che 106 prof. j. t. spencer 1 che 106: general chemistry u chapter six copyright © james t. spencer...

CHE106Prof. J. T. Spencer

1CHE 106: General Chemistry

CHAPTER SIX

Copyright © James T. Spencer 1995 - 1999

Tyna L. Heise 2001-2002

All Rights Reserved


2Chapter Six: Electronic Chapter Six: Electronic

StructureStructure Closer look at atomic inner workings Prior to 1926, Many experiments in the structure

of matter showed several important relationships:– Light has BOTHBOTH wavelike and particulate (solid

particle-like) properties.– Even solid particles display BOTHBOTH wavelike and

particulate properties. – Whether the wavelike or particulate properties

are predominantly observed depends upon the nature of the experiment (what is being measured).


3Electromagnetic RadiationElectromagnetic Radiation = c

– where = wavelength, = frequency,

c = light speed

amplitudeamplitude

wavelength (wavelength ())


4Electromagnetic RadiationElectromagnetic Radiation = c

– where = wavelength, = frequency,

c = light speed

Wavelength (m)Wavelength (m)GammaGamma X-rayX-ray UV/VisUV/Vis InfraredInfraredMicrowaveMicrowaveRadioRadio

1010-11-11mm 10 m10 m


5Electromagnetic RadiationElectromagnetic Radiation Electromagnetic radiation consists of BOTH

electric and magnetic components. The wave properties seen in radiation is due to the oscillation of these properties

All radiation moves at the speed of light, so wavelength and frequency are related

= c


6Electromagnetic RadiationElectromagnetic Radiation

Sample exercise: A laser is used in eye surgery to fuse detached retinas produces radiation with a frequency of 4.69 x 1014 s-1. What is the wavelength of this radiation?


7Electromagnetic RadiationElectromagnetic Radiation

Sample exercise: A laser is used in eye surgery to fuse detached retinas produces radiation with a frequency of 4.69 x 1014 s-1. What is the wavelength of this radiation?

= c


8Electromagnetic RadiationElectromagnetic RadiationSample exercise: A laser is used in

eye surgery to fuse detached retinas produces radiation with a frequency of 4.69 x 1014 s-1. What is the wavelength of this radiation?

= c

x(4.69 x 1014 s-1) = 3.00 x 108 m/s


9Electromagnetic RadiationElectromagnetic RadiationSample exercise: A laser is used in

eye surgery to fuse detached retinas produces radiation with a frequency of 4.69 x 1014 s-1. What is the wavelength of this radiation?

= c

x = 3.00 x 108 m/s

4.69 x 1014 s-1


10Electromagnetic RadiationElectromagnetic RadiationSample exercise: A laser is used in eye

surgery to fuse detached retinas produces radiation with a frequency of 4.69 x 1014 s-1. What is the wavelength of this radiation?

= c

x = 3.00 x 108 m/s = 6.40 x 10-7 m

4.69 x 1014 s-1


11Visible LightVisible Light

The rhodopsin molecule is the first link in the chain that leads from light’s hitting the eye to the brain’s acknowledging that light.

RhodopsinRhodopsin


12Louis de BroglieLouis de Broglie

Light Had Both Particulate and Wave-like Properties

HOW?

Duality of Nature Relationships

(1892-1987)(1892-1987)


13Light: Dual PropertiesLight: Dual Properties

Light has both wave-like and particle-like nature

electrons ejected from bulk

material

Particulate Particulate BehaviorBehavior

Wave-like Wave-like BehaviorBehavior

Photoelectric Effect Dispersion by Prism

White Light Source


14Matter: Dual PropertiesMatter: Dual Properties

Matter has both wave-like and particle-like natureParticulate Particulate

BehaviorBehaviorWave-like Wave-like BehaviorBehavior

Electron Ionization Electron Diffraction

ElectronBeam Source

electrons ejected


15Max PlanckMax Planck

Blackbody radiation

II

2000°2000°

1500°1500°

predictedpredicted

•WavelengthWavelength distribution of hot distribution of hot objects depends upon objects depends upon temperature. (red temperature. (red cooler than white)cooler than white)•PredictionsPredictions on all on all theory led to very poor theory led to very poor agreementagreement•PlanckPlanck ASSUMED that ASSUMED that energy can be released energy can be released only in discrete packets only in discrete packets


