CHEMISTRY
The Central Science
9th Edition
Chapter 6
Electronic Structure of Atoms
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Chapter 6
6.1: The Wave Nature of Light
• Electromagnetic Radiation carries energy through space
• Speed of EMR through a vacuum: 3.00x108 m/s
• wavelike characteristics:
• wavelength, l
(distance from crest to crest)
• amplitude, A (height)
• frequency, n (# of cycles which pass a point in 1 second)
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Chapter 6
The wave nature is
due to periodic
oscillations of the
intensities of
electronic and
magnetic forces
associated with the
radiation
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Chapter 6
The # of times the
cork bobs up and
down is the
frequency
Text, P. 200
• The speed of a wave, c, is given by its frequency
multiplied by its wavelength:
c  nl
• For light, speed = c (that is 3.00 x 108m/s)
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Chapter 6
• Modern atomic theory arose out of studies of the
interaction of radiation with matter
• Example: the visible spectrum
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Chapter 6
The Electromagnetic Spectrum, P. 201
(or Hz)
Text, P. 201
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Chapter 6
• Sample Problem #7
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Chapter 6
6.2: Quantized Energy and Photons
• Problems with wave theory:
– Emission of light from hot objects
• “black body radiation”: stove burner, light bulb filament
– The photoelectric effect
– Emission spectra
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Chapter 6
• Planck: energy can only be absorbed or released from
atoms in certain amounts called quanta
• The relationship between energy and frequency is
E  hn
where h is Planck’s constant (6.626  10-34 J-s)
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Chapter 6
Quantization Analogy:
Consider walking up a ramp versus walking up stairs:
For the ramp, there is a continuous change in height
Movement up stairs is a quantized change in height
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Chapter 6
The Photoelectric Effect
• Evidence for the particle nature of light -- “quantization”
• Light shines on the surface of a metal: electrons are
ejected from the metal
• threshold frequency must be reached
• Below this, no electrons are ejected
• Above this, the # of electrons ejected depends on the
intensity of the light
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Chapter 6
Text, P. 204
• Einstein assumed that light traveled in energy packets
called photons
• The energy of one photon:
E  hn
• Energy and frequency are directly proportional
• Therefore radiant
energy must be quantized!
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Chapter 6
• Sample Problems # 13, 17, 19
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Chapter 6
6.3: Line Spectra and the Bohr Model
Line Spectra
• Radiation that spans an array of different wavelengths:
continuous
• White light through a prism: continuous spectrum of colors
• Spectra tube emits light unique to the element in it
• Looking at it through a prism, only lines of a few
wavelengths are seen
• Black regions correspond to wavelengths that are absent
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Chapter 6
Continuous Visible Spectrum, P. 206
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Chapter 6
Bohr Model
• Rutherford model of the atom: electrons orbited the
nucleus like planets around the sun
• Physics: a charged particle moving in a circular path
should lose energy
• Therefore the atom should be unstable
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Chapter 6
3 Postulates for Bohr’s theory:
1. Electrons move in orbits that have defined energies
2. An electron in an orbit has a specific energy
3. Energy is only emitted or absorbed by an electron as it
changes from one allowed energy state to another
(E=hν)
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Chapter 6
• Since the energy states are quantized,
the light emitted from excited atoms must be quantized and
appear as line spectra
• Bohr showed that
18  1 
E   2.18  10
J 
 n2 
where n is the principal quantum number (i.e., n = 1, 2,
3, … and nothing else)
(
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
Chapter 6
• The first orbit in the Bohr model has n = 1, is closest to
the nucleus, and has the lowest energy (ground state)
• The furthest orbit in the Bohr model has n close to
infinity
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Chapter 6
• Electrons in the Bohr model can only move between orbits
by absorbing and emitting energy in quanta (hν)
• The amount of energy absorbed or emitted on movement
between states is given by
E  E f  Ei  hn
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Chapter 6
Sample
Problems # 21 and 27
Line Spectra, P. 207
The Balmer series for Hydrogen (nf = 2, which is in the visible region)
The Rydberg Equation (P. 206)
allows for the calculation of
wavelengths for all the spectral lines

