Chapter 6 Electronic Structure of Atoms
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Transcript of Chapter 6 Electronic Structure of Atoms
ElectronicStructureof Atoms
Chapter 6Electronic Structureof Atoms
Chemistry, The Central Science, 10th editionTheodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten
John D. BookstaverSt. Charles Community College
St. Peters, MO 2006, Prentice Hall, Inc.
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6.1The Wave Nature of
Light
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Light
• Much of our understanding of electronic structure of atoms comes from analysis of the light absorbed or emitted by substances
• The light that we see as colors is only a very small portion of the electromagnetic spectrum
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Radiant Energy
• Electromagnetic radiation is also know as radiant energy because it carries (or radiates) energy through space
• Although each type of radiant energy is unique, they all share certain fundamental characteristics…They all behave as waves with
wavelike properties
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Waves
• wavelength () = distance between corresponding points on adjacent waves crest to crest, trough to troughunits of meters (m) or nanometers (nm)
• amplitude = height of the wave
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Waves• frequency ( ) = the # of
complete wavelengths, or cycles, passing a given point per unit of time units of s–1 or hertz (Hz)
• For waves traveling at the same velocity, the longer the , the smaller the and are inversely
proportional (as one increases, the other)
Short = High
Long = Low
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• All radiation moves through a vacuum at the same velocity:
speed of light (c) = 3.0 x 108 m/s
• This common speed allows and to have a quantitative relationship c =
Shared Characteristics of Radiant Energy
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The Electromagnetic Spectrum
ElectronicStructureof Atoms
• Which of the following has the highest frequency? Ultraviolet (UV) waves or Infrared (IR) waves?
• Which type of radiation has the longest wavelength? Visible light (VIS) or microwaves?
• Which color of light has the shortest wavelength, and thus highest frequency?
Concept Questions:
violet
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6.2Quantized Energy and
Photons
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• While the wave model explains many aspects of the nature of light, there are several phenomena it does not explain
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The Nature of Energy
• It doesn’t explain how an object can glow when its temperature increases (blackbody radiation) or why the color of the glowing objects varies with the temperaturered-hot objects are
cooler than white-hot
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The Nature of Energy• Max Planck physicist who
explained the relationship between temperature, light intensity, & wavelengths of emitted radiation
• Planck assumed energy could only be released or absorbed by atoms in discrete “chunks” called quanta (the smallest quantity of energy emitted/absorbed by radiation)
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• A single quanta has a distinct amount of energy as given in the following equation: E = h h = 6.63 10−34 J•s (Planck’s constant)
• Since energy is emitted or absorbed in discrete chunks, energy can only be absorbed/released as a whole # multiple of Plank’s constant x frequencyh , 2h, 3h Since energy is restricted to multiples only, it is
said to be quantized (staircase analogy)
Quantized Energy & Quantum Theory
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Photoelectric Effect
• In 1905, Einstein used Planck’s quantum theory to explain the photoelectric effect.In experiments, it was observed that light shining on
a clean metal surface causes e– to be emittedFor each unique metal, light below a minimum
threshold frequency resulted in NO e– being emitted
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Photoelectric Effect• The details of this effect contradicted classical
physics which says radiation acts as wavesWave theory cannot predict why frequency is the
crucial factor for electron emission (wave theory supports that intensity of light would be the main factor but even the most intense light at a low frequency will not emit e–)
• Einstein explained the photoelectric effect by assuming that light is made up of photons (particles) each with an energy given by, E = h
http://phet.colorado.edu/en/simulation/photoelectric
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The Nature of Energy
• Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light:
c = E = h
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Practice Question:• A photon of energy has a frequency of 4.13
x1014 Hz. What is the wavelength, in nanometers, of this photon. What color of the visible spectrum would it appear to be?
• c = = 3.0 x 108 m/s 4.13 x1014 Hz
= 7.26 x 10-7 m 109 nm = 726 nm = red 1 m
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Practice Question:• The red light from a helium-neon laser has a
wavelength of 633 nm . What is the energy of one photon?