16Max PlanckMax Planck

Blackbody radiation

II

2000°2000°

1500°1500°

predictedpredicted

•Assumed that energy Assumed that energy can be released only in can be released only in discrete ‘chunks’ of discrete ‘chunks’ of some minimum sizesome minimum size•gives the name gives the name ‘quanta’ to this ‘quanta’ to this minimum energy minimum energy absorbed or emittedabsorbed or emitted•proposes that this proposes that this energy is related to the energy is related to the frequency of the frequency of the radiationradiation•ProposedProposed E = hv E = hv


17Microscopic PropertiesMicroscopic Properties

Light energy may behave as waves or as small particles (photons).

Particles may also behave as waves or as small particles.

Both matter and energy (light) occur only in only in discrete units (quantized)discrete units (quantized).

Quantized(can stand only on steps)

Non-Quantized(can stand at any position on the ramp)


18What is QuantizationWhat is Quantization

Examples of quantization (when only discrete only discrete and defined quantities or states are and defined quantities or states are possiblepossible):Quantized Non-Quantized

Piano Violin or GuitarStair Steps RampTypewriter Pencil and PaperDollar Bills Exchange ratesFootball Game Score Long Jump DistanceLight Switch (On/Off) Dimmer SwitchEnergyMatter



Sample exercise: A laser emits light with a frequency of 4.69 x 1014 s-1. What is the energy of one quantum of this energy?




E = hv




E = hv

= 6.63 x 10-34 J-s(4.69 x 1014

s-1)




E = hv

= 6.63 x 10-34 J-s(4.69 x 1014

s-1)

= 3.11 x 10-19 J



Sample exercise: The laser emits its energy in pulses of short duration. If the laser emits 1.3 x 10-2 J of energy during a pulse, how many quanta of energy are emitted during the pulse?




1.3 x 10-2 J




1.3 x 10-2 J 1 quatum3.11 x 10-19 J




1.3 x 10-2 J 1 quatum3.11 x 10-19 J

= 4.2 x 1016 quanta


27Albert EinsteinAlbert Einstein

Photoelectric Effect

Relativity

Nuclear Non-proliferation

Nobel Prize

(1879-1955)(1879-1955)


28Photoelectric EffectPhotoelectric Effect

Vacuum TubeVacuum Tubelightlight

electronselectrons

Voltage SourceVoltage Source CurrentCurrentMeterMeter

metalmetal

metalmetal


29

Wave Properties of Wave Properties of MatterMatter

De Broglie - particles behave under some circumstances as if they are waves (just as light behaves as particles under some circumstances). Determines relationship:

= h/mv

= wavelengthh = Planck’s const.m = massv = velocity

Particle mass (kg) v (m/sec) (pm)electron 9 x 10-31 1 x 105 7000He atom (a) 7 x 10-27 1000 90Baseball

fast ball 0.1 20 3 x 10-22

slow ball 0.1 0.1 7 x 10-20


30Niels Bohr (Denmark)Niels Bohr (Denmark)

Built upon Planck, Einstein and others work to propose explanation of line spectra and atomic structure.

Nobel Prize 1922 Worked on

Manhatten Project Advocate for

peaceful nuclear applications


31Bohr’s ModelBohr’s Model

Continuous Spectra vs. Line Spectra


Dispersion by Prism

SunlightSunlight


Dispersion by Prism

HydrogenHydrogen


32Hydrogen EmissionHydrogen Emission

RedRed BlueBlue UltravioletUltraviolet

A Swiss schoolteacher in 1885 (J. Balmer) A Swiss schoolteacher in 1885 (J. Balmer) derived a simple formula to calculate the derived a simple formula to calculate the wavelengths of the emission lines (purely a wavelengths of the emission lines (purely a mathematical feat with no understanding of mathematical feat with no understanding of why this formula worked)why this formula worked)

frequency = C ( 1 - 1 ) where n = 1, 2, 3, etc...frequency = C ( 1 - 1 ) where n = 1, 2, 3, etc... 2222 n n22 C = constantC = constant

656.

3 n

m

486.

1 n

m

434.

0 n

m

410.

2 n

m

364.

