Download Chapter 6 Electronic Structure of Atoms

Chapter 6
Electronic Structure
of Atoms
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Where are electrons (electrons
distribution) ?
-First question we will ask is: how are
electrons distributed if we know that they
interact through electromagnetic forces
with nuclei and other electrons?
-Second question we ask is how well
could the such interaction mechanisms be
described? (physical/mechanical model) Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
EM radiation
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
What do you know about light : simple experiments
(experiment 3)
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Electronic
Structure
of4Atoms
What do you know about light : simple experiments
(experiment 3)
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Electronic
Structure
of5Atoms
What makes the light- the light
sources
• Atoms can release EM light or
absorb it
• Atoms don’t emit EM of all
colors, only very specific
wavelengths
– in fact, the spectrum of
wavelengths can be used to
identify the element
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Electronic
Structure
of6Atoms
Emission Spectrum
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Electronic
Structure
of7Atoms
Spectra
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Electronic
Structure
of8Atoms
What we know about the EM radiation: Electromagnetic
Waves: check your radio, telephone or TV frequency or
wavelength?
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Electronic
Structure
of9Atoms
•
The Electromagnetic
Spectrum
light passed through a prism is separated into all
its colors - this is called a continuous spectrum
• the color of the light is determined by its
wavelength
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Electronic
Structure
of
10Atoms
Spectrum of white light
Radiation composed of only one wavelength =
monochromatic (one color).
Radiation that spans a whole array of different
wavelengths = continuous.
White light = continuous spectrum of colors.
Dark= no light.
When light interacts with material it can be scattered,
absorbed or emitted. Depending on the material, the
interaction with different radiation will be different.
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Electronic
Structure
of11Atoms
Types of Electromagnetic
Radiation
• Classified by the Wavelength
– Radiowaves = l > 0.01 m
• low frequency and energy
– Microwaves = 10-4m < l < 10-2m
– Infrared (IR) = 8 x 10-7 < l < 10-5m
– Visible = 4 x 10-7 < l < 8 x 10-7m
• ROYGBIV
– Ultraviolet (UV) = 10-8 < l < 4 x 107m
– X-rays = 10-10 < l < 10-8m
– Gamma rays = l < 10-10
• high frequency
energy
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Electronic
Structure
of
12Atoms
Light as well as electrons can be described through
wave-like observables
• Waves are described by
wavelength, l, amplitude, A
and frequency, n.
• The speed of a wave, c, is
given by its frequency
multiplied by its wavelength:
Velocity ( c ) = nl
• C = 2.9979 * 108 m/s (in
vacuum)
Electronic
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Structure
of
13Atoms
Low Frequency Wave
l
l
High Frequency Wave
l
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Electronic
Structure
of
14Atoms
Waves
• To understand the electronic structure of
atoms, one must understand the nature of
electromagnetic radiation.
• The distance between corresponding points
on adjacent waves is the wavelength (l). Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Waves
• The number of waves
passing a given point per
unit of time is the
frequency (n).
• For waves traveling at
the same velocity, the
longer the wavelength,
the smaller the
frequency.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Electromagnetic Radiation
• All electromagnetic
radiation travels at the
same velocity: the speed
of light (c),
3.00 108 m/s.
• Therefore,
c=n
l
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Sources of Light
• For atoms and
molecules one does
not observe a
continuous spectrum,
as one gets from a
white light source.
