CH1Notes - Chapter
One
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Unformatted text preview: Chapter
One
 Atoms:

The
Quantum
World
 CHEM
1211K
 Fall
2010
 1
 Objec9ves 
 •  Understand
the
structure
of
the
atom
and
gain
familiarity
with
 subatomic
par@cles.
 •  Characterize
the
wave
and
par@cle
nature
of
light.
 –  Energy,
frequency,
and
wavelength
 –  The
work
of
Rydberg
with
atomic
spectra
 •  Correlate
the
duality
of
light
to
the
dual
nature
of
subatomic
 par@cles,
the
electron
in
par@cular.
 •  Combine
the
photoelectric
effect,
uncertainty
principle,
and
the
 Schrodinger
equa@on
to
develop
an
understanding
of
where
 electrons
are
located
in
the
atom.
 •  Use
quantum
numbers
to
describe
the
most
probably
loca@ons
of
 electrons
in
atoms.
 •  Write
electron
configura@ons
to
describe
the
filling
of
electrons
and
 correlate
to
the
periodic
table.
 2
 •  Define
periodic
proper@es
and
explain
their
trends.
 Key
Ideas 
 •  MaPer
is
composed
of
atoms
 •  The
structures
of
atoms
can
be
understood
in
 terms
of
the
theory
of
maPer
known
as
 quantum
mechanics,
in
which
the
proper@es
 of
par@cles
and
waves
merge.
 3
 Why
is
quantum
 
 chemistry
important? 
 •  Atoms
are
the
fundamental
building
blocks
of
maPer.
 
 Almost
all
the
explana@ons
of
chemical
phenomena
 are
expressed
in
terms
of
atoms.
 •  This
chapter
explores
the
periodic
varia@on
of
atomic
 proper@es
and
shows
how
quantum
mechanics
is
 used
to
account
for
the
structures
and
therefore
the
 proper@es
of
atoms.
 •  This material is the founda1on for almost all explana1ons of chemistry. 4
 Characteris9cs
of
 Electromagne9c
Radia9on
(1.2) 
 •  Light
is
a
form
of
electromagne1c radia1on,
 which
consists
of
oscilla@ng
(@me‐varying)
 electric
and
magne@c
fields.
 •  All forms of electromagne1c radia1on transfer energy from one region of space to another. 5
 Characteris9cs
of
 Electromagne9c
Radia9on
(1.2) 
 •  Important
aPributes
of
light:
 Wavelength Amplitude Intensity Similar to Figure 1.7 6
 Characteris9cs
of
 Electromagne9c
Radia9on
(1.2) 
 •  Frequency
is
the
number
of
cycles
of
a
wave
 per
second.
 –  Measured
in
Hertz
(Hz)
 Not in text 7
 Characteris9cs
of
 Electromagne9c
Radia9on
(1.2) 
 •  The
shorter
the
wavelength
of
light,
the
more
 oscilla@ons
pass
a
given
point
in
one
second.
 •  The
longer
the
wavelength
of
light,
the
fewer
 oscilla@ons
pass
a
given
point
in
one
second.
 See Example 1.1 in your text. 8
 8/30/10
 Zumdahl
Chapter
12
 Similar to Figure 1.9 9 9
 Atomic
Spectra
(1.3) 
 •  When
electric
current
is
passed
through
a
 sample
of
H2
gas,
the
sample
emits
light.
 –  Current
“excites”
hydrogen
atoms
to
higher
 energies.
 –  Light
is
emiPed
as
the
atoms
release
energy.
 10
 Atomic
Spectra
(1.3) 
 Figure 1.10 Images such as these are called emission spectra. 1 1 ν = R 2 − 2 n1 n 2 11
 Atomic
Spectra
(1.3) 
 •  Sec@on
summary
 –  The observa8on of discrete spectral lines suggests that an electron in an atom can have only certain energies. 12
 Radia9on,
Quanta,
and
Photons
(1.4) 
 •  Important
clues
about
the
nature
of
 electromagne@c
radia@on
came
from
 observa@ons
of
objects
as
they
are
heated.
 •  Mak Planck
proposed
that
the
exchange
of
 energy
between
maPer
and
radia@on
occurs
 in
quanta
or
packets
of
energy.
 E = hν 13
 Radia9on,
Quanta,
and
Photons
(1.4) 
 •  Experimental
evidence
to
support
Planck’s
 theory
was
provided
by
the
photoelectric effect.
 Figure 1.15 14
 Radia9on,
Quanta,
and
Photons
(1.4) 
 •  Albert Einstein explained
the
photoelectric
 effect.
 http://tinyurl.com/297sw7b 15
 Radia9on,
Quanta,
and
Photons
(1.4) 
 •  Text
Example
1.4:

What
is
the
energy
of
a
single
 photon
of
blue
light
of
frequency
6.4
x
1014
Hz?
 What
is
the
energy
of
a
mole
of
photons
of
the
same
 frequency?
 16
 Radia9on,
Quanta,
and
Photons
(1.4) 
 •  Sec@on
Summary:
 –  Studies of blackbody radia8on led to Planck’s hypothesis of the quan8za8on of electromagne8c radia8on. –  The photoelectric effect provides evidence of the par8culate nature of electromagne8c radia8on. 17
 The
Wave‐Par9cle
Duality
 
 of
MaQer
(1.5) 
 •  Construc@ve
interference
 •  Destruc@ve
interference
 Figure 1.20 18
 The
Wave‐Par9cle
Duality
 
 of
MaQer
(1.5) 
 •  If
light
can
be
a
wave
and
a
par@cle,
why
can’t
 other
par@cles
also
act
like
waves?!?!
 19
 The
Wave‐Par9cle
Duality
 
 of
MaQer
(1.5) 
 •  Sec1on summary –  Photoelectric
effect
 •  Light
behaves
as
a
par@cle
 –  x‐ray
diffrac@on
 •  Light
behaves
as
a
wave
 From Zumdahl, 5th ed. 20
 The
Uncertainty
Principle
(1.6) 
 •  A
par@cle
has
a
definite
trajectory—the
path
 on
which
loca@on
and
linear
momentum
are
 specified
at
each
instant.
 •  We cannot specify the precise loca1on of a par1cle if it behaves like a wave. 21
 The
Uncertainty
Principle
(1.6) 
 •  Loca@on
and
momentum
are
complimentary —
 •  The
Heisenberg uncertainty principle
 expresses
the
complementarity
of
loca@on
 and
momentum:
 22
 The
Uncertainty
Principle
(1.6) 
 •  Sec@on
summary
 –  The loca1on and momentum of a par1cle are complementary. –  The loca1on and the momentum cannot both be known simultaneously with arbitrary precision. –  The quan1ta1ve rela1onship between the precision of each measurement is described by the Heisenberg uncertainty principle. 23
 Wavefunc9ons
and
 
 Energy
Levels
(1.7) 
 •  Erwin Schrodinger
recognized
that
it
would
be
 beneficial
to
replace
the
precise
trajectory
of
a
 par@cle
(unrealis@c
due
to
the
dual
nature)
 with
a
wavefunc1on.
 •  Max Born’s
interpreta@on
of
the
wavefunc@on
 is
that
the probability of finding the par8cle in a region is propor8onal to the square of the wavefunc8on. 24
 Wavefunc9ons
and
 
 Energy
Levels
(1.7) 
 •  When
ψ2
is
zero,
the
par@cle
has
zero
 probability
density.
 •  A
loca@on
where
ψ
passes
through
zero
is
 called
a
node.
 Figure 1.24 25
 Wavefunc9ons
and
 
 Energy
Levels
(1.7) 
 •  Sec@on
summary
 –  The probability density for a par1cle at a loca1on is propor1onal to the square of the wavefunc1on at that point. –  The wavefunc1on is found by solving the Schrodinger equa1on for that par1cle. –  When the equa1on is solved, it is found that the par1cle can posses only certain discrete energies.
 26
 The
Principle
Quantum
Number
(1.8) 
 •  There
are
many,
many
solu@ons
to
the
 Schrodinger
equa@on.
 •  Each
solu@on
consists
of
a
wave
func@on.
 •  Each
wave
func@on
results
in
specific
values
of
the
 three
quantum
numbers.
 27
 The
Principle
Quantum
Number
(1.8) 
 •  The
principle quantum number
(n)
 –  Describes
the
main
energy level
(shell)
that
 the
electron
occupies.


 –  n
may
be
any
posi@ve
integer.
 28
 The
Principle
Quantum
Number
(1.8) 
 •  The
lowest
energy
possible
for
an
electron
(in
 a
hydrogen
atom)
is
obtained
when
n
=
1.
 –  This
lowest
energy
state
is
called
the
ground state.
 Figure 1.28 29
 The
Principle
Quantum
Number
(1.8) 
 •  Sec@on
Summary
 –  The energy levels of a hydrogen atom are defined by the principle quantum number, n = 1, 2, …and form converging series as shown in Figure 1.28. 30
 Atomic
Orbitals
(1.9) 
 •  The
angular momentum quantum number
(l):
 •  