6 n

m



Electrons in circular orbits around nucleus with quantized (allowed) energy states

When in a state, no energy is radiated but when it changes states, energy is emmitted or gained equal to the energy difference between the states

Emission from higher to lower, absorption from lower to higher

n=1n=1

n=2n=2

n=3n=3n=4n=4

n=œn=œ

electronic electronic transitionstransitions

““Microscopic Solar Syatem”Microscopic Solar Syatem”



The electrons in these orbits have certain specific radii, and represent an energy which fits a mathematical formula

En = (-RH)(1/n2) RH is the Rydberg

constant The integer n is equal

to the principal quantum number n=1n=1

n=2n=2

n=3n=3n=4n=4

n=œn=œ

electronic electronic transitionstransitions




Sample exercise: Calculate the wavelength of hydrogen emission line that corresponds to the transition of the electron from the n=3 to the n=1 state. In what portion of the electromagnetic spectrum is this line found?




Sample exercise: Calculate the wavelength of hydrogen emission line that corresponds to the transition of the electron from the n=3 to the n=1 state.

v = E = RH 1 _ 1

h h in2 fn2





v = E = 2.18 x 10-18 J 1 _ 1

h 6.63 x 10-34 J-s in2

fn2





v = E = 2.18 x 10-18 J 1 _ 1

h 6.63 x 10-34 J-s 32 12





v = E = 2.18 x 10-18 J 1 _ 1

h 6.63 x 10-34 J-s 32 12

= (3.29 x 1015 s-1)(-0.889)




Sample exercise: Calculate the wavelength of hydrogen emission line that corresponds to the transition of the electron from the n=3 to the n=1 state. v = E = 2.18 x 10-18 J 1 _ 1

h 6.63 x 10-34 J-s 32 12

= (3.29 x 1015 s-1)(-0.889)

= -2.92 x 1015 s-1





v = -2.92 x 1015 s-1

c = v





v = -2.92 x 1015 s-1

c = v3.00 x 108 m/s = (2.92 x 1015 s-1)x = 1.03 x 10-7 m = 103 nm




Sample exercise: In what portion of the electromagnetic spectrum is this line found?

= 1.03 x 10-7 m = 103 nm




Sample exercise: In what portion of the electromagnetic spectrum is this line found?

= 1.03 x 10-7 m = 103 nm

ultraviolet range



45Wave Behavior of Wave Behavior of

MatterMatterLouis de Broglie boldly extended the idea of

energy having dual properties:if energy can have dual properties, so can

matter.the characteristic wavelength of any

particle of matter depends on its mass = h

mvthe wavelength for most objects is so small

it is not observable, only on an atomic scale will matter waves be important



MatterMatterSample exercise: At what velocity

must a neutron be moving in order for it to exhibit a wavelength of 500 pm?





= h mv





= h 5.00 x 10-10 m = 6.63 x 10-34 J-s mv (1.67 x 10-27 kg)x



MatterMatterSample exercise: At what velocity must

a neutron be moving in order for it to exhibit a wavelength of 500 pm?

= h 5.00 x 10-10 m = 6.63 x 10-34 J-s mv (1.67 x 10-27 kg)x

(5.00 x 10-10 m)(1.67 x 10-27 kg)x = 6.63 x 10-34 J-s





(5.00 x 10-10 m)(1.67 x 10-27 kg)x = 6.63 x 10-34 J-s

x = 6.63 x 10-34 J-s5.00 x 10-10 m)(1.67 x 10-27 kg)





(5.00 x 10-10 m)(1.67 x 10-27 kg)x = 6.63 x 10-34 J-s

x = 6.63 x 10-34 (kg/m2-s2)s5.00 x 10-10 m)(1.67 x 10-27 kg)



MatterMatterSample exercise: At what velocity must a

neutron be moving in order for it to exhibit a wavelength of 500 pm?

(5.00 x 10-10 m)(1.67 x 10-27 kg)x = 6.63 x 10-34 J-s

x = 6.63 x 10-34 (kg*m2/s2)s5.00 x 10-10 m)(1.67 x 10-27 kg)

x = 7.94 x 102 m/s


53Principle Quantum Principle Quantum

NumberNumber Each orbit corresponds to a different value of n The radius of the orbit gets larger as the n

value increases First allowed energy level is n = 1, then n=2

and so on Radius of orbital for n = 1 is 0.529 angstroms,

the 2nd energy level is 22 or 4 times larger, n=3 would be 32 or 9 times larger and so on

If all electrons are in lowest energy this If all electrons are in lowest energy this is the GROUND STATEis the GROUND STATE


54Uncertainty PrincipleUncertainty Principle

For a macroscopic particle, “classical” mechanics (Newtonian) says that the position, direction and velocity of the particle may be determined exactly.exactly.