• c = and E = h l = 633 nm 1 m = 6.33 x 10-7 m
109 nm
E = hc = (6.63 x 10-34 Js)(3.0 x 108 m/s)
6.33 x 10-7 m
= 3.14 x10-19 J
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6.3Line
Spectra + Bohr Model
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Q1: The Nature of Energy
Another mystery that could not be explained by wave theory involved the emission spectra observed from energy emitted by atoms and molecules.
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Q1: Continuous Spectra
• Some sources of radiation emit a single wavelength (laser)This radiation is monochromatic (of one color)
• Most radiant energy emits several wavelengths at once (lightbulbs = white light = all colors and wavelengths reflected)When this type of radiation is sent through a
prism, it is separated into its component wavelengths (forms a continuous spectrum of the rainbow)
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Q1: Line Spectra• Not all radiation produces a continuous
spectrum of colorsWhen gases are placed under pressure in a tube
(and electricity is applied) the gases emit different colors of light (sodium = yellow, neon = red-orange)
When this light is passed through a prism, the result is a spectrum containing only a few specific wavelengths (this is known as a line emission spectra)
Every gas has a unique line spectra often referred to as it’s “fingerprint”
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Line Spectra
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• Niels Bohr assumed e– moved around the nucleus in distinct circular paths called orbits (aka: planetary model)Each orbit around the nucleus
has a different “n” value (known as the principle quantum number) • As “n” increases, so does
the radius size of the orbit and the distance of the orbit from the nucleus
Q2 & 3: Bohr Model of the Atom
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Q2,3,&4: Bohr Model of the Atom• Each orbit has a specific quantity
of energy which increases as the value of “n” increases Bohr, like Planck, believed
energy was quantized• n = 1 is the lowest energy level; e–
in this orbit are known as ground state e– and are the most stable
• When electrons are in higher energy level (n = 2 through 7) they are called excited state e–
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Q2 & 4: Electron “Jumping”• According to Bohr, electrons can “jump”
between energy levels only if the exact amount of energy needed was gained or lost by the e– (like rungs on a ladder)
• e– demotion = moving from higher lower “n” will emit radiant energy (energy released)
• e– promotion = moving from lower higher “n” will absorb radiant energy (energy required)
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The Rydberg Equation
The energy absorbed or emitted (ΔE) from the process of electron “jumping” can be calculated by the equation:
E = −RH ( )1nf
2
1ni
2-
• RH = Rydberg constant = 2.18 10−18 J
• ni and nf = initial and final energy levels of the e– e– demotion = - ΔE e– promotion = + ΔE
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Explanation - Line Emission Spectra• The specific spectral lines seen when an
element’s radiant energy is separated through a prism can mathematically be related to the Rydberg equation Thus, the existence of these spectral lines is
due to the quantized jumps made by e– between energy levels
Since each element has a different # of e– (in different energy levels), the energy of each “jump” will be different, resulting in unique (and colors) for every element = unique line emission spectra!!!
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Q5: Limitations of Bohr Model• Bohr model offers an accurate explanation for the
Hydrogen line emission spectra (b/c it only has one e–), but does not as accurately apply to the spectra of other atoms
• Also, his model only views the electron as a particle and ignores the wavelike properties that exist
• Thus, the Bohr model was only a step towards a more comprehensive atomic model, but it did produce two significant ideas:
1) electrons can only exist in discrete energy levels
2) energy is involved in moving electrons between the energy levels
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6.4The Wave
Behavior of Matter
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• Louis de Broglie postulated that if light can behave as particles of matter, then matter should also be able to exhibit wave properties (“matter waves”)Ex) e– moving about the nucleus as a wave would
have characteristic wavelength & frequencyThe (in m) of any matter would depend on its
mass (in kg) & velocity (m/s)
For matter with an ordinary mass (even just a golf ball) the would be so tiny it would be imperceptible
Q1: The Wave Behavior of Matter
= hmv
1 J = 1 kg•m2
s2
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The de Broglie Equation
Determine the wavelength of the following:
a) A 7000 g bowling ball rolls with a velocity of 8.0 m/s.
