REVIEWS!

Irwin SchrodingerIrwin Schrodinger Wave equation Wave equation

– helps locate probable regions of helps locate probable regions of electron population if considered it electron population if considered it to be like a wave. to be like a wave.

– general paths of the electrons general paths of the electrons around the nucleus can be around the nucleus can be determineddetermined

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MAP IT OUT!MAP IT OUT!

Electrons may be described by a set of four quantum numbers which serve as 3-D for electron location.

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D.C. Map ActivityD.C. Map Activity

FindFind– Union StationUnion Station– Nat’l Air & Space Nat’l Air & Space

MuseumMuseum– Watergate ComplexWatergate Complex– CapitolCapitol– Ford’s TheaterFord’s Theater– White HouseWhite House– Lincoln MemorialLincoln Memorial– Kennedy CenterKennedy Center

A-B 5A-B 5++

C-D 4C-D 4

A-B 0A-B 0 C 5C 5 B 3-4B 3-4 B 2B 2 C 1C 1 B 0B 0

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The Quantum NumbersThe Quantum Numbers principle quantum number (n)principle quantum number (n)

– n = 1, 2, 3...n = 1, 2, 3...– Distance of electron from nucleus.Distance of electron from nucleus.

– Electrons exist ONLY in the energy levels. Electrons exist ONLY in the energy levels. – No electrons have energies to exist between energy levels No electrons have energies to exist between energy levels

[nodes].[nodes]. aangular momentumngular momentum ( (azimuthal) quantum number (l)azimuthal) quantum number (l)

– l = s, p, d, fl = s, p, d, f– Shape of paths, subshells, sublevels, Shape of paths, subshells, sublevels,

magnetic quantum number (m)magnetic quantum number (m)– m = 1, 3, 5, 7m = 1, 3, 5, 7– Spatial orientation to x, y, z axesSpatial orientation to x, y, z axes

spin quantum number (s)spin quantum number (s)– s = clockwise, counterclockwises = clockwise, counterclockwise– Electron spinElectron spin

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FIRST PRINCIPLE of FIRST PRINCIPLE of QUANTUM MECHANICSQUANTUM MECHANICS Only specific energy levels are Only specific energy levels are

possible for electrons. possible for electrons. The principle quantum number that The principle quantum number that

corresponds to the energy levels corresponds to the energy levels begins with 1, 2, 3, etc. beginning with begins with 1, 2, 3, etc. beginning with the level closest to the nucleus the level closest to the nucleus – K energy level is 1K energy level is 1– L energy level is 2L energy level is 2– M energy level is 3M energy level is 3– N energy level is 4, etc. N energy level is 4, etc.

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SECOND PRINCIPLE of SECOND PRINCIPLE of QUANTUM MECHANICSQUANTUM MECHANICS The maximum number of electrons The maximum number of electrons

that can occupy and energy level is that can occupy and energy level is given by the equationgiven by the equation

2(n)2(n)22 = maximum number of e-= maximum number of e-– n is the principle quantum number of the n is the principle quantum number of the

energy level.energy level.– Principle quantum number is 2, the Principle quantum number is 2, the

electron maximum is 2(2)electron maximum is 2(2)22 = 8 = 8– Principle quantum number is 3, the Principle quantum number is 3, the

electron maximum is 2(3)electron maximum is 2(3)22 = 18 = 18

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DIVIDE and CONQUER!DIVIDE and CONQUER!

energy levels are actually several energy levels are actually several closely bound bands of energy closely bound bands of energy

Each of the bands represents a sub Each of the bands represents a sub level level

The number of sublevels is the same The number of sublevels is the same as the principle quantum numberas the principle quantum number

It is represented by the It is represented by the angular angular momentum numbersmomentum numbers – s, p, d, and f.s, p, d, and f.