Since particles also have wave-like properties and waves continue to an undefined location in space, is it really possible to exactly determine the position, direction and velocity of a particle exactlyexactly??

Werner HeisenbergWerner Heisenberg (1901-1976) concluded that the duality of nature limits how precisely we can know the location and momentum of a particle. UNCERTAINTY PRINCIPLEUNCERTAINTY PRINCIPLE


55Werner HeisenbergWerner Heisenberg

Uncertainty Principle

Quantum Mechanics

Became Full Professor at 25 yrs.

Nobel Prize at 32

(1901-1976)(1901-1976)



Consider: determine exactlyexactly the position andand velocity (or momentum) of an atomic particle (i.e., an electron - a very small item).– To “see” the particle, light (photons) must

bounce off it to be detected by our eyes and thus allow is to measure its position.

– BUT, in the interaction of light with the particle some energy is transferred to the particle changing it velocity (or momentum).

– Thus, the act of measurement affects what we are measuring.

– Heisenberg - (x) (mv) h/4�



Very Fast Shutter SpeedVery Fast Shutter Speed - can determine position very accurately but cannot determine

direction or speed very accurately

Very Slow Shutter SpeedVery Slow Shutter Speed - can determine direction very accurately but cannot determine

position very accurately


58Duality of NatureDuality of Nature

Uncertainty principleUncertainty principle says that the position and momentum of a particle (such as an electron) cannot be exactly determined. Thus, how can we understand an electron’s “actions” in an atom?

How can the two seemingly very different properties (wave-like and particulate) of light and matter be possible? How does quantization of energy and matter fit into the picture?


59Erwin SchrödingerErwin Schrödinger

Quantum Mechanics

(1887-1961)(1887-1961)

Erwin Schrödinger (1887-1961) developed a new way of dealing with this dual nature - Quantum Mechanics.Quantum Mechanics.


60


61Quantum MechanicsQuantum Mechanics

Schrödinger - starts with the measurable energies of atoms and works towards the description of the atom, basically solving the problem backwards.– Wave equationWave equation - equation used to describe

the wave properties of an electron. If you understand all the features of the equation, then you can know all that's possible about the electron.

– solutions to the wave equation are called wave functions (wave functions () or orbitals) or orbitals - contain information about the energy and electron’s 3D position in space (probability).


62Wave EquationWave Equation

n = 1

“Stable” solution to the jump-rope wave equation

n = 2

n = 3


63

Wave functions () are without physical meaning BUTBUT 2 gives the probability of finding an electron within a given region of space.

Quantum MechanicsQuantum Mechanics

Probability of finding an

electron within a region of

space ()

Wave Equation

Wave function or

Orbital ()solve

How does an electron get from position A to Position B? The question is unanswerable since it assumes

particle behavior of electron and NOT wave properties.


64

Home

Visitors

Probability (Probability (22))Orbital (Orbital (22)) - a region of space within which there is a certain probability of finding the electron.

similar to a baseball field; there is a certain probability of finding the baseball during a game within the park and a higher probability of finding it in the infield than in the outfield. A ball can be hit over the fence which is equivalent to electron ionization.


65

probability of finding

the baseball

during the game

pitcher’s moundinfield

warning track

home run

distance from home plate

Probability (Probability (22))

Plot of Probabilitynce increases.


66

2

Prob. of finding

the electron

distance from nucleus

Probability (Probability (22))

1 D Plot (probability and distance measured along red arrow)

3D Plot (spherical surface within which the electron

spends x% of its time)

2D Contour Plot (lines within which the electron

spends x% of its time)

1s

Orbital is a region of high probability of finding the electron (no trajectory/path information)


67OrbitalsOrbitals

Probability or Electron DensityProbability or Electron Density - probability of finding the electron at a particular location. Regions with a high probability of finding the electron have a high electron density.