 –  Designates
the
sublevel
that
the
electron
 occupies.
 –  l may
have
any
value
from
0…(n‐1)
 31
 Atomic
Orbitals
(1.9) 
 •  Each
value
of
l
represents
a
subshell.
 Value
of
l 0
 1
 2
 3
 Orbital
 type
 s
 p
 d
 f
 Number
 of
orbitals
 in
subshell
 1
 3
 5
 7
 32
 Atomic
Orbitals
(1.9) 
 •  The
magne1c quantum number
(ml):
 –  Designates
the
specific
orbital
within
a
subshell
 that
the
electron
occupies.
 33
 Atomic
Orbitals
(1.9) 
 Figure 1.30 34
 Atomic
Orbitals
(1.9) 
 •  The
boundary
surface
for
a
p
orbital
has
two
 lobes
separated
by
a
nodal
plane.
 Figure 1.35 Figure 1.36 35
 Atomic
Orbitals
(1.9) 
 •  The
five
d
orbitals
of
a
given
energy
level
 Figure 1.37 •  The
seven
f
orbitals
 Figure 1.38 36
 Atomic
Orbitals
(1.9) 
 •  The
total
number
of
orbitals
in
a
shell
with
 principle
quantum
number
n
is
n2.
 •  How
many
electrons
are
in
a
shell
with
 principle
quantum
number
n?
 37
 Atomic
Orbitals
(1.9) 
 •  Sec@on
summary
 –  The loca1on of an electron in an atom is described by a wavefunc1on known as an atomic orbital. –  Atomic orbitals are designated by the quantum numbers n, l, and ml and fall into shells and subshells . 38
 Electron
Spin
(1.10) 
 •  Electrons
behave
in
some
respects
like
a
 planet
rota@ng
on
its
axis.

This
property
is
 called
spin.
 –  These
two
spin
states
are
dis@nguished
 



by
a
fourth
quantum
number,
 



the
spin quantum number.
 Figure 1.40 39
 Electron
Spin
(1.10) 
 •  Sec@on
Summary
 –  An electron has a property of spin. –  The spin is described by the quantum number ms, which may have only one of two values. 40
 The
Electronic
Structure
of
 Hydrogen
(1.11) 
 •  The
ground state
for
the
single
electron
of
 hydrogen
is
n
=
1.

What
four
quantum
 numbers
can
we
use
to
describe
its
loca@on?
 41
 The
Electronic
Structure
of
 Hydrogen
(1.11) 
 •  Example:

What
type
of
orbital
is
described
 the
set
of
quantum
numbers?
 n
=
3, l =
2,
ml
=
‐2
 n
=
1, l =
0,
ml
=
0,
ms
=
+1/2 42
 The
Electronic
Structure
of
 Hydrogen
(1.11) 
 •  Example:

How
many
electrons
are
in
the
n
=
5
 shell?
 •  How
many
electrons
are
in
the l =
4
subshell?
 •  How
many
electrons
in
an
atom
with
n
=
4
can
 have
ml
=
‐2?
 43
 The
Electronic
Structure
of
 Hydrogen
(1.11) 
 •  Sec@on
Summary
 –  The state of an electron in a hydrogen atom is defined by the four quantum numbers n, l, ml , and ms. –  As the value of n increases, the size of the atom increases. 44
 Orbital
Energies
(1.12) 
 •  The
energies
of
the
orbitals
in
many‐electron
 atoms
are
not
the
same
as
those
in
hydrogen.
 45
 Orbital
Energies
(1.12) 
 •  In
addi@on
to
being
more
aPracted
to
the
 nucleus,
the
mul@ple
electrons
in
a
many‐ electron
atoms
repel
one
another.
 46
 Orbital
Energies
(1.12) 
 •  The
shielding
of
other
electrons
effec@vely
 reduces
the
pull
of
the
nucleus
on
the
 electron.
 •  The
effec1ve nuclear charge (Zeffe)
 47
 Orbital
Energies
(1.12) 
 •  Sec@on
summary
 –  In a many‐electron atom, because of the effects of penetra1on and shielding, the order of energies of orbitals in a give shell is s < p < d < f 48
 Orbital
Energies
(1.12) 
 s
orbitals
 p
orbitals
 d
orbitals
 f
orbitals
 49
 49
 The
Building‐Up
Principle
(1.13) 
 •  Electron configura1on
is
a
list
of
all
occupied
 orbitals
with
the
number
of
electrons
that
 each
one
contains
for
a
specific
atom. 50
 The
Building‐Up
Principle
(1.13) 
 •  The
Pauli exclusion principle
says
that
no
 more
than
two
electrons
may
occupy
any
 given
orbital.
 51
 The
Building‐Up
Principle
(1.13) 
 1H: 1s1 Li: 1s22s1 3 5B: 8O: 1s22s22px22py12pz1 10Ne: 52
 The
Building‐Up
Principle
(1.13) 
 •  Noble gas configura1on
is
short
hand
based
 on
the
idea
that
any
atom
contains
all
of
the
 same
electrons
possessed
by
the
noble
gas
 immediately
preceding
it. 53
 The
Building‐Up
Principle
(1.13) 
 •  We
can
think
of
many‐electron
atoms
as
 consis@ng
of
core electrons
and
valence electrons. –  Core –  Valence
 54
 The
Building‐Up
Principle
(1.13) 
 •  Excep@ons
to
electron
configura@on
“rules”
 center
around
full
or
half
full
d
subshells.
 55
 The
Building‐Up
Principle
(1.13) 
 •  Sec@on
summary:
 –  We account for the ground‐state electron configura1on of an atom by using the building‐ up principle in conjunc1on with the energies of orbitals (see Figure 1.41), the Pauli exclusion principle, and Hund’s rule. –  See Toolbox 1.1 on page 36 of your text. 56
 The
Periodicity
of
Atomic
 Proper9es 
 •  The
periodic
trends
we
will
discuss
are
primarily
 the
result
of
shielding
or
screening.
 –  Inner
(core)
electrons
shield
the
outer
(valence)
 electrons
from
the
effects
of
the
posi@vely
 charged
nucleus.
 –  Electrosta@c
aPrac@on
decreases,
so
valence
 electrons
are
not
pulled
in
as
@ghtly.


