CHAPTER 6
• The Structure of Atoms
1
Electromagnetic Radiation
Mathematical theory that describes all
forms of radiation as oscillating (wavelike) electric and magnetic fields
2
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)
3
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?
4
Electromagnetic Spectrum
wavelength increases
energy increases
frequency increases?
5
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)
6
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
7
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?
8
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)
9
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
10
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
11
Adsorption/Emission Spectra
12
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
R  1.097  107 m -1
Principle quantum number
n1  n 2
n’ s refer to the numbers
of the energy levels in the
emission spectrum of hydrogen
13
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
14
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)
15
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
16
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...
17
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)
18
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)
19
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
20
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
21
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
22
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
23
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
24
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)
25
The Principal Quantum Number (n)
-
8
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)
26
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)
27
Atomic suborbital
• s orbitals are spherically symmetric
s orbital properties:
one s orbital for every n-level: l = 0
28
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
29
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
30
Atomic suborbital
• s orbitals are spherically symmetric
s orbital properties:
31
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)
32
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
33
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)
34
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
35
d Orbital Shape
36
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
37
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
38
f Orbital Shape
One of 7 possible f orbitals
All have 3 planar surfaces
39
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
40
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
41
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
42