OrbitalsOrbitals - solutions to the wave equation - have specific energies and probability profiles. (orbitals have characteristic shapes and energies).– OrbitOrbit (orbit implies pathway) - Bohr models uses 1

quantum value (n) to describe the orbit Quantum NumbersQuantum Numbers - (from wave equation) each

orbital) has 3 quantum numbers.– describe shapes and energies of orbitals.– accounts for quantized (allowed) energies.


68

Quantum Numbers Quantum Numbers (QN)(QN)

Principal Quantum Number (Principal Quantum Number (n n )) - may have integral values >0 (i.e., 1, 2, 3, 4,...). Dictates the size and energy level of an orbital As n increases both the size and energy of the orbital increases.

Angular Momentum Azimuthal) Quantum Number (Angular Momentum Azimuthal) Quantum Number (l l )) - may have values from 0 to (n-1). Defines the 3D shape of the orbital. Often referred to by letter (i.e., l = 0 = s, l = 1 = p, etc...) When more than 1 electron exists, the l Q.N. also describes energy.

Magnetic Quantum Number (Magnetic Quantum Number (mml l )) - may have values of -l to +l. Defines the spatial orientation of the orbital along a standard coordinate axis system.


69

Collection of orbitals with the same n Q.N. value is called an electron shell or principal energy level.

Collection of orbitals with the same n and l values is called an electron subshell.– Each shell is divided into subshells equal to

the principal quantum number (n)– Each subshell is divided into orbitals

n l subshell ml spatial orient.1 0 s 02 1 p 1, 0, -1 3 2 d 2, 1, 0, -1, -2

4 3 f 3, 2, 1, 0, -1, -2, -3

Quantum Numbers Quantum Numbers (QN)(QN)


70Quantum Number/AddressQuantum Number/Address

Quantum numbers may be thought of as energy and space addresses.

Quantum NumberAddress

nbuildingl floor

ml room


71Quantum NumbersQuantum Numbers

Combinations of the quantum numbers specifies which specific electron we are referring to in an atom (address)

n l subshell mlno. of orbs no. of e-l

1 0 1s 0 1 22 0 2s 0 1 2

1 2p 1, 0, -1 3 63 0 3s 0 1 2

1 3p 1, 0, -1 3 62 3d 2, 1, 0, -1, -2 510

22

88

1818


72

2 electrons

max

Quantum NumbersQuantum Numbers Quantum Numbers also specify energy of the

occupying electrons,

1s

2s

3s4s

2p

3p4p

3d4d 4f

ENERGY

0

n = 1

n = 2

n = 3

n = 4

n =

2+6=8 electrons

max

2+6+10=18

electrons max

2+6+10+14=32

electrons max

l = 0 l = 1 l = 2 l = 3



Sample exercises: What is the designation for the subshell with n=5 and l = 1?




n = 5 is 5th principle energy level




n = 5 is 5th principle energy level

l = 1 is the p subshell



Sample exercises: What is the designation for the subshell with n=5 and l = 1? How many orbitals are in this subshell?



Sample exercises: What is the designation for the subshell with n=5 and l = 1? How many orbitals are in this subshell?

p subshell has 3 orbitals



Sample exercises: What is the designation for the subshell with n=5 and l = 1? How many orbitals are in this subshell? Indicate the values of ml for each of these orbitals.



Sample exercises: What is the designation for the subshell with n=5 and l = 1? How many orbitals are in this subshell? Indicate the values of ml for each of these orbitals.

p subshell has 3 orbitals, labeled -1, 0, 1


80OrbitalsOrbitals

Ground stateGround state - when an electron is in the lowest energy orbital.

Excited stateExcited state - when an electron is in another orbital.

All orbitals of the same l values are the same shape (different relative sizes and energies).

1s 2s 3s


81s Orbitalss Orbitals

1s 2s 3s

2

(1s)2

(2s)2

(3s)

NodeNode NodesNodes

Node - where 2 goes to zero

radius radius radius

Boundary Plots (angular)

Radial Plots

l = 0


82

2s 3s


83p Orbitalsp Orbitalsl = 1

2pz 3px


84p Orbitalsp Orbitals

pxpypz

x

y

z

x

y

z

x

y

z

x

y

z

l = 1

2

(p)

radius

2p

3p

Radial Electron

Distribution


85l = 2 d orbitalsd orbitals

dx2-y2dz2


86d orbitalsd orbitals

dxy

x

y

z

l = 2

x

y

z

x

y

zdx2-y2 dz2

dyzdxz

x

y

z

x

y

zorbital shapes are approx. the same for each l

value except for their

relative sizes (and energies).