 57
 The
Periodicity
of
Atomic
 Proper9es 
 •  All
three
elements
have
two
core
electrons.
 58
 The
Periodicity
of
Atomic
 Proper9es 
 Effective nuclear charge vs. atomic number Figure 1.45 59
 Atomic
Radius
(1.15) 
 •  The
atomic radius
of
an
element
is
defined
as
 half
the
distance
between
neighboring
atoms.
 From Zumdahl, 5th edition 60
 Atomic
Radius
(1.15) 
 •  What
is
the
general
trend
in
atomic
radii?
 Figure 1.46 61
 Atomic
Radius
(1.15) 
 •  Sec@on
Summary:
 –  Atomic radii generally decrease from le] to right across a period as the atomic number increases, and they increase down a group of successive shells are occupied. 62
 Ionic
Radius
(1.16) 
 •  The
ionic radius
of
an
element
is
its
share
of
 the
distance
between
neighboring
ions
in
an
 ionic
solid.
 63
 Ionic
Radius
(1.16) 
 Figure 1.49 64
 Ionic
Radius
(1.16) 
 65
 Figure 1.48 Ionic
Radius
(1.16) 
 •  Atoms
and
ions
with
the
same
number
of
 electrons
are
called
isoelectronic.
 Na+ 
 
 
F‐ 
 
 
Mg2+ 
 66
 Ionic
Radius
(1.16) 
 •  Sec@on
summary:
 –  Ionic radii generally increase down a group and decrease from le] to right across a period. –  HOWEVER, ca1ons are smaller than their parent atoms and anions are larger. 67
 Ioniza9on
Energy
(1.17) 
 •  The
first ioniza1on energy
is
the
minimum
 energy
needed
to
remove
an
electron
from
a
 neutral
atom
in
the
gas
phase.
 •  What
is
the
second ioniza1on energy?
 68
 Ioniza9on
Energy
(1.17) 
 •  In
general,
first
ioniza@on
energy
increases
up
 a
group
and

 



from
leo
to
 



right
across
a
 Figure 1.51 



period.
 69
 Ioniza9on
Energy
(1.17) 
 •  The
general
trend
indicates
that
O
should
have
 a
higher
first
ioniza@on
energy
than
N,
but
it
 does
not.

Why?
 70
 Ioniza9on
Energy
(1.17) 
 •  Sec@on
Summary:
 –  The first ioniza1on energy is highest for elements close to helium and is lowest for elements close to cesium. –  Second ioniza1on energies are higher than first ioniza1on energies (for the same element) and very much higher if the electron is to be removed from a closed shell. 71
 Electron
Affinity
(1.18) 
 •  Electron affinity
is
the
energy
released
when
an
 electron
is
added
to
a
gas‐phase
atom.
 –  Posi@ve
electron
affinity
means
that
energy
is
 released
when
an
electron
aPaches
to
an
atom.
 –  Nega@ve

 


electro

affinity
 


means
that

 


energy
must

 


be
supplied
to
 


push
an

 


electron
onto
 


an
atom.
 Figure72
 1.54 Electron
Affinity
(1.18) 
 Figure 1.55 73
 Electron
Affinity
(1.18) 
 •  Sec@on
summary:
 –  Elements with the highest (most nega1ve) electron affini1es are those in Group 16 (VIA). 74
 The
Periodicity
of
Atomic
 Proper9es 
 •  Example:
Arrange
these
elements
in
order
of
 increasing
electron
affinity,
atomic
radius,
and
 ioniza@on
energy.
 Al,
Mg,
Si,
Na
 75
 Diagonal
Rela9onships
(1.20) 
 The
General
Proper9es
of
Elements
(1.21) 
 •  Omit.
 76
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