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Modern Atomic Theory
Chapter 10
1
Electromagnetic Radiation
• Classical physics says matter made up of
particles, energy travels in waves
• Electromagnetic Radiation is radiant energy,
both visible and invisible
• Electromagnetic radiation travels in waves
• All waves are characterized by their velocity,
wavelength, amplitude, and the number of
waves that pass a point in a given time
2
Figure 10.1 (a): A light wave
3
Electromagnetic Waves
• velocity = c = speed of light
– 2.997925 x 108 m/s
– all types of light energy travel at the same speed
• amplitude = A = measure of the intensity of the
wave, “brightness”
• wavelength = = distance between two consecutive
peaks or troughs in a wave
– generally measured in nanometers (1 nm = 10-9 m)
– same distance for troughs
• frequency = = the number of waves that pass a
point in space in one second
– generally measured in Hertz (Hz),
– 1 Hz = 1 wave/sec = 1 sec-1
• c=x
4
Figure 10.2: The different wavelengths of
electromagnetic radiation
5
Planck’s Revelation
• Showed that light energy could be thought
of as particles for certain applications
• Stated that light came in particles called
quanta or photons
• Particles of light have fixed amounts of
energy
– Basis of quantum theory
• The energy of the photon is directly
proportional to the frequency of light
– Higher frequency = More energy in photons
E h
E
hc
6
Figure 10.3: Electromagnetic radiation
7
Problems with Rutherford’s
Nuclear Model of the Atom
• Electrons are moving charged particles
• Moving charged particles give off energy
• Therefore the atom should constantly be
giving off energy
• And the electrons should crash into the
nucleus and the atom collapse!!
8
Atomic Spectra
• Atoms which have gained extra energy release that
energy in the form of light
• The light atoms give off or gained is of very
specific wavelengths called a line spectrum
– light given off = emission spectrum
– light energy gained = absorption spectrum
– extends to all regions of the electromagnetic spectrum
• Each element has its own line spectrum which can
be used to identify it
9
Figure 10.5: Absorption and Emission Processes
Absorption
Emission
10
Figure 10.6: When an excited H atom returns to a
lower energy level, it emits a photon that contains
the energy released by the atom
11
Atomic Spectra
• The line spectrum must be related to energy
transitions in the atom.
– Absorption = atom gaining energy
– Emission = atom releasing energy
• Since all samples of an element give the exact
same pattern of lines, every atom of that element
must have only certain, identical energy states
• The atom is quantized
– If the atom could have all possible energies, then the
result would be a continuous spectrum instead of lines
12
Figure 10.7: When excited hydrogen atoms return to
lower energy states, they emit photons of certain
energies, and thus certain colors
13
Figure 10.9: Each
photon emitted by
an excited
hydrogen atom
corresponds to a
particular energy
change in the
hydrogen atom
14
Bohr’s Model
• Explained spectra of hydrogen
• Energy of atom is related to the distance
electron is from the nucleus
• Energy of the atom is quantized
– atom can only have certain specific energy states
called quantum levels or energy levels
– when atom gains energy, electron “moves” to a
higher quantum level
– when atom loses energy, electron “moves” to a
lower energy level
– lines in spectrum correspond to the difference in
energy between levels
15
Figure 10.10:
(a) Continuous
energy levels.
(b) Discrete
(quantized)
energy levels.
16
Figure 10.11: The difference between continuous
and quantized energy levels
17
Bohr’s Model
• Atoms have a minimum energy called the ground state
– therefore they do not crash into the nucleus
• The ground state of hydrogen corresponds to having its
one electron in an energy level that is closest to the
nucleus
• Energy levels higher than the ground state are called
excited states
– the farther the energy level is from the nucleus, the
higher its energy
• To put an electron in an excited state requires the addition
of energy to the atom; bringing the electron back to the
ground state releases energy in the form of light
18
Figure 10.13: The Bohr model of the hydrogen atom
19
Bohr’s Model
• Distances between energy levels decreases as the
energy increases
– light given off in a transition from the second energy
level to the first has a higher energy than light given off
in a transition from the third to the second, etc.
– Electrons “orbit” the nucleus much like planets orbiting
the sun
• 1st energy level can hold 2e-1, the 2nd 8e-1, the 3rd
18e-1, etc.