87Many Electron AtomsMany Electron Atoms

Wave equation solved for only the smallest atoms (very intensive calculations). Larger atoms calculated by approximations.

Shapes of orbitals for larger atoms (>H) are essentially the same as those found for hydrogen.

The energies of the orbitals are, however, significantly changed in many electron systems.

For H, the energy of an orbital depends only on n, while for larger atoms, the l value also affects energy levels due to electron-electron repulsionselectron-electron repulsions.


88Many Electron AtomsMany Electron Atoms

1s

2s

3s

4s

2p

3p

4p3d

ENERGY

0n = 1 n = 2 n = 3 n = 4

5s

n = 5

s (l = 0)p (l = 1)d (l = 2)


89 In many electron atoms, electron-electron

repulsions (besides electron-nuclear attractions) become important.

Estimate the energy of an electron in an orbital by considering how it, on the average, interacts with its electronic environment (treat electrons individually).

The net attractive force that an electron will feel is the effective nuclear chargeeffective nuclear charge (Zeff). Zeff = Z - S

Screening is the average number of other electrons that are between the electron and the nucleus.

Effective Nuclear Effective Nuclear ChargeCharge

Z = nuclear chargeS = screening valueZ = nuclear chargeS = screening value


90

Effective Nuclear Effective Nuclear ChargeCharge

r

Average electronic charge (S) between the nucleus and the electron of interest

Electrons outside of sphere of radius r have very little effect

on the effective nuclear charge experienced by the electron at

radius r

Zeff = Z - S

Z

The larger the Zeff an

electron feels leads to a lower energy for

the electron


91

Shielding (Screening Shielding (Screening Effect)Effect)

– the offensive linemen can screen one defensive player completely (they spend all of their time in front of the quarterback).

– the half backs, since they are further back, can only partially screen out a defensive player.

– the fullbacks are behind the QB and can’t screen out any defensive players.

X

X

XX XXXX

X X X

11 11 Defensive Defensive

PlayersPlayers

QB

“Football” Screening effect (at the ball snap!):


92ScreeningScreening

For a given n value, the Zeff decreases with increasing values of l (screening ability; s>p>d>f).

For a given n value, the energy of an orbital increases with increasing values of l.

2

radius

3p

3s

3d

s electrons spend more time near the nucleus than do the p electrons (and p>d). Thus s electrons shield better than p and p better than d.



Sample exercise: The sodium atom has 11 electrons. Two occupy a 1s orbital, two occupy a 2s orbital, and one occupies a 3s orbital. Which of these s electrons experiences the smallest effective nuclear charge?



Sample exercise: The sodium atom has 11 electrons. Two occupy a 1s orbital, two occupy a 2s orbital, and one occupies a 3s orbital. Which of these s electrons experiences the smallest effective nuclear charge?

3s electrons are farthest from the nucleus and shielded.


95Electron SpinElectron Spin

Electrons have spin properties (spin along axis).

Electron spin is quantized

ms = + 1/2 or - 1/2

NN

Magnetic Fields

-- --


96

Experimental Electron Experimental Electron SpinSpin

Passing an atomic beam (neutral atoms) which contained an odd number of electrons (1 unpaired electron, see later) through a magnetic field caused the beam to split into two spots.

Showed the possible states of the single (unpaired) electron as quantized into ms = +1/2 or - 1/2.

NN

SS

Magnetic FieldSlits

Atom Beam

Generator

Viewing Screen

two electron spin states


97Nuclear Spin Nuclear Spin

Like electrons, nuclei spin and because of this spinning of a charged particle (positively charged), it generates a magnetic field. Two states are possible for the proton (1H).

NN

SS NN

SS

++ ++


98Nuclear Spin Nuclear Spin

NN

SS NN

SS

NN

SS

NN

SS

Degenerate

Parallel

Antiparallel

EE

External Magnetic FieldExternal Magnetic Field

Similar to a canoe Similar to a canoe paddling either upstream paddling either upstream

or downstreamor downstream


99

Magnetic Resonance Magnetic Resonance Imaging MRIImaging MRI

Hydrogen atom has two nuclear spin quantum numbers possible (+1/2 and -1/2).