= 6.63 x 10-34 J•s = 1.18 x 10-35 m
(7.0 kg)(8.0 m/s)
b) What is the wavelength of an electron moving at 5.31 x 106 m/s? The mass of an electron is 9.11 x 10-31 kg
= 6.63 x 10-34 J•s = 1.37 x 10-10 m
(9.11 x 10-31 kg)(5.31 x 106 m/s)
=h
mv
http://www.youtube.com/watch?v=JIGI-eXK0tg
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Proof of de Broglie Theory• A few years after his proposed theory,
experimental results backed de BroglieElectrons passed through a solid crystal and were
diffracted (broken up around slits just like a beam of light)
The double-slit experiment, demonstrates that matter and energy can display characteristics of both waves and particles
This technique leads to the development of the electron scanning microscope
http://www.youtube.com/watch?v=MTuyEn-ngIQ
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Chicken Embryo; Termite; Dust Mite; Spider
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Q2: The Uncertainty Principle• The dual nature of matter places a fundamental
limitation on how accurately both the speed and position of an object can be knownThis limitation becomes important only when matter is
of subatomic size
• Werner Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known:Therefore, it is impossible to know both the
location and momentum of an electron
(x) (mv) h4
The smaller the mass, the more uncertainty there is in its position
http://www.youtube.com/watch?v=32oUlB2BfEA
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Bohr’s Model… incorrect• Why does the Bohr model of the atom violate
the uncertainty principle?• Bohr thought e– traveled in orbits
this cannot be true, b/c then the exact path and position of an e– would be known at all times
• De Broglie’s hypothesis and Heisenberg's uncertainty principle set the stage for a new model of the atomRecognizes the wave nature of e– and the
distinct energy levels that Bohr founded to describe the probable location of an e–
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Quiz Review: 6.1 – 6.4• List all 7 types of radiation on the EM Spectrum in
order of increasing frequency.Radio, Microwaves, IR, Visible, UV, X-rays, Gamma rays
• There is a(n) ____________ relationship between wavelength and frequency.
• Energy and frequency are _____________ proportional to one another, meaning as one increases, the other _____________.
• The units for: Frequency: _______________ Wavlength: _______________ Energy: ______________
indirect
directly
increases
Hz = s-1
m or nm
J
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Quiz Review: 6.1 – 6.4• Important Equations to MEMORIZE (constants will
be given) c = = E h [Rydberg]
E = hc = h
E = −RH ( )1nf
2
1ni
2-
• Continuous spectra vs. line spectra• Photoelectric effect – Einstein proved that waves behaved as particles• Bohr model of the atom
Energy levels/orbits, ground state vs. excited state Useful parts of the Bohr model?
• Absorbtion/Emissison of energy & electron jumping (relationship to quantized energy
• Heisenberg’s Uncertainty Principle – how does Bohr’s model violate this principle?
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6.5Quantum Mechanics & Atomic Orbitals
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Quantum Mechanics• In 1926, Erwin Schrödinger developed an equation
(Schrodinger’s wave equation), which incorporated both the wave and particle natures of matter
• This new way of dealing with subatomic particles is known as quantum mechanics.
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Quantum Mechanical Model• Applies Heisenberg’s
uncertainty principle and distinct energy levels from Bohr model
• The quantum mechanical model of the atom statistically describes a general region of space around the nucleus where an electron is likely to be found at any given instant
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Electron Density Distribution• From Schrodinger’s
wave equation, locations around the nucleus with the highest density of plotted “dots” represent the areas around the nucleus where an e– is most likely to be found
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Quantum Numbers
• Mathematically solving the wave equation gives a set of wave functions (aka: orbitals) and their corresponding energies.
• Each orbital …describes the distribution of electron
density in space.has a characteristic energy & shape
• An orbital is described by a set of three quantum numbers.
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Principal Quantum Number, n• Also seen in Bohr model, this quantum
number describes the energy level in which the orbital resides.
• n values are positive integers (starting at 1) • As n increases…
the orbital become larger e– spend more time further from the
nucleus e– have a higher energy
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Azimuthal Quantum Number, l
• This quantum number defines the shape of the orbital
• Values of l are integers ranging from 0 to n − 1.