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KK energy level energy level – principle quantum number is principle quantum number is 11. . – 1 sub level, 1 sub level, ss

LL energy level energy level – principle quantum number is principle quantum number is 22. . – 2 sublevels, 2 sublevels, s, ps, p

MM energy level energy level – principle quantum number is principle quantum number is 33. . – 3 sublevels, 3 sublevels, s, p, ds, p, d

NN energy level energy level – principle quantum number isprinciple quantum number is 4 4– 4 sublevels 4 sublevels s, p, d, f.s, p, d, f.

The energy within a level varies. The energy within a level varies. Lowest EnergyLowest Energy Highest EnergyHighest Energy ss >>> >>> pp >>> >>> dd >>> >>> ff

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Sublevels have Sublevels have characteristic shapes characteristic shapes

ss

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pp

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dd

6161

ff

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Magnetic Quantum Magnetic Quantum Number Number 1, 3, 5, 71, 3, 5, 7 represents the represents the numbernumber of of

different paths (orbits) that the different paths (orbits) that the electron can take in relationship electron can take in relationship to the three axes of space to the three axes of space

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Wolfgang Pauli Wolfgang Pauli

electron spectra affected by electron spectra affected by magnetic fields magnetic fields

indicated that the electrons could indicated that the electrons could be spinning in two different be spinning in two different directions within the orbital directions within the orbital – clockwise clockwise – counterclockwise counterclockwise

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Pauli Exclusion Pauli Exclusion PrinciplePrinciple

Spinning in one direction causes a Spinning in one direction causes a magnetic field that is attracted to the magnetic field that is attracted to the north pole of a magnetnorth pole of a magnet

Spinning in the opposite direction Spinning in the opposite direction causes it to be attracted to a south polecauses it to be attracted to a south pole

If two electrons occupy the same If two electrons occupy the same orbital then they must spin in opposite orbital then they must spin in opposite directionsdirections

If they did not they would repel each If they did not they would repel each other as two like magnetic poles repel other as two like magnetic poles repel each other. each other.

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North PoleNorth Pole

South PoleSouth Pole

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Energy Levels are Energy Levels are Subdivided Subdivided

ENERGY LEVELS

SUBLEVEL SUB SHELL s p d f

ORBITALS

1 1 2 3 1 2 3 4 5

1 2 3 4 5 6 7

1 2 1 21 21 2 1 2 1 2 1 2 1 2 1 2

1 21 21 21 21 21 2 1 2

ELECTRON PAIRS

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HierarchyHierarchy

no two electrons in same atom no two electrons in same atom can have same set of four can have same set of four quantum numbers. quantum numbers.

What is the maximum number of What is the maximum number of quantum numbers that can be quantum numbers that can be shared by two electrons?shared by two electrons?

33

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Summary ChartSummary Chart

E N E R G Y L E V E L

P R IN C IP L EQ U A N T U M N O . S U B L E V E L S

O R B IT A LP E R S U B L E V E L

O R B IT A LP E R L E V E L

E L E C T R O N SP E R S U B L E V E L

E L E C T R O N SP E R L E V E L

K 1 s 1 1 2 2

L 2 s 1 4 2 8 p 3 6

M 3 s 1 9 2 1 8p 3 6d 5 1 0

N 4 s 1 1 6 2 3 2p 3 6d 5 1 0f 7 1 4

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I'D RATHER STAY I'D RATHER STAY SINGLESINGLE most stable state of an atom - most stable state of an atom -

ground stateground state actual arrangement of the actual arrangement of the

electrons in atom referred to as electrons in atom referred to as thethe electron configurationelectron configuration

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Hund's RuleHund's Rule

electrons arrange themselves in such electrons arrange themselves in such a way as to MAXIMIZE THE NUMBER a way as to MAXIMIZE THE NUMBER OF UNPAIRED ELECTRONS in a sub OF UNPAIRED ELECTRONS in a sub levellevel