When placed in an external magnetic field, 1H can either align with the field (“parallel” - lower energy) or against the field (“antiparallel” - higher energy).

Energy added (E) can raise the energy level of an electron from parallel to antiparallel orientation (by absorbing radio frequency irradiation).

Electrons (also “magnets”) in “neighborhood” affect the value of E (i.e., rocks in stream).

By detecting the E values as a function of position within a body, an image of a body’s hydrogen atoms may be obtained.


100MRIMRI

AdvantagesAdvantages– non-invasive.– no ionizing or other “dangerous” radiation

(such as X-rays of positrons).– Can be done frequently to monitor progress of

treatment.– images soft tissues (only those with hydrogen

atoms (almost all “soft” tissues).– images function through the use of contrast

media. DisadvantagesDisadvantages

– Relatively expensive equipment


101MRI; HardwareMRI; Hardware


102MRIMRI


103MRIMRI


104MRIMRI


105MRIMRI


106MRIMRI


107Wolfgang PauliWolfgang Pauli

explained the electron spin experiments in terms of quantum mechanics

Austrian Physicist who explained that no electrons in an atom may occupy the same quantum state .....Have the same four quantum numbers

1945 Nobel Prize for Exclusion Principle

1900-19581900-1958


108

Pauli Exclusion Pauli Exclusion PrinciplePrinciple

Pauli exclusion principlePauli exclusion principle - no two electrons in an atoms can have the same set of four quantum numbers (n, l, ml, ms).

For a given orbital, n, l, and ml are set but each orbital can hold 2 electrons with opposite ms values (ms = +1/2 and -1/2).

= an electron with ms = -1/2= an electron with ms = +1/2

1s 2s 2px 2py 2pz

EnergyEnergy


109Electron ConfigurationsElectron Configurations

Fill orbitals with electrons STARTING at lowest energy (ground state configuration). [just as filling a glass with water starts at the bottom and fills up.

No more that two electrons per orbital (Pauli).

1s 2s 2px 2py 2pz

EnergyEnergy

Orbital Diagram

Written

1s22s12p0 etc...

Paired ElectronsPaired Electrons

Unpaired ElectronUnpaired Electron


110Electron ConfigurationsElectron Configurations

1s

2s

3s

4s

2p

3p

4p3d

ENERGY

0n = 1 n = 2 n = 3 n = 4

5s

n = 5

s (l = 0)p (l = 1)d (l = 2)

fill orbitals with electrons from

lowest to highest energy (bottom to top) just as if

filling a glass with water

1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 etc...


111

Electronic Electronic ConfigurationsConfigurations

EnergyEnergyOrbital Diagram

1s 2s 2px 2py 2pz 3s 3px 3py 3pz

55BB

66CC

Degenerate Orbitals Degenerate Orbitals

1s1s22 2s 2s22 2p 2p22

1s1s22 2s 2s22 2p 2p11

1s1s22 2s 2s22 2p 2p00

66CC

66CC

What do we do with Carbons 2 p electrons?What do we do with Carbons 2 p electrons?


112Hund’s RuleHund’s Rule

Hund’s rule (of maximum multiplicity)Hund’s rule (of maximum multiplicity) - the lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli exclusion principle in a given set of degenerate orbitals (group of orbitals with the same energy) with all unpairedaving parallel spins.

1s 2s 2px 2py 2pz


Degenerate Orbitals (all at the same energy)

Where does the Where does the next electron go?next electron go?


113




33LiLi

44BeBe

55BB

66CC

77NN

Degenerate Orbitals Degenerate Orbitals

1s1s22 2s 2s22 2p 2p33

1s1s22 2s 2s22 2p 2p22

1s1s22 2s 2s22 2p 2p11

1s1s22 2s 2s22 2p 2p00

1s1s22 2s 2s11 2p 2p00


114EnergyEnergyOrbital Diagram


88OO

99FF

1010NeNe

1111NaNa

1212MgMg 1s1s22 2s 2s22 2p 2p66 3s 3s22

1s1s22 2s 2s22 2p 2p663s3s11

1s1s22 2s 2s22 2p 2p66

1s1s22 2s 2s22 2p 2p55

1s1s22 2s 2s22 2p 2p44



115 Electron Configurations:

– Obey Pauli Exclusion Principle– Obey Hund’s rule (where applicable)– Fill from lowest to highest energies– Shorthand;

» 11Na: [Ne] 3s1 equivalent to 1s2 2s2 2p6 3s1

» 19K: [Ar] 4s1 equivalent to 1s2 2s2 2p6 3s2 3p6 4s1

Closed shell (filled), half filled, and empty orbital configurations most stable.