– farther from nucleus = more space = less repulsion
• The highest energy occupied ground state orbit is
called the valence shell
20
Figure 10.9: Each
photon emitted by
an excited
hydrogen atom
corresponds to a
particular energy
change in the
hydrogen atom
21
Problems with the Bohr Model
• Only explains hydrogen atom spectrum
– and other 1 electron systems
• Neglects interactions between electrons
• Assumes circular or elliptical orbits for
electrons - which is not true
22
Wave Mechanical
Model of the Atom
• Experiments later showed that electrons could be
treated as waves
– just as light energy could be treated as particles
– de Broglie
• The quantum mechanical model treats electrons as
waves and uses wave mathematics to calculate
probability densities of finding the electron in a
particular region in the atom
– Schrödinger Wave Equation
– can only be solved for simple systems, but approximated for
others
23
Figure 10.15:
The probability
map, or orbital,
that describes
the hydrogen
electron in its
lowest possible
energy state
24
Orbitals
• Solutions to the wave equation give regions in space
of high probability for finding the electron - these
are called orbitals
– usually use 90% probability to set the limit
– three-dimensional
• Orbitals are defined by three integer terms that are
added to the wave equation to quantize it - these are
called the quantum numbers
• Each electron also has a fourth quantum number to
represent the direction of spin
25
Figure 10.16: The hydrogen 1s orbital
26
Orbitals and Energy Levels
• Principal energy levels identify how much energy
the electrons in the orbital have
– n
– higher values mean orbital has higher energy
– higher values mean orbital has farther average distance
from the nucleus
• Each principal energy level contains one or more
sublevels
– there are n sublevels in each principal energy level
– each type of sublevel has a different shape and energy
– s<p<d<f
• Each sublevel contains one or more orbitals
– s = 1 orbital, p = 3, d = 5, f = 7
27
Figure 10.17: The first
four principal energy
levels in the hydrogen
atom
28
Figure 10.18: Principal levels can be divided into
sublevels
29
Figure 10.19:
Principal level
2 shown
divided into the
2s and 2p
sublevels
30
Figure 10.20: The relative sizes of the 1s and 2s
orbitals of hydrogen
31
Figure 10.21: The three 2p orbitals: (a) 2px, (b) 2pz,
(c) 2py.
32
Figure 10.22: A diagram of principal energy levels 1
and 2 showing the shapes of orbitals that compose
the sublevels
33
Figure 10.23: The relative sizes of the spherical 1s,
2s, and 3s orbitals of hydrogen
34
Figure 10.24: The shapes and labels of the five 3d
orbitals
35
Pauli Exclusion Principle
• No orbital may have more than 2 electrons
• Electrons in the same orbital must have
opposite spins
• s sublevel holds 2 electrons
• p sublevel holds 6 electrons
• d sublevel holds 10 electrons
• f sublevel holds 14 electrons
36
Orbitals, Sublevels & Electrons
• for a many electron atom, build-up the energy
levels, filling each orbital in succession by energy
• ground state
• 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d <
5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p
• degenerate orbitals are orbitals with the same
energy
– each p sublevel has 3 degenerate p orbitals
– each d sublevel has 5 degenerate d orbitals
– each f sublevel has 7 degenerate f orbitals
37
Figure 10.28: A box diagram
showing the order in which
orbitals fill to produce the
atoms in the periodic table
38
Hund’s Rule
• for a set of degenerate orbitals, half fill each orbital
first before pairing
• highest energy level called the valence shell
– electrons in the valence shell called valence electrons
– electrons not in the valence shell are called core electrons
– often use symbol of previous noble gas to represent core
electrons
1s22s22p6 = [Ne]
39
Electron Configuration
• Elements in the same column on the
Periodic Table have
– Similar chemical and physical properties
– Similar valence shell electron configurations
• Same numbers of valence electrons
• Same orbital types
• Different energy levels
40
s1
1
2
3
4
5
6
7
s2
p 1 p 2 p 3 p 4 p 5 s2
p6
d1 d2 d3 d4 d5 d6 d7 d8 d9 d10
f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14
41
Figure 10.25: The electron configurations in the
sublevel last occupied for the first eighteen
elements
42
The Modern Periodic Table
• Columns are called Groups or Families
• Rows are called Periods
– Each period shows the pattern of properties
repeated in the next period
• Main Groups = Representative Elements
• Transition Elements
• Bottom rows = Lanthanides and Actinides
– really belong in Period 6 & 7
43
Figure 10.26: Partial electron configurations for the
elements potassium through krypton
44
Figure 10.27: The orbitals being filled for elements
in various parts of the periodic table
45
Metallic Character
• Metals
• Metalloids
– malleable & ductile
– shiny, lustrous
– conduct heat and
electricity
– most oxides basic
and ionic
– form cations in
solution
– lose electrons in
reactions - oxidized
• Nonmetals
Also known as
semi-metals
Show some
metal and some
nonmetal
properties
brittle in solid state
dull
electrical and
thermal insulators
most oxides are
acidic and molecular
form anions and
polyatomic anions
gain electrons in
reactions - reduced
46
Figure 10.31: The classification of elements as
metals, nonmetals, and metalloids
47
Metallic Character
• Metals are found on the left of the table,
nonmetals on the right, and metalloids in between
• Most metallic element always to the left of the
Period, least metallic to the right, and 1 or 2
metalloids are in the middle
• Most metallic element always at the bottom of a
column, least metallic on the top, and 1 or 2
metalloids are in the middle of columns 4A, 5A,
and 6A
48
Reactivity
• Reactivity of metals increases to the left on
the Period and down in the column
– follows ease of losing an electron
• Reactivity of nonmetals (excluding the
noble gases) increases to the right on the
Period and up in the column
49
Trend in Ionization Energy
• Minimum energy needed to remove a valence electron
from an atom
– gas state
• The lower the ionization energy, the easier it is to
remove the electron
– metals have low ionization energies
• Ionization Energy decreases down the group
– valence electron farther from nucleus
• Ionization Energy increases across the period
– left to right
50
Trend in Atomic Size
• Increases down column
– valence shell farther from nucleus
• Decreases across period
– left to right
– adding electrons to same valence shell
– valence shell held closer because more protons
in nucleus
51
Figure 10.32:
Relative atomic
sizes for
selected atoms.
Note that
atomic size
increases down
a group and
decreases
across a period
52