• Only a line spectrum of
discrete wavelengths
is observed.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Absorption Spectrum
Emission Spectrum
Absorption Spectrum
656.3
486.1
Emission Spectrum
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434.1 410.2
Electronic
Structure
of
19Atoms
# Note that electromagnetic structures can
be very complex, this is just a simple wavelike
approximation
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
EM radiation interacting with
electrons
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
What is inside atom-experimental
evidence
Electronic
Structure
of Atoms
A Simple Book-keeping Model of Electrons in EM
radiation field drivers in Atom
Electronic
Structure
of Atoms
Experiments show that
structures have well defined wavelike
patterns
Electronic
Structure
of Atoms
What are electron distributions?
electrons behave like wave like physical structures
Electronic
Structure
of Atoms
Interferences - Wave-like observables
Electronic
Structure
of Atoms
The Nature of Electron Distribution in
EM fields
• Consequences : causal relationships
between observables can explain
phenomenological relations such as the
one between mass and wavelength at
certain conditions
h
l = mv
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Consequence: causal relations
(“uncertainty principle”)
(x) (mv) 
h
4
For some systems
h can be used , h= Planck’s constant, 6.626  10−34 J-s.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Causal relationships can help:
For example approximation phenomenological relation:
Electron energy+ Bonding energy = h n
E = hn
where h is Planck’s constant,
6.626  10−34 J*s.
Electronic
Structure
of Atoms
How to measure electron distributions in atoms?
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
How to see electrons inside atoms?
Can EM radiation help?
Electronic
In 1800s Hertz started kicking electrons with EM radiation
Structure
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of
31Atoms
How to see electrons inside
atoms? Can EM radiation help?
In 1800s Rydberg’s analysis of atomic
line spectra (Na,H):
*observables using h constant
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Electronic
Structure
of
32Atoms
The Electronic Structure of Atoms
•
Experimental evidence:
Electrons in an atom are seen as
going from one well defined area
to the other. Each of these areas
(orbitals) corresponds to certain
energy, so the colors we see
correspond to the energies of
photons that are equal to the
energy difference between these
orbital energies.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Electronic Structure of Atoms
•
Electrons stay in well
defined areas like standing
waves stay in a resonance
box and they do not gain or
lose energy for certain time:
we say they are in a certain
state.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Electronic Structure of Atoms
Energy can be absorbed or
emitted: if absorbed electron
will slow down to an outermost
orbital, if emitted an electron
will go down closer to the
nucleus .
The energy difference is
Ei –Ef =Ephoton = hn = h c/l
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Brings us back to the question how can we
see electrons inside atoms with EM
radiation.
Experiment
Model ?
Experiment
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Electronic
Structure
of
36Atoms
The Electronic Structure of Atoms
The energy absorbed or emitted
from the process of electron
promotion or demotion can be
calculated by the equation:
E = −RH (
1
1
- 2
nf2
ni
)
where RH is the Rydberg
constant, 2.18  10−18 J, and ni
and nf are the initial and final
energy levels of the electron. Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
What about a mechanical
model?
• How to describe these quantum waves?
• Quantum or wave mechanics and
• The future
Electronic
Structure
of Atoms
How to describe the mechanics of
electron motion in many-electron
atoms and 3 dimensions?
• Answer: Use any mechanics that describes
what you see in experiments. If you use wavemodels make sure that you accurately
represent observed properties of electrons!
Example: (Schroedinger wave equation) If
electrons have wavelike patterns use a wave
mechanics to describe it !! Also take into
account 3 dimensions (x, y, z).
Electronic
Structure
of Atoms
Mechanics of electrons
(probability as density)
in
atoms
Electronic
Structure
of Atoms
Orbits vs. Orbitals
Pathways vs. Probability-Pathways
Kicking “waves” is not as precise as kicking
localized objects!
Electronic
Structure
of Atoms
Wave-like baseball:
• Here, you cannot have “straight” hits, the path
of the ball has wavelike distribution and
interferes with other objects, players etc.!
• The person catching the ball should expect
“wavelike” distribution of incoming balls! The
forces and interactions here are wavelike.
• See again our slit experiment and assume
that the slit is a bat and detector is a
“catcher”. This analogy requires more
detailed knowledge of physics!
