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CHAPTER 6
• The Structure of Atoms
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Electromagnetic Radiation
Mathematical theory that describes all
forms of radiation as oscillating (wavelike) electric and magnetic fields
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Figure 7.1
Wave Properties
Wavelength (l):
distance between consecutive crests or troughs
Frequency (n):
number of waves that pass a given point in some unit
of time (1 sec)
-units of frequency 1/time such as 1/s = s-1 = Hz
Amplitude (A):
Amplitude
the maximum height of a wave
Nodes:
points of zero amplitude
-every l/2
wavelength
Node (l/2)
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Wave Properties
• c = l
for electromagnetic radiation
Speed of light (c):
2.99792458 x 108 m/s
Example: What is the frequency of green light of
wavelength 5200 Å?
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Electromagnetic Spectrum
wavelength increases
energy increases
frequency increases?
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Planck’s Equation
E = h•n
Maxwell Planck
h = Planck’s constant = 6.6262 x 10-34 J•s
Any object can gain or lose energy by absorbing
or emitting radiant energy
-only certain vibrations (n) are possible (Quanta)
-Energy of radiation is proportional to frequency
(n)
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Planck’s Equation
Maxwell Planck
E = h • n =hc/l
Light with large l (small n) has a small E
Light with a short l (large n) has a large E
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Planck’s Equation
What is the energy of a photon of green
light with wavelength 5200 Å? What is
the energy of 1.00 mol of these
photons?
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Einstein and the Photon
Photoelectric effect: the production of electrons (e-)
when light (photons) strikes the surface of a metal
-introduces the idea that light has particle-like
properties
-photons: packets of massless “particles” of
energy
-energy of each photon is proportional to the
frequency of the radiation (Planck’s equation)
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Atomic Spectra and the Bohr Atom
Line emission spectrum: electric current passing
through a gas (usually an element) causing the atoms
to be excited
-This is done in a vacuum tube (at very low
pressure) causing the gas to emit light
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Atomic Spectra and the Bohr Atom
• Every element has a unique spectrum
– -Thus we can use spectra to identify elements.
– -This can be done in the lab, with stars, in fireworks, etc.
H
Hg
Ne
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Adsorption/Emission Spectra
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Atomic Spectra
• Balmer equation (Rydberg equation):
relates the wavelengths of the lines (colors) in the
atomic spectrum
 1
1
1 
 R  2  2 
l
 n1final n 2int
R is the Rydberg constant
Principle quantum number
R  1.097  107 m -1
n1  n 2
n’ s refer to the numbers
of the energy levels in the
emission spectrum of hydrogen
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Atomic Spectra
What is the wavelength of light emitted when
the hydrogen atom’s energy changes from
n = 4 to n = 2?
nfinal = 2
ninitial = 4
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The Bohr Model
 Bohr’s greatest contribution to
science was in building a simple
model of the atom
 It was based on an understanding
of the SHARP LINE EMISSION
SPECTRA of excited atoms
Niels Bohr
(1885-1962)
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The Bohr Model
Early view of atomic structure from the beginning of the
20th century
-electron (e-) traveled around the nucleus in an orbit
-
 Any orbit should be possible and so is any energy
 But a charged particle moving in an electric field
should emit (lose) energy
 End result is all matter should self-destruct
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The Bohr Atom
• In 1913 Neils Bohr incorporated Planck’s
quantum theory into the hydrogen spectrum
explanation
– Here are the postulates of Bohr’s theory:
1. Atom has a definite and discrete number of
energy levels (orbits) in which an electron
may exist
n – the principal quantum number
As the orbital radius increases so does the
energy (n-level) 1<2<3<4<5...
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The Bohr Atom
2. An electron may move from one discrete energy
level (orbit) to another, but to do so energy is
emitted or absorbed
3. An electron moves in a spherical orbit around the
nucleus
-If e- are in quantized energy states,
then ∆E of states can have only certain
values
-This explains sharp line spectra
(distinct colors)
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Atomic Spectra and Niels Bohr
Niels Bohr
 Bohr’s theory was a great
accomplishment
 Received Nobel Prize, 1922
 Problem with this theory- it only
worked for H
-introduced quantum idea artificially
-new theory had to developed
(1885-1962)
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Wave Properties of the Electron
de Broglie (1924)
 proposed that all moving objects
have wave properties
For light:
Louis de Broglie
(1892-1987)
E = mc2
E = hn = hc/l
Therefore, mc = h/l
For particles:
(mass)(velocity) = h/l
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The Wave Properties of the Electron
In 1925 Louis de Broglie published his Ph.D. dissertation
•  Electrons have both particle and wave-like
characteristics
 All matter behave as both a particle and a wave
– This wave-particle duality is a fundamental property of
submicroscopic particles
de Broglie’s Principle:
h
l
mv
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h  Planck’ s constant, m  massof particle, v  velocity of particle
The Wave Nature of the Electron
Determine the wavelength, in meters, of an electron,
with mass 9.11 x 10-31 kg, having a velocity of
5.65 x 107 m/s
Remember Planck’s constant is 6.626 x 10-34 J s which is also
equal to 6.626 x 10-34 kg m2/s, because 1 J = 1 kg m2/s2
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Quantum (Wave) Mechanics
 Schrödinger applied ideas of ebehaving as a wave to the problem of
electrons in atoms
-He developed the WAVE EQUATION
-The solution gives a math expressions
called WAVE FUNCTIONS, 
Erwin Schrödinger
1887-1961
y2
-Each  describes an allowed energy
state for an e- and gives the probability
(2) of the location for the e-
 Quantization is introduced naturally
200 pm
.
