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Transcript
Quantum Mechanical Model of
the Atom
• Many scientists contributed to the
development of the quantum mechanical
model of the atom.
– Bohr
– Planck
– DeBroglie
– Heisenberg
– Schrodinger
– Pauli
2
What was already known..
• Early 1900’s…believed that
– Energy is quantized
– Electrons have both wave and matter
properties
– Electrons can be at a variety of specific
energy levels in an atom
• Energy levels are called orbits (Bohr model)
– Proposed that electron had both wave and
matter properties
3
Next round of research
• Goal was to describe electrons in atoms
• Ultimately describe for each electron:
– Energy level & size of the region it occupies
(n)
– 3-D shape of the region it occupies (l)
– Orientation of the region/orbital (ml)
– Spin on the electron (ms)
4
Schrodinger & deBroglie
• S & deB pictured the electron bound to the
atom in a standing wave
5
Schrodinger
• Sch.. Proposed that electrons move
around the nucleus in standing waves
– Each orbit represents some whole number
multiple of a wavelength
– Schrodinger analyzed the hydrogen data
based on the assumption that the electrons
behaved as standing waves.
6
Standing Waves
7
Schrodinger
– Schrodinger’s equation takes into account:
• The position of the electron in 3D space (its x,y,z
coordinates)
• Potential energy of the atom due to the attraction
between electrons and protons
• Kinetic energy of the electron
8
Schrodinger’s Equation!
9
Schrodinger
• Schrodinger’s equation has many
solutions
– Each solution is called a wave function (y)
and is correlated to a specific amount of
energy
• Each wave function is more commonly called
an orbital.
10
Orbitals
Each solution to Schrodinger’s equation
describes a specific wave function (y)
/orbital
– The square of a wave function, (y)2,
generates a probability distribution for an
electron in that orbital
• Also called an electron density map for a given
orbital
• (y)2 describes the shape, size, and orientation of
the orbital
11
Orbitals
• Orbitals are regions in space where an
electron is likely to be found
– 90% of the time the electron is within the
boundaries described by the electron density
map
• Can describe its energy, shape, and orientation
– The exact path of an electron in a given
orbital is not known!
12
Heisenberg
• Heisenberg uncertainty principle states
that we cannot know both the position and
the momentum of an electron at the same
time.
– Therefore, we do not know the exact path of
the electron in an orbital.
13
Orbitals
– The lowest energy solution to Sch..’s equation
for an electron in a hydrogen atom describes
what is known as the 1s orbital.
14
Describing Orbitals
•
Use quantum numbers to describe
orbitals. A given orbital can be described
by a set of 3 quantum numbers:
1. Principal quantum number (n)
2. Angular momentum quantum number (l)
3. Magnetic quantum number (ml)
15
Principal Quantum Number (n)
• (n) describes the size and energy of the
oribital
– Possible values: whole number integer
• 1, 2, 3, …
– As “n” increases so does the size and energy
of the orbital
16
Angular momentum quantum
number (l)
• (l) is related to the shape of the orbital
– Possible values: (l) is an integer between 0
and n-1
– Each (l) value is also assigned a letter
designation
17
Angular momentum quantum
number (l)
(l) Value
Letter Designation
0
s
1
p
2
d
3
f
18
n
Possible
l values
1
2
0
0
1
0
1
2
1s
2s
2p
3s
3p
3d
0
1
2
3
4s
4p
4d
4f
3
4
Designation
19
Magnetic quantum number (ml)
• (ml) is related to the orientation of the
orbital in 3-D space
– Possible values: - l to + l
20
Magnetic quantum number (ml)
• Consider the p orbital…it has an l value of
1 and thus the possible ml values are -1,
0, +1
– These 3 ml values correspond to the 3
possible orientations of the p orbital
21
Ml and Orbitals
l
ml
# orbitals
0 (s)
0
1
1 (p)
-1, 0, 1
3
2 (d)
-2, -1, 0, 1, 2
5
3 (f)
-3, -2, -1, 0, 1, 2, 3
7
22
23
Quantum Number Summary
• See page 256 and board.
– A set of 3 quantum numbers describes a
specific orbital
• Energy and size - n
• Shape - l
• Orientation – ml
24
4th Quantum Number!
• A 4th quantum number was added to
describe the spin on a given electron.
– Called the electron spin quantum number - ms
• Possible values: +1/2 and -1/2
25
More on electron spin.
• Each orbital can hold a maximum of 2
electrons of opposite spin.
• Pauli exclusion principle states that no two
electrons in an atom can have the same
set of 4 quantum numbers
26
Summary
• Three quantum numbers describe a
specific orbital
– Energy and size, shape, and orientation
• Four quantum numbers describe a specific
electron in an atom
27
7.9 Polyelectronic atoms
• The Schrodinger model was based on H
and works in principle for atoms with more
than one electron.
– The shapes and possible orientations of the
hydrogen based orbitals holds true for
polyelectronic atoms.
– However, the size and energy of the orbitals
in polyelectronic atoms differ from those
calculated for hydrogen.
28
Polyelectronic Atoms
• In general, find that in a given principal
quantum number (n)
– S is lower energy than p, which is lower
energy than d…..