• We use alphabetical letters (s, p, d, f) to
communicate the different values of l and, therefore, the shapes and types of orbitals (seen in section 6.6)
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Magnetic Quantum Number, ml
• Describes the three-dimensional orientation of the orbital (how the shape is oriented in space)
• Values are integers ranging from -l to l :
−l ≤ ml ≤ l• Therefore, on any given energy level,
there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.
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Quantum NumbersValue of n 1 2 3 4
Value of l(n-1)
0 1 2 3
Type of orbital s p d f
Value of ml
(-l l )
0
(1)
-1, 0, 1
(3)
-2, -1, 0, 1, 2
(5)
-3, -2, -1, 0, 1, 2, 3
(7)
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• Orbitals with the same principle quantum number, n, form an electron shell.
• Different orbital types within a shell are subshells 1s; 2s, 2p; 3s, 3p, 3d; 4s, 4p, 4d, 4f
Table 6.2
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Practice:• What is the designation for the subshell
with…n = 5 and l = 3?n = 3 and l = 2?
• How many magnetic quantum #s (ml ) are involved in each subshell? Label them n = 5 and l = 3? n = 3 and l = 2?
… 5f
… 3d
… 7 = -3, -2, -1, 0 , 1, 2, 3
… 5 = -2, -1, 0 , 1, 2
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6.6Representat
ions of Orbitals
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Orbital Shapes• Recall…the shape of an orbital is described
by its azimuthal quantum #, l• l = 0 = s
every n value has an l of 0, thus an s orbital
• l = 1 = p only n = 2 or above has an l of 1, thus a p orbital
• l = 2 = d only n = 3 or above has an l of 2, thus a d orbital
• l = 3 = f only n = 4 or above has an l of 3, thus a f orbital
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s Orbitals
• Lowest energy orbitals• Spherical in shape• Radius of sphere
increases with increasing value of n
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s OrbitalsGraph - 6.18: Probability of finding an e– Vs. distance from the nucleus…
s orbitals possess nodes, which are regions where there is zero probability of finding an e–
The likelihood of finding e– further from then nucleus increases as the n value increases
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p Orbitals• “dumbbell” shaped
e– density concentrated on either side of the nucleus (two lobes with a node between them)
• Since there are 3 ml values for p orbitals, there are 3 orientations in space (px, py, pz)For the same n value, each orientation is the same size
& of equal energy (larger n = bigger & more energy)
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d Orbitals• There are five d
orbital orientations4 of them have 4
lobes like “four-leaf clovers”
the 5th resembles a p orbital with a doughnut around the center.
For a given n, all 5 orientations have equal energy (orbitals w/same energy are known as degenerate)
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f Orbitals• There are seven f orbital orientations
For a given n, all 7 orientations are degenerate (have equal energy)
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6.7Many-
Electron Atoms
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Energies of Orbitals• In a hydrogen atom, (where there is only one e–)
all the orbitals with the same n value have the same amount of energy regardless of orbital shape (s, p, d, & f are degenerate)
ElectronicStructureof Atoms
Energies of Orbitals• For multi-electron atoms, as the # of e–
increases, so does the repulsion between them.• Therefore, in multi-electron atoms, orbitals of the
same n energy level are NOT degenerate.
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• The energy of the orbital increases as the l value increasesEnergy for a
given n value is, s < p < d < f
* notice, all five 3d orbitals are still degenerate (same energy level) but 3s < 3p < 3d
Energy Level
Diagram
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• In the 1920s, it was discovered that 2 e– in the same orbital, say a 2s, do not have exactly the same energy.
