che 106 prof. j. t. spencer 1 che 106: general chemistry u chapter six copyright © james t. spencer...
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CHE106Prof. J. T. Spencer
1CHE 106: General Chemistry
CHAPTER SIX
Copyright © James T. Spencer 1995 - 1999
Tyna L. Heise 2001-2002
All Rights Reserved
CHE106Prof. J. T. Spencer
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).
CHE106Prof. J. T. Spencer
3Electromagnetic RadiationElectromagnetic Radiation = c
– where = wavelength, = frequency,
c = light speed
amplitudeamplitude
wavelength (wavelength ())
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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?
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
12Louis de BroglieLouis de Broglie
Light Had Both Particulate and Wave-like Properties
HOW?
Duality of Nature Relationships
(1892-1987)(1892-1987)
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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)
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
19What is QuantizationWhat is Quantization
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?
CHE106Prof. J. T. Spencer
20What is QuantizationWhat is Quantization
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
CHE106Prof. J. T. Spencer
21What is QuantizationWhat is Quantization
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
= 6.63 x 10-34 J-s(4.69 x 1014
s-1)
CHE106Prof. J. T. Spencer
22What is QuantizationWhat is Quantization
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
= 6.63 x 10-34 J-s(4.69 x 1014
s-1)
= 3.11 x 10-19 J
CHE106Prof. J. T. Spencer
23What is QuantizationWhat is Quantization
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?
CHE106Prof. J. T. Spencer
24What is QuantizationWhat is Quantization
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
CHE106Prof. J. T. Spencer
25What is QuantizationWhat is Quantization
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 quatum3.11 x 10-19 J
CHE106Prof. J. T. Spencer
26What is QuantizationWhat is Quantization
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 quatum3.11 x 10-19 J
= 4.2 x 1016 quanta
CHE106Prof. J. T. Spencer
27Albert EinsteinAlbert Einstein
Photoelectric Effect
Relativity
Nuclear Non-proliferation
Nobel Prize
(1879-1955)(1879-1955)
CHE106Prof. J. T. Spencer
28Photoelectric EffectPhotoelectric Effect
Vacuum TubeVacuum Tubelightlight
electronselectrons
Voltage SourceVoltage Source CurrentCurrentMeterMeter
metalmetal
metalmetal
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
31Bohr’s ModelBohr’s Model
Continuous Spectra vs. Line Spectra
Wave-like Wave-like BehaviorBehavior
Dispersion by Prism
SunlightSunlight
Wave-like Wave-like BehaviorBehavior
Dispersion by Prism
HydrogenHydrogen
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
33Bohr’s ModelBohr’s Model
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”
CHE106Prof. J. T. Spencer
34Bohr’s ModelBohr’s Model
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
““Microscopic Solar Syatem”Microscopic Solar Syatem”
CHE106Prof. J. T. Spencer
35Bohr’s ModelBohr’s Model
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?
““Microscopic Solar Syatem”Microscopic Solar Syatem”
CHE106Prof. J. T. Spencer
36Bohr’s ModelBohr’s Model
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
““Microscopic Solar Syatem”Microscopic Solar Syatem”
CHE106Prof. J. T. Spencer
37Bohr’s ModelBohr’s Model
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 in2
fn2
““Microscopic Solar Syatem”Microscopic Solar Syatem”
CHE106Prof. J. T. Spencer
38Bohr’s ModelBohr’s Model
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
““Microscopic Solar Syatem”Microscopic Solar Syatem”
CHE106Prof. J. T. Spencer
39Bohr’s ModelBohr’s Model
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)
““Microscopic Solar Syatem”Microscopic Solar Syatem”
CHE106Prof. J. T. Spencer
40Bohr’s ModelBohr’s Model
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
““Microscopic Solar Syatem”Microscopic Solar Syatem”
CHE106Prof. J. T. Spencer
41Bohr’s ModelBohr’s Model
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 = -2.92 x 1015 s-1
c = v
““Microscopic Solar Syatem”Microscopic Solar Syatem”
CHE106Prof. J. T. Spencer
42Bohr’s ModelBohr’s Model
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 = -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
““Microscopic Solar Syatem”Microscopic Solar Syatem”
CHE106Prof. J. T. Spencer
43Bohr’s ModelBohr’s Model
Sample exercise: In what portion of the electromagnetic spectrum is this line found?
= 1.03 x 10-7 m = 103 nm
““Microscopic Solar Syatem”Microscopic Solar Syatem”
CHE106Prof. J. T. Spencer
44Bohr’s ModelBohr’s Model
Sample exercise: In what portion of the electromagnetic spectrum is this line found?
= 1.03 x 10-7 m = 103 nm
ultraviolet range
““Microscopic Solar Syatem”Microscopic Solar Syatem”
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
46Wave Behavior of Wave Behavior of
MatterMatterSample exercise: At what velocity
must a neutron be moving in order for it to exhibit a wavelength of 500 pm?
CHE106Prof. J. T. Spencer
47Wave Behavior of Wave Behavior of
MatterMatterSample exercise: At what velocity
must a neutron be moving in order for it to exhibit a wavelength of 500 pm?