• s<p<d<f
– Already know that 1s < 2s < 3s… and 2p < 3p
< 4p…. (in terms of size and energy)
29
7.11 The Aufbau Principle
• Putting electrons in to orbitals…
– Aufbau means “building up” in German
– Electrons always enter the lowest energy
orbital with room
30
Hund’s Rule
• The orbitals of a given sublevel (e.g. p, or
d, or f) are degenerate (of the same
energy).
• The lowest energy state occurs with the
maximum number of unpaired electrons.
– Meaning…..electrons enter an empty orbital
of a given sublevel before pairing up.
31
Goals
• To be able to write for any atom:
– Electron configuration
– Box/energy diagram
– Lewis dot symbol
• State the quantum numbers for each
electron in an atom.
• To relate the electron configuration of an
atom to its location on the periodic table
and its properties.
32
Goals Elaborated
• Electron configuration – shows the number
of electrons in each sublevel
– Format: 1s22s22p4
or [He] 2s22p4
• Box/energy diagram – shows electrons as
arrows and each orbital as a box.
Electrons of opposite spin are indicated by
up and down arrows.
– Format:
33
Periodic Table and Electron Configurations
34
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s…
35
Goals Elaborated
• Lewis Dot Symbol – shows valence
electrons as dots around the symbol for
the atom
– Maximum of 2 electrons per side of the
symbol
– Valence electrons are all of the electrons in
the highest occupied principle quantum level
(n)
– Format:
36
The fun part - practice!
• Representative elements – IA – 8A
– Ions formed by above
• Transition metals
– Iron
• Ion formation
– Exceptions
• Cr – expect ___ electrons in 3d
– Actually…..
• Cu – expect ___ electrons in 3d
– Actually…..
37
CH 7: Atomic Structure and
Periodicity
Sections 7.10 -7.13
38
Periodic Trends
• Models explain observed behavior.
– The better the model the fewer the exceptions
– Consider computer weather models vs. kinetic
molecular theory
39
Periodic Trends
• The quantum mechanical model of the
atom explains many trends in the
properties observed for the elements.
– Trends in physical properties
• Atomic radius
• Size of the ion vs. the “parent” atom
– Trends in reactivity:
• Charge on the ion formed
• Ease of removing or adding an electron to an atom
40
Atomic Radius
• Measuring/defining atomic radius
– Metals: atomic radius is half the distance
between nuclei in a solid
Cu
– Nonmetals; atomic radius is half the distance
between the nuclei of atoms in a diatomic
molecule
H H
41
Atomic radius trends (pg 276)
• Atomic radius increases down a group
– Valence electrons are in higher (larger)
principal quantum levels with increased
shielding.
•
•
•
•
H 1s1
Li …..2s1
Na ……......3s1
K ………………..4s1
42
Atomic radius trends
• Atomic radius decreases across a period
of representative elements
– Valence shell (PEL) remains the same across
a period, same shielding across the
period……however…
– The # protons increases across a period
• The increased nuclear charge “pulls” shells closer
to the nucleus
43
Atomic Radius
Consider the 2nd period…filling n = 2
Li Be B C N O F Ne
# p 3 4 5 6 7 8 9 10
 decreasing atomic radius
44
Atomic radius
• Atomic radius remains ~same across a
row of transition metals
– Why?
45
Ionization Energy
• Ionization Energy – energy needed to
remove the highest energy electron from
an atom in its gaseous state.
– See page 272/273, IE > 0
Na(g)  Na+ (g) + e
IE1 = 495 kJ/mole
46
IE Trends
• First IE (IE1 ) becomes less endothermic
(less +) down a group
– See table 7.5 on page 272
– Why?
• As you go down a group, the electron being
removed is farther from the nucleus and shielded
by more core electrons from the attractive forces of
the nucleus.
• Therefore, it’s easier to remove.
47
IE Trends
• In general, first IE (IE1 )increases across a
period.
– See figure 7.31 on page 273
– Why?
• Atoms become smaller across a period and the #
core electrons (shielding) remains the same while
nuclear charge increases.
• Electron to be removed is held more tightly to the
nucleus across a period.
48
Exceptions to IE Trends
• A dip in IE1 is observed for elements in
group 3A and 6A.
– 3A elements are all ns2p1
• Hypothesized that the s2 electrons shield the first p
electron
– 6A elements are all ns2p4
• Hypothesized that the first pairing of p electrons
increases repulsions and thus this electron is
easier to remove.
49
Trends in Successive IE
• IE increases as additional electrons are
removed from a given element
– see table 7.5 on page 272
Na(g)  Na+ (g) + e
Na+ (g) 
____ +
IE1 = 495 kJ/mole
e
IE2 = 4560 kJ/mol
50
Trends in Successive IE
• IE jumps when the first core electron is
removed.
– Why?
Na(g)  Na+ (g) + e
(val. e)
Na+ (g) 
(core e)
____ +
e
IE1 = 495 kJ/mole
IE2 = 4560 kj/mol
51
Electron Affinity
• EA – energy change associated with the
addition of an electron to a gaseous atom.
– In this text, EA < 0 (convention varies)
– See page 275
X (g) + e  X-(g)
52
EA Trends
• MANY EXCEPTIONS!
• In general, EA becomes less negative
down a group.
• In general, EA becomes more negative
across a period.
53
Periodic Trends
1. Atomic radius
2. Ionization Energy (>0)
•
•
First IE and successive IE
3A and 6A exceptions
3. Electron Affinity (<0)
54