• The “spin” of an e– describes the direction it spins in a magnetic field, which affects its energy.This lead to 4th quantum #
• The spin quantum number has only 2 values: +1/2 and −1/2
The 4th Quantum Number:Spin Magnetic Quantum Number, ms
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Pauli Exclusion Principle• NO two e– in the same
atom can have the same set of all 4 quantum numbers n, l, ml , ms
Each orbital may hold a maximum of 2 e–, provided they have opposite spins (ms
values)Ex) A 3px orbital has the
same n, l, ml values but one e– must be +1/2 & one -1/2 to exist in the same orbital
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Orbitals & Electrons in Sublevels
Sublevel # Orbitals Max # electrons
s 1 2
p 3 6
d 5 10
f 7 14
* Each orbital can hold a max. of 2 e–
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6.8 - 6.9Electron Configurati
ons
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Three rules are used to build the electron configuration:
Pauli Exclusion Principle
Aufbau principle
Hund’s Rule
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• An orbital can hold only a max. of two electrons and they must have opposite spins.
• Electron Spin: +1/2 or -1/2
Pauli Exclusion Principle
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Aufbau Principle
• Electrons occupy orbitals of lowest energy first.
Generally, as n increases, the energy increases and s < p < d < f
However, this is not always the case…
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Incr
easi
ng e
nerg
y
1s
2s
3s
4s
5s6s
7s
2p
3p
4p
5p
6p
3d
4d
5d
7p 6d
4f
5f
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Diagram:Orbital Filling
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Blocks in the Periodic Table
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Hund’s Rule
• For degenerate orbitals (ex: the three p, five d, or seven f orbitals), the most stable atom (lowest energy) is attained when the number of e– with the same spin is maximized• e– fill orbitals with parallel spins before
paring up
Analogy: Students fill each seat of a school bus, one person at a time, before sitting together.
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Types of Electron Configurations
• Orbital Diagrams shows electrons filling the sublevels in ordereach box represents one orbital subleveluses arrows to represent e–
direction of the arrow represents the spin of the electron.
• Standard Electron Configuration
• Condensed Electron Configurationuses the noble gases as a shortcut
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Orbital Diagram for Hydrogen# e– = 1
Aufbau Principal!
WS Packet pg. 1
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OrbitalDiagram for
Helium
# e– = 2
Pauli Exclusion Principal!
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Orbital Diagram for
Lithium
# e– = 3
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Orbital Diagram for
Beryllium
# e– = 4
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Orbital Diagram for
Boron
# e– = 5
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OrbitalDiagram for
Carbon# e– = 6
Hunds Rule!
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Orbital Diagram for
Nitrogen
# e– = 7
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Orbital Diagram for
Oxygen
# e– = 8
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Electron Configurations
• Distribution of all e– in an atom
• Consist of… Number denoting
the principle energy level, n (also called an e– shell)
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Electron Configurations
• Consist of …Letter denoting
the type of orbital (subshell)
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Electron Configurations
• Consist of… Superscript
denoting the number of electrons in that orbital/subshell.
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Standard Electron Configurations
• Oxygen, 8 e–
1s22s22p4
• Neon, 10 e–
1s22s22p6
notice that the 2nd energy level (shell) is completely full 2 s and 6 p = 8 e– (octet)
outer most energy level being full makes noble gases very stable
ElectronicStructureof Atoms
Condensed (Noble Gas) E.C.• Use the LAST noble gas that is located in the
periodic table right before the element.• Write the symbol of the noble gas in brackets.• Write the remaining configuration after the
brackets.Aluminum: 1s22s22p63s23p1 or [Ne] 3s23p1
• The noble gas represents the inner “core” e–
• The remaining configuration focuses on the valence e– in the outermost shell (energy level)
ElectronicStructureof Atoms
Valence Electron Trend - down a column -
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Some Anomalies
• Some irregularities occur when there are enough e– to half-fill s and d orbitals on a given row.
• Ex) Chromium:
we would expect: [Ar] 4s2 3d4.
but really the E.C. is: [Ar] 4s1 3d5
• Because the 4s and 3d orbitals are very close in energy, an e– is moved from the s to the d orbital so that both are HALF-FULL
• Molybdenum and Tugsten behave the same way
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Some Anomalies
• A similar instance occurs with copper• Ex) Copper:
we would expect: [Ar] 4s2 3d 9.
but really the E.C. is: [Ar] 4s1 3d10
• Because the 4s and 3d orbitals are very close in energy, an e– is moved from the s to the d orbital so that the s is HALF-FULL and the d is COMPLETELY FULL
• Silver and Gold behave the same way