50 pm
0
100
r (pm)
200
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Uncertainty Principle
The problem with defining
the nature of electrons in
atoms was solved by W.
Heisenberg
 the position and momentum
(momentum = m•v) cannot
be define simultaneously for
Werner Heisenberg
an electron
1901-1976
  ??? we can only define eenergy exactly but we
cannot know the exact
n-levels
position of the e- to any
degree of certainty. Or vice
versa
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Schrödinger’s Atomic Model
Atomic orbitals: regions of space where the probability
of finding an electron around an atom is greatest
• quantum numbers: letter/number address describing
an electrons location (4 total)
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The Principal Quantum Number (n)
-
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n = 1, 2, 3, 4, ...
electron’s energy depends mainly on n
n determines the size of the orbit the e- is in
each electron in an atom is assigned an n value
atoms with more than one e- can have more
than one electron with the same n value (level)
- each of these e- are in the same electron energy
level (or electron shell)
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Angular Momentum (l)
l = 0, 1, 2, 3, 4, 5, .......(n-1)
l = s, p, d, f, g, h, .......(n-1)
-the names and shapes of the corresponding
subshells (or suborbitals) in the orbital/energy level
(n-level)
– -each l corresponds to a different suborbital shape
or suborbital type within an n-level
If n=1, then l = 0 can only exist (s only)
If n=2, then l = 0 or 1 can exist (s and p)
If n=3, then l = 0, 1, or 2 can exist (s, p and d)
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Atomic suborbital
• s orbitals are spherically symmetric
s orbital properties:
one s orbital for every n-level: l = 0
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p Orbital
The three p-orbitals lie 90o apart in space
There are 3 p-orbitals for every n-level (when n ≥ 2):
l=1
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Magnetic Quantum Number (ml)
ml = - l , (- l + 1), (- l +2), .....0, ......., (l -2), (l -1), +l
– Example: ml for l = 0, 1, 2, 3, …l
– 0, +1 0 -1, +2 +1 0 -1 -2, +3 +2 +1 0 -1 -2 -3, …+l through –l
-This describes the number of suborbitals and direction each suborbital faces
within a given subshell (l) within an orbital (n)
-There is no energy difference between each suborbital (ml) set
– If l = 0 (or an s orbital), then ml = 0 for every n
• Notice that there is only 1 value of ml.
This implies that there is one s orbital per n value, when n  1
– If l = 1 (or a p orbital), then ml = -1, 0, +1 for n-levels >2
• There are 3 values of ml for p suborbitals.
Thus there are three p orbitals per n value, when n  2
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Atomic suborbital
• s orbitals are spherically symmetric
s orbital properties:
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one s orbital for every n-level: l = 0 and only 1 value for ml
p Orbital Properties
The first p orbitals appear in the n = 2 shell
-p orbitals have peanut or dumbbell shaped volumes
-They are directed along the axes of a Cartesian
coordinate system.
• There are 3 p orbitals per n-level:
– -The three orbitals are named px, py, pz.
– -They all have an l = 1 with different ml
– -ml = -1, 0, +1 (are the 3 values of ml)
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p Orbitals
When n = 2, then l = 0 and/or 1
Therefore, in n = 2 shell there are
2 types of suborbitals/subshells
For l = 0
ml = 0
this is an s subshell
For l = 1
ml = -1, 0, +1
this is a p subshell
with 3 orientations
When l = 1, there is
a single PLANAR
NODE thru the
nucleus
• p orbitals are peanut or dumbbell shaped
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d Orbital Properties
The first d suborbitals appear in the n = 3 shell
• -The five d suborbitals have two different shapes:
–
4 are clover shaped
–
1 is dumbbell shaped with a doughnut
around the middle
• -The suborbitals lie directly on the Cartesian axes
or are rotated 45o from the axes
There are 5d orbitals per n level:
–The
five orbitals are named d xy , d yz , d xz , d x 2 - y2 , d z 2
–They all have an l = 2 with different ml
ml = -2,-1,0,+1,+2 (5 values of m l)
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d Orbitals
s orbitals l = 0, have no planar
node, and so are spherical
p orbitals l = 1, have 1 planar
node, and so are “dumbbell”
shaped
This means d orbitals with l = 2,
have 2 planar nodes, and so
have 2 different shapes
(clover and dumbbell with a
donut)
Figure 7.16
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d Orbital Shape
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f Orbitals
• There are 7 f orbitals with l =3
• ml = -3, -2,-1,0,+1,+2, +3
(7 values of ml)
-These orbitals are hard to visualize or describe
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f Orbitals
When n = 4, l = 0, 1, 2, 3 so there are 4 subshells in
this orbital (energy level)
For l = 0, ml = 0
---> s subshell with single suborbital
For l = 1, ml = -1, 0, +1
---> p subshell with 3 suborbitals
For l = 2, ml = -2, -1, 0, +1, +2
---> d subshell with 5 suborbitals
For l = 3, ml = -3, -2, -1, 0, +1, +2, +3
---> f subshell with 7 suborbitals
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f Orbital Shape
One of 7 possible f orbitals
All have 3 planar surfaces
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Spin Quantum Number (ms)
Describes the direction of the spin the electron
has
only two possible values:
ms = +1/2 or -1/2
ms = ± 1/2
proven experimentally that electrons have spins
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Spin Quantum Number
Spin quantum number effects:
Every orbital can hold up to two electrons
Why?
The two electrons are designated as having:
one spin up  and one spin down 
Spin describes the direction of the electron’s
magnetic fields
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Electron Spin and Magnetism
Diamagnetic:
NOT attracted to a magnetic field
-they are repelled by magnetic fields
-no unpaired electrons
Paramagnetic:
are attracted to a magnetic field
-unpaired electrons
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