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