Outer electrons (max. n for atom) are valencevalence elec. Inner electrons (not max. n for atom) are corecore elec.



116 Transition elements (metals) fill d orbitals.


2222TiTi

2323VV

2424CrCr

2525MnMn

2929CuCu4s 3d 3d 3d 3d 3d 4p 4p 4p

[Ar] 4s[Ar] 4s22 3d 3d55

[Ar] 4s[Ar] 4s11 3d 3d55

[Ar] 4s[Ar] 4s11 3d 3d1010

[Ar] 4s[Ar] 4s22 3d 3d22

[Ar] 4s[Ar] 4s22 3d 3d33


117

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1H 2He

3Li 4Be 5B 6C 7N 8O 9F 10Ne

11Na 12Mg 13Al 14Si 15P 16S 17Cl 18Ar

19K 20Ca 21Sc 22Ti 23V 24Cr 25Mn 26Fe 27Co 28Ni 29Cu 30Zn 31Ga 32Ge 33As 34Se 35Br 36Kr

37Rb 38Sr 39Y 40Zr 41Nb 42Mo 43Tc 44Ru 45Rh 46Pd 47Ag 48Cd 49In 50Sn 51Sb 52Te 53I 54Xe

55Cs 56Ba 57La 72Hf 73Ta 74W 75Re 76Os 77Ir 78Pt 79Au 80Hg 81Tl 82Pb 83Bi 84Po 85At 86Rn

87Fr 88Ra 89Ac 104Unq 105Unp 106Unh 107Ns 108Hs 109Mt

58Ce 59Pr 60Nd 61Pm 62Sm 63Eu 64Gd 65Tb 66Dy 67Ho 68Er 69Tm 70Yb 71Lu

90Th 91Pa 92U 93Np 94Pu 95Am 96Cm 97Bk 98Cf 99Es 100Fm 101Md 102No 103Lr

s orbitals

p orbitals

d orbitals

f orbitals

closed shell

Periodic TablePeriodic Table

3d3d

4d4d

5d5d

6d6d

2s2s

3s3s

4s4s

5s5s

6s6s

7s7s

2p2p

3p3p

4p4p

5p5p

6p6p

4f4f

5f5f


118CationsCations

To determinens (usually the last one added). EXCEPT for transition metal ions - which have

NO n(max)s electrons.

2525MnMn

2525MnMn+1+1

4s 3d 3d 3d 3d 3d 4p 4p 4p


119

Sample exercise: What family of elements is characterized by having an ns2p2 outer-electron configuration?



120

Sample exercise: What family of elements is characterized by having an ns2p2 outer-electron configuration?

2 + 2 = 4 valence electrons, so this is Group IVA, or Group 14.



121

Sample exercise: Use the periodic table to write the electron configurations for the following atoms by giving the appropriate noble-gas inner core plus the electrons beyond it:

Co

Te



122


Co : [Ar]4s23d7

Te



123


Co : [Ar]4s23d7

Te: [Kr]5s24d105p4



124End Chapter SixEnd Chapter Six

Duality of Nature (wave-like and particulate properties), DeBroglie

Quantization and the Schrödinger Equation Heisenberg Uncertainty Principle Atomic Orbitals and Wave Functions (solutions

to Wave Equation). Quantum Numbers Orbital Energies, Shapes, Nodes Multi-electron Atoms, Screening and Zeff

Pauli Exclusion Principle Hund’s Rule of Maximum Multiplicity

ContinuedContinued


125Chapter Six (Con’t)Chapter Six (Con’t)

Electron Spin Nuclear Spin (MRI) Electronic Configurations Periodic Table and orbital filling

che 106 prof. j. t. spencer 1 che 106: general chemistry u chapter six copyright © james t. spencer...

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