Electronic
Structure
of Atoms
How we describe the path
of the ball ?:
position (x, y, z coordinates)
And how we describe the path of
the electron ?:
Wave-like distribution (quantum
numbers n, l, m)
Electronic
Structure
of Atoms
Quantum or Wave Mechanics
Schrödinger’s equation and 3 quantum
numbers:Principal Quantum Number, n. This is the same as
Bohr’s n. As n becomes larger, the atom becomes larger and the
electron is further from the nucleus.
Angular Quantum Number, l. This quantum number
depends on the value of n. The values of l begin at 0 and
increase to (n - 1). We usually use letters for l (s, p, d and f
for l = 0, 1, 2, and 3). Usually we refer to the s, p, d and forbitals.
Magnetic Quantum Number, ml. This quantum number
depends on l. The magnetic quantum number has integral
values between -l and +l. Magnetic quantum numbers give
Electronic
the 3D orientation of each orbital.
Structure
of Atoms
Quantum Mechanics
• Erwin Schrödinger
developed a
mathematical treatment
into which both the
wave and particle nature
of matter could be
incorporated.
• It is known as quantum
or wave mechanics.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Quantum Mechanics
• The wave equation is designated
with a lower case Greek psi (Y).
• The square of the wave
equation, Y2, gives a probability
density map of where an electron
has a certain statistical likelihood
of being at any given instant in
time.
• Note: y is the solution of wave
mechanical (Schrödinger)
equation, so it represents a
wavelak distribution- the symbol
l could also have been chosen
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Quantum Numbers
• Solving the wave equation gives a set of
wave functions, or orbitals, and their
corresponding energies.
• Each orbital describes a spatial
distribution of electron density.
• An orbital is described by a set of three
quantum numbers.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Principal Quantum Number (n)
• The principal quantum number, n,
describes the energy level on which the
orbital resides.
• The values of n are integers ≥ 1.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Angular Momentum Quantum
Number (l)
• This quantum number defines the
shape of the orbital.
• Allowed values of l are integers ranging
from 0 to n − 1.
• We use letter designations to
communicate the different values of l
and, therefore, the shapes and types of
Electronic
orbitals.
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Angular Momentum Quantum
Number (l)
Value of l
0
1
2
3
Type of orbital
s
p
d
f
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Magnetic Quantum Number (ml)
• The magnetic quantum number
describes the three-dimensional
orientation of the orbital.
• Allowed values of ml are integers
ranging from -l to l:
−l ≤ ml ≤ l.
• Therefore, on any given energy level,
there can be up to 1 s orbital, 3 p
orbitals, 5 d orbitals, 7 f orbitals, etc.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Magnetic Quantum Number (ml)
• Orbitals with the same value of n form a shell.
• Different orbital types within a shell are
subshells.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
s Orbitals
• The value of l for s
orbitals is 0.
• They are spherical in
shape.
• The radius of the
sphere increases with
the value of n.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
s Orbitals
Observing a graph of
probabilities of finding
an electron versus
distance from the
nucleus, we see that s
orbitals possess n−1
nodes, or regions
where there is 0
probability of finding an
electron.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
p Orbitals
• The value of l for p orbitals is 1.
• They have two lobes with a node between
them.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
d Orbitals
• The value of l for a
d orbital is 2.
• Four of the five d
orbitals have 4
lobes; the other
resembles a p
orbital with a
doughnut around
the center.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Energies of Orbitals
• For a one-electron
hydrogen atom,
orbitals on the same
energy level have
the same energy.
• That is, they are
degenerate.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Energies of Orbitals
• As the number of
electrons increases,
though, so does the
repulsion between
them.
• Therefore, in manyelectron atoms,
orbitals on the same
energy level are no
longer degenerate.Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Spin Quantum Number, ms
• In the 1920s, it was
discovered that two
electrons in the same
orbital do not have
exactly the same energy.
• The “spin” of an electron
describes its magnetic
field, which affects its
energy.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Spin Quantum Number, ms
• This led to a fourth
quantum number, the
spin quantum number,
ms.