 1
1
 (RH 

l Prentice Hall ©
n 2f2003 ni2

1





where RH 1.0974107 m 1
Chapter 6
Note the units
Paschen Series
Figure 6.14, P. 208
Balmer Series Energy Level
Diagram
Using the Rydberg Equation,
the existence of spectral lines
can be attributed to the
quantized jumps of electrons
between energy levels
(therefore justifying Bohr’s
model of the atom)
Sample Problems # 29 and 31
Lyman Series
The Electromagnetic Spectrum, P. 201
(or Hz)
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Chapter 6
Limitations of the Bohr Model
• It can only explain the line spectrum of hydrogen
adequately
• Electrons are not completely described as small particles
• It doesn’t account for the wave properties of electrons
• DEMOS!
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Chapter 6
6.4:The Wave Behavior of Matter
• Using Einstein’s and Planck’s equations, de Broglie
showed:
h
l
mv
• The momentum, mv, is a particle property, but l is a
wave property
• Sample Exercise 6.5, P. 210
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Chapter 6
The Uncertainty Principle
• Heisenberg’s Uncertainty Principle: we cannot
determine exactly the position, direction of motion, and
speed of an electron simultaneously
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Chapter 6
6.5: Quantum Mechanics and
Atomic Orbitals
• Erwin Schrödinger proposed an equation that contains
both wave and particle terms
• Solving the equation leads to wave functions (shape of
the electronic orbital)
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Chapter 6
Text, P. 213
The electron density
distribution in the ground
state of the hydrogen atom
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Chapter 6
•
•
•
•
Orbitals and Quantum Numbers
If we solve the Schrödinger equation, we get wave
functions
for the
wave functions.
If we solveand
theenergies
Schrödinger
equation,
we get wave
• We calland
functions
wave
energies
functions
for the
orbitals
wave(regions
functionsof highly
electron
location).
• probable
We call wave
functions
orbitals (regions of highly
probable electron location)
Schrödinger’s equation requires 3 quantum numbers:
1.
Principal Quantum
Number,
n 3 quantum numbers:
Schrödinger’s
equation
requires
This isQuantum
the same asNumber,
Bohr’s n.
1. Principal
n
becomes
ThisAs
is nthe
same aslarger,
Bohr’sthe
n atom becomes larger and the electron
further from
thethe
nucleus.
As nisbecomes
larger,
atom becomes larger and the electron is
further from the nucleus
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Chapter 6
2. Azimuthal Quantum Number, l
This quantum number depends on the value of n
The values of l begin at 0 and increase to (n - 1)
We usually use letters for l (s, p, d and f for l = 0, 1, 2, and 3)
Usually we refer to the s, p, d and f-orbitals (the shape of the
orbital) (AKA “subsidiary quantum number”)
3. Magnetic Quantum Number, ml
This quantum number depends on l
The magnetic quantum number has integral values
between -l and +l
Magnetic quantum numbers give the 3D orientation of each orbital
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Chapter 6
•As n increases, note that
the spacing between
energy levels becomes
smaller
“Aufbau Diagram”:
electrons fill low
energy orbitals first
Figure 6.17, P. 215
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Chapter 6
• Sample Problems # 41, 43, & 45
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Chapter 6
6.6: Representations of Orbitals
The s-Orbitals
• All s-orbitals are spherical
• As n increases, the s-orbitals get larger
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Chapter 6
Text, P. 216
the s orbitals
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Chapter 6
The p-Orbitals
• There are three p-orbitals px, py, and pz
• The three p-orbitals lie along the x-, y- and z- axes of a
Cartesian system
• The letters correspond to allowed values of ml of -1, 0,
and +1
• The orbitals are dumbbell shaped
• As n increases, the p-orbitals get larger
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Chapter 6
Text, P. 216
the p orbitals
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Chapter 6
The d and f-Orbitals
• There are five d and seven f-orbitals
FYI for the d-orbitals:
•
•
•
•
Three of the d-orbitals lie in a plane bisecting the x-, y- and z-axes
Two of the d-orbitals lie in a plane aligned along the x-, y- and z-axes
Four of the d-orbitals have four lobes each
One d-orbital has two lobes and a collar
•
Text, P. 217
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Chapter 6
the d orbitals
Text, P. 217
the f orbitals
(not in text)
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Chapter 6
• http://www.uky.edu/~holler/html/orbitals_2.html
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Chapter 6
Text, P. 214
Max = (n-1)
l  letter
(-l to +l)
(n2)
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Chapter 6
6.7: Many-Electron Atoms
Orbitals and Their Energies
• Orbitals of the same energy are said to be degenerate
• For n  2, the s- and p-orbitals are no longer degenerate
because the electrons interact with each other
• Therefore, the Aufbau diagram looks slightly
different for many-electron systems
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Chapter 6
BOHR
MODERN
Text, P. 215
Text, P. 218
Electron Spin and the Pauli Exclusion
Principle
• Since electron spin is also
quantized, we define
• ms = spin quantum # =  ½
Text, P. 219
• Pauli’s Exclusion Principle: no two electrons can have
the same set of 4 quantum numbers
•
•
•
Therefore, two electrons in the same orbital must have
opposite spins
Electron capacity of sublevel = 4l + 2
Electron capacity of energy level = 2n2
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Chapter 6
• Sample Problems # 51 & 55
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Chapter 6
6.8: Electron Configurations
Hund’s Rule
• Electron configurations tell us in which orbitals the
electrons for an element are located
• Three rules are applied:
•
•
•
Aufbau Principle
Pauli’s Exclusion Principle
Hund’s Rule: for degenerate orbitals, electrons fill each
orbital singly before any orbital gets a second electron
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Chapter 6
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Chapter 6
Aufbau Diagram
Types of electron configurations
• Electron configuration notation: energy level, subshell,
# of electrons per orbital
• Orbital notation: each ml value is represented by a line,
electrons are also shown
• Noble gas configuration: “condensed configuration”
[Proceeding noble gas] electron configuration notation for
outer shell electrons
Inner
shell
e
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Chapter 6
6.9: Electron Configurations and
the Periodic Table
• The periodic table can be used as a guide for electron
configurations
• The period number is the value of n
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Chapter 6
# of columns is related to the
number of electrons that can fit
in the subshells
Regular
trends
Irregularities: half filled and
completely filled subshells are
stable
Text, P. 227
• Sample Problems # 59, 61, 63 & 65
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Chapter 6
End of Chapter 6
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Chapter 6