Only after one electron occupies each Only after one electron occupies each of the sublevel’s orbitals do the of the sublevel’s orbitals do the electrons begin to pair up and share electrons begin to pair up and share the same orbitalthe same orbital

ee- - spin oppositely when in same spin oppositely when in same orbital orbital

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NucleusNucleus

K Energy LevelK Energy Level

OUTERMOSOUTERMOST Energy T Energy

LevelLevel

NEXT to the NEXT to the OUTERMOSOUTERMOS

T Energy T Energy LevelLevel22ndnd from the from the

OUTERMOST OUTERMOST Energy LevelEnergy Level

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POSTULATES of POSTULATES of QUANTUM MECHANICSQUANTUM MECHANICS1.1. The K energy level is the most tightly bound in The K energy level is the most tightly bound in

any atom.any atom.2.2. The outermost energy level NEVER has more The outermost energy level NEVER has more

than than 8 electrons.8 electrons. 3.3. The next to the outermost level NEVER has The next to the outermost level NEVER has

more than more than 18 electrons.18 electrons.4.4. IF the next to the outermost level does not IF the next to the outermost level does not

contain its maximum number of electrons (18 contain its maximum number of electrons (18 e-), THEN the outermost energy level can hold e-), THEN the outermost energy level can hold no more than 2 electrons.no more than 2 electrons.

5.5. IF the second from the outermost energy level IF the second from the outermost energy level does not contain its maximum amount of does not contain its maximum amount of electrons (2n2), THEN the next to the outermost electrons (2n2), THEN the next to the outermost energy level can hold energy level can hold no more than 9 electrons.no more than 9 electrons.

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The The Aufbau PrincipleAufbau Principle

Experimental data indicates that Experimental data indicates that sublevels within the energy levels sublevels within the energy levels sometimes overlap the sublevels of sometimes overlap the sublevels of other energy levels other energy levels

electrons electrons fill the subshells of the fill the subshells of the lowest energies firstlowest energies first

Since overlapping occurs, a means of Since overlapping occurs, a means of remembering the order of sub level remembering the order of sub level energies is helpful energies is helpful

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Aufbau Diagram Aufbau Diagram (from German (from German Aufbauprinzip,Aufbauprinzip, “building-up principle”) “building-up principle”)

Electrons enter Electrons enter atom in this orderatom in this order

Electons are Electons are removed from removed from atom in the atom in the reverse orderreverse order

Last in first out.Last in first out.

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ORBITAL NOTATIONORBITAL NOTATION

Example: Oxygen Example: Oxygen 8 protons, 8 electrons, 8 neutrons8 protons, 8 electrons, 8 neutrons

Notice the application of Hund's Rule, where Notice the application of Hund's Rule, where unpaired electrons are maximized.unpaired electrons are maximized.

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ELECTRON ELECTRON CONFIGURATION CONFIGURATION

NOTATIONNOTATION compare this method to the orbital notation.compare this method to the orbital notation.

1s1s22 2s 2s22 2p 2p44

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ELECTRON DOT ELECTRON DOT NOTATIONNOTATION

shows only the electrons in the outer shows only the electrons in the outer energy level (valence electrons)energy level (valence electrons)

the ethe e-- that are involved in chemical that are involved in chemical reactions reactions

illustrates the electrons that bond illustrates the electrons that bond with other atoms with other atoms

outer (valence) energy level can outer (valence) energy level can hold no more than hold no more than eight electronseight electrons (2nd postulate of quantum (2nd postulate of quantum mechanics) mechanics)

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Oxygen Oxygen 8 protons, 8 8 protons, 8 electronselectrons

chemical symbol is chemical symbol is written in the center written in the center of the notation of the notation

right of the symbol right of the symbol represents the s represents the s orbital orbital

top, left and bottom top, left and bottom represent each of the represent each of the three orbitals in the p three orbitals in the p sub level, sub level, respectively. respectively.

1 quantum mechanics chapters 4 & 5. 2 way way back in time... greek philosopher democritus (460-...

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