• The spin quantum
number has only 2
allowed values: +1/2
and −1/2.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Pauli Exclusion Principle
• No two electrons in the
same atom can have
exactly the same energy.
• Therefore, no two
electrons in the same
atom can have identical
sets of quantum
numbers.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Electron Configurations
• This shows the
distribution of all
electrons in an atom.
• Each component
consists of
– A number denoting the
energy level,
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Electron Configurations
• This shows the
distribution of all
electrons in an atom
• Each component
consists of
– A number denoting the
energy level,
– A letter denoting the type
of orbital,
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Electron Configurations
• This shows the
distribution of all
electrons in an atom.
• Each component
consists of
– A number denoting the
energy level,
– A letter denoting the type
of orbital,
– A superscript denoting
the number of electrons
in those orbitals.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Orbital Diagrams
• Each box in the
diagram represents
one orbital.
• Half-arrows represent
the electrons.
• The direction of the
arrow represents the
relative spin of the
electron.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Hund’s Rule
“For degenerate
orbitals, the lowest
energy is attained
when the number of
electrons with the
same spin is
maximized.”
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Periodic Table
• We fill orbitals in
increasing order of
energy.
• Different blocks on the
periodic table (shaded
in different colors in
this chart) correspond
to different types of
orbitals.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Some Anomalies
Some
irregularities
occur when there
are enough
electrons to halffill s and d
orbitals on a
given row.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Some Anomalies
For instance, the
electron
configuration for
Cu and Cr. For
Cr it is
[Ar] 4s1 3d5
rather than the
expected
[Ar] 4s2 3d4.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Some Anomalies
• This occurs
because the 4s
and 3d orbitals
are very close in
energy.
• These anomalies
occur in f-block
atoms, as well.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Electron Configurations
Electronic
Structure
of Atoms
7s
6s
Energy
5s
4s
6p
5p
6
d
5d
5f
4f
4d
4p
3d
3p
3s
2p
2s
1s
Electronic
Structure
of Atoms
Order of Subshell Filling
in Ground State Electron
Configurations
start by drawing a diagram
putting each energy shell on
a row and listing the subshells,
(s, p, d, f), for that shell in
order of energy, (left-to-right)
next, draw arrows through
the diagonals, looping back
to the next diagonal
each time
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
5f
6s
6p
6d
7s
Electronic
Structure
of Atoms
Example – Write the Ground State
Orbital Diagram and Electron
Configuration of Magnesium.
2. Draw 9 boxes to represent the first 3
energy levels s and p orbitals
1s
2s
2p
3s
3p
Electronic
Structure
of Atoms
Example – Write the Ground State
Orbital Diagram and Electron
Configuration of Magnesium.
3. Add one electron to each box in a set,
then pair the electrons before going to
the next set until you use all the
electrons
•
When pair, put in opposite arrows


1s
2s
  
2p

3s
3p
Electronic
Structure
of Atoms
Example – Write the Ground State
Orbital Diagram and Electron
Configuration of Magnesium.