= h mv
CHE106Prof. J. T. Spencer
48Wave Behavior of Wave Behavior of
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
CHE106Prof. J. T. Spencer
49Wave Behavior of Wave Behavior of
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
CHE106Prof. J. T. Spencer
50Wave Behavior of Wave Behavior of
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 J-s5.00 x 10-10 m)(1.67 x 10-27 kg)
CHE106Prof. J. T. Spencer
51Wave Behavior of Wave Behavior of
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)
CHE106Prof. J. T. Spencer
52Wave Behavior of Wave Behavior of
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
55Werner HeisenbergWerner Heisenberg
Uncertainty Principle
Quantum Mechanics
Became Full Professor at 25 yrs.
Nobel Prize at 32
(1901-1976)(1901-1976)
CHE106Prof. J. T. Spencer
56Uncertainty PrincipleUncertainty Principle
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�
CHE106Prof. J. T. Spencer
57Uncertainty PrincipleUncertainty Principle
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
CHE106Prof. J. T. Spencer
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?
CHE106Prof. J. T. Spencer
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.
CHE106Prof. J. T. Spencer
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).
CHE106Prof. J. T. Spencer
62Wave EquationWave Equation
n = 1
“Stable” solution to the jump-rope wave equation
n = 2
n = 3
CHE106Prof. J. T. Spencer
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.
CHE106Prof. J. T. Spencer
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.
CHE106Prof. J. T. Spencer
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.
CHE106Prof. J. T. Spencer
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)
CHE106Prof. J. T. Spencer
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.
CHE106Prof. J. T. Spencer
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.
CHE106Prof. J. T. Spencer
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)
CHE106Prof. J. T. Spencer
70Quantum Number/AddressQuantum Number/Address
Quantum numbers may be thought of as energy and space addresses.
Quantum NumberAddress
nbuildingl floor
ml room
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
73Quantum Number/AddressQuantum Number/Address
Sample exercises: What is the designation for the subshell with n=5 and l = 1?
CHE106Prof. J. T. Spencer
74Quantum Number/AddressQuantum Number/Address
Sample exercises: What is the designation for the subshell with n=5 and l = 1?
n = 5 is 5th principle energy level
CHE106Prof. J. T. Spencer
75Quantum Number/AddressQuantum Number/Address
Sample exercises: What is the designation for the subshell with n=5 and l = 1?
n = 5 is 5th principle energy level
l = 1 is the p subshell
CHE106Prof. J. T. Spencer
76Quantum Number/AddressQuantum Number/Address
Sample exercises: What is the designation for the subshell with n=5 and l = 1? How many orbitals are in this subshell?
CHE106Prof. J. T. Spencer
77Quantum Number/AddressQuantum Number/Address
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
CHE106Prof. J. T. Spencer
78Quantum Number/AddressQuantum Number/Address
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.
CHE106Prof. J. T. Spencer
79Quantum Number/AddressQuantum Number/Address
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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).
CHE106Prof. J. T. Spencer
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.
CHE106Prof. J. T. Spencer
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)
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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!):
CHE106Prof. J. T. Spencer
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.
CHE106Prof. J. T. Spencer
93ScreeningScreening
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?
CHE106Prof. J. T. Spencer
94ScreeningScreening
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.
CHE106Prof. J. T. Spencer
95Electron SpinElectron Spin
Electrons have spin properties (spin along axis).
Electron spin is quantized
ms = + 1/2 or - 1/2
NN
Magnetic Fields
-- --
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
++ ++
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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.
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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...
CHE106Prof. J. T. Spencer
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?
CHE106Prof. J. T. Spencer
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
EnergyEnergyOrbital Diagram
Degenerate Orbitals (all at the same energy)
Where does the Where does the next electron go?next electron go?
CHE106Prof. J. T. Spencer
113
Electronic Electronic ConfigurationsConfigurations
EnergyEnergyOrbital Diagram
1s 2s 2px 2py 2pz 3s 3px 3py 3pz
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
CHE106Prof. J. T. Spencer
114EnergyEnergyOrbital Diagram
1s 2s 2px 2py 2pz 3s 3px 3py 3pz
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
Electronic Electronic ConfigurationsConfigurations
CHE106Prof. J. T. Spencer
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.
Electronic Electronic ConfigurationsConfigurations
CHE106Prof. J. T. Spencer
116 Transition elements (metals) fill d orbitals.
Electronic Electronic ConfigurationsConfigurations
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
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
CHE106Prof. J. T. Spencer
119
Sample exercise: What family of elements is characterized by having an ns2p2 outer-electron configuration?
Electronic Electronic ConfigurationsConfigurations
CHE106Prof. J. T. Spencer
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.
Electronic Electronic ConfigurationsConfigurations
CHE106Prof. J. T. Spencer
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
Electronic Electronic ConfigurationsConfigurations
CHE106Prof. J. T. Spencer
122
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 : [Ar]4s23d7
Te
Electronic Electronic ConfigurationsConfigurations
CHE106Prof. J. T. Spencer
123
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 : [Ar]4s23d7
Te: [Kr]5s24d105p4
Electronic Electronic ConfigurationsConfigurations
CHE106Prof. J. T. Spencer
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