4. Use the diagram to write the electron
configuration
– Write the number of electrons in each set as
a superscript next to the name of the orbital
set
1s22s22p63s2 = [Ne]3s2


1s
2s
  
2p

3s
3p
Electronic
Structure
of Atoms
Valence Electrons
• the electrons in all the subshells with
the highest principal energy shell are
called the valence electrons
• electrons in lower energy shells are
called core electrons
• chemists have observed that one of the
most important factors in the way an
atom behaves, both chemically and
physically, is the number of valence
Electronic
electrons
Structure
of Atoms
Valence Electrons
Rb = 37 electrons = 1s22s22p63s23p64s23d104p65s1
• the highest principal energy shell of Rb that
contains electrons is the 5th, therefore Rb has 1
valence electron and 36 core electrons
Kr = 36 electrons = 1s22s22p63s23p64s23d104p6
• the highest principal energy shell of Kr that
contains electrons is the 4th, therefore Kr has 8
valence electrons and 28 core electrons
Electronic
Structure
of Atoms
Electrons Configurations and
the Periodic Table
Electronic
Structure
of Atoms
Electron Configurations from
the Periodic Table
• elements in the same period (row) have
valence electrons in the same principal
energy shell
• the number of valence electrons
increases by one as you progress
across the period
• elements in the same group (column)
have the same number of valence
electrons and they are in the same kindElectronic
Structure
of Atoms
of subshell
Electron Configuration & the
Periodic Table
• elements in the same column have
similar chemical and physical
properties because their valence shell
electron configuration is the same
• the number of valence electrons for
the main group elements is the same
as the group number
Electronic
Structure
of Atoms
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
Electronic
Structure
of Atoms
Electron Configuration from
the Periodic Table
• the inner electron configuration is the same as the
noble gas of the preceding period
• to get the outer electron configuration, from the
preceding noble gas, loop through the next period,
marking the subshells as you go, until you reach
the element
– the valence energy shell = the period number
– the d block is always one energy shell below the period
number and the f is two energy shells below
Electronic
Structure
of Atoms
Electron Configuration from
the Periodic Table
8A
1A
1
2
3
4
5
6
7
3A 4A 5A 6A 7A
2A
Ne
P
3s2
3p3
P = [Ne]3s23p3
P has 5 valence electrons
Electronic
Structure
of Atoms
Electron Configuration from
the Periodic Table
8A
1A
1
2
3
4
5
6
7
3A 4A 5A 6A 7A
2A
3d10
4s2
Ar
As
4p3
As = [Ar]4s23d104p3
As has 5 valence electrons
Electronic
Structure
of Atoms
The Noble Gas
Electron Configuration
• the noble gases have 8 valence
electrons
– except for He, which has only 2 electrons
• we know the noble gases are especially
nonreactive
– He and Ne are practically inert
• the reason the noble gases are so
nonreactive is that the electron
configuration of the noble gases is
especially stable
Electronic
Structure
of Atoms
Everyone Wants to Be Like a Noble
Gas!
The Alkali Metals
• the alkali metals have one more
electron than the previous noble
gas
• in their reactions, the alkali
metals tend to lose their extra
electron, resulting in the same
electron configuration as a noble
gas
– forming a cation with a 1+ charge
Electronic
Structure
of Atoms
Everyone Wants to Be Like a Noble
Gas!
The
Halogens
• the electron configurations of the
halogens all have one fewer electron
than the next noble gas
• in their reactions with metals, the
halogens tend to gain an electron and
attain the electron configuration of the
next noble gas
– forming an anion with charge 1-
• in their reactions with nonmetals they
tend to share electrons with the other
nonmetal so that each attains the
electron configuration of a noble gas
Electronic
Structure
of Atoms
Everyone Wants to Be
Like a Noble Gas!
• as a group, the alkali metals are the most
reactive metals
– they react with many things and do so rapidly
• the halogens are the most reactive group of
nonmetals
• one reason for their high reactivity is the fact
that they are only one electron away from
having a very stable electron configuration
– the same as a noble gas
Electronic
Structure
of Atoms
Stable Electron Configuration
And Ion Charge
• Metals form cations
by losing enough
Atom
electrons to get the
same electron
configuration as the Na
previous noble gas
Mg
• Nonmetals form
Al
anions by gaining
O
enough electrons to
F
get the same
electron
configuration as the
next noble gas
Atom’s
Electron
Config
[Ne]3s1
Na+
Ion’s
Electron
Config
[Ne]
[Ne]3s2
Mg2+
[Ne]
[Ne]3s23p1
Al3+
[Ne]
[He]2s2p4
O2-
[Ne]
[He]2s22p5
F-
[Ne]
Ion
Electronic
Structure
of Atoms
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.