Transcript Chapter 6 Electronic Structure of Atoms

CHM 1045: General Chemistry and
Qualitative Analysis
Unit 7
Electronic Structure
of Atoms
Dr. Jorge L. Alonso
Miami-Dade College –
Kendall Campus
Miami, FL
Textbook Reference:
•Module #9
Electronic
Structure
of Atoms
Atoms and Electromagnetic Radiation
Atoms absorb and emit energy, often in the form of electromagnetic radiation
(visible light, microwaves, radio & TV waves, u.v., infrared,etc)
{Fireworks}
Electronic
Structure
of Atoms
The Nature of Light Energy
(1) White Light is not white, it is colored: the Spectrum:
Spectroscope
(2) Light is electrical
and magnetic
(electromagnetic)
(3) Light does not
travel in truly
straight lines, it
travels in waves
{3D-Wave}
VIB G.Y O R
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n
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l
l
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e
d
Electronic
Structure
of Atoms
Light Energy as Waves: two important characteristics

short

long
 = high
 = low
For waves traveling at the same
velocity, the longer the wavelength,
the smaller the frequency
Knowing 
and , you
calculate the
speed of light
1. wavelength (): the
distance (m) between
corresponding points on
adjacent waves
2. frequency () or (f ): the
number of waves passing
a given point per unit of
time (1/s = s1-)
constant (c)
1
 
 


c     (m) (1/sec)
SPEED = DISTANCE x PER UNITElectronic
TIME
Structure
Speed (c) = wave length (λ) x frequency ()
of Atoms
m/sec =
m
x 1/sec
Electromagnetic Radiation
A form of energy characterized by waves (or pulses) of
varying frequencies () and wavelengths ().
c  
c


{*Light Waves}
{3D-Wave}
{Wavelength of v. l.}
Electronic
Structure
of Atoms
Electromagnetic Radiation
Speed of Light: All
electromagnetic radiation
travels at the same velocity (c),
3.00  108 m/s.
Einstein’s Theory of
Special Relativity: Energy and
mass are different forms of the
same thing
1
 α

E  mc2
c
Frequency (f )
Problem: What is the wavelength of a photon of light that has a
frequency of 3.8 x 109 s-1 ?
c
c


3.00 x 108 m s -1

3.8 x 109 s -1
= 7.89x10-2Electronic
m
Structure
of Atoms
The Nature of Energy:
Discrete vs. Continuous
Digital:
0110100101001
Analog
Eggs:
Water:
Quanta (Photon):
particles
Waves:
Electronic
Structure
of Atoms
Energy as a Particle (Photon, Quanta)
When light energy shines
on a metal, an electron
current is generated.
Light
Energy
waves
particles
Light is behaving as
a particle (photon)
that knocks-off
valence electrons
from the metal.
{Photoelectric Effect}
Electronic
Structure
of Atoms
Energy as a Particle (Photon, Quanta)
{Metals & EM Radiation}
• The wave nature of light does
not explain how an object can
glow when its temperature
increases.
• Max Planck explained it by
assuming that energy comes in
packets called quanta (energy
bundle, photon).
Max Planck (1848-1947)
Planck concluded that energy (E) is proportional to frequency():

E  h
For any particular frequency () there is a particular
bundle of Energy (E) that exists as a discrete quantity
(quanta) that is a multiple of Planck’s constant (h).
where h is Planck’s constant, 6.63  10−34 J-s.
Electronic
Energy from electrons comes in discrete quantities (bundles)
that
Structure
of Atoms
are whole number multiples of h. 1
2
The Nature of Energy
Since c = , then
E
c
 

c
 h  h   
 

Therefore, if one knows the wavelength
of light, one can calculate the energy in
one photon, or packet, of that light.
Problem: What is the wavelength
(in Å) of a ray whose energy is
6.16 x 10-14 erg? {Note: Modules
use erg =10-7 Joule}
Electronic
Structure
of Atoms
The Nature of Energy
c

E = h  h  

Problem: What is the wavelength (in Å) of a ray whose energy
is 6.16 x 10-21 Joules?
{Note: Modules use erg =10-7 Joule}
8

c
3
.
0
x
10
m / se c 
- 34
  h    6.63 x 10 Joule s.sec

- 21
E
 6.16 x 10 Joules
  3.23x 10 m
-5
 1Å 
5

3
.
23
x
10
Å


? Å  3.23x 10 m
-10
 10 m 
-5
Electronic
Structure
of Atoms
Electronic
Structure
of Atoms
Energy as……
(1) Waves

c = 
c
 

E
c 
 hE  h   
 
(2) Particle (Photon, Quanta)

ΔE =h
(3) Matter
E  mc2
Electronic
Structure
of Atoms
The Wave-Particle Duality of Matter
•
Electromagnetic radiation can behave as
a particle or as wave phenomena
•
Louis de Broglie posited that if light can
have material properties, matter should
exhibit wave properties.
•
{ElectonWaves}
He demonstrated that the relationship
between mass (m) and wavelength ()
was:

1
∝m
h
 = mv
velocity (v)
(where h is Planck’s constant, 6.63  10
of light)
−34
J-s, and v is velocity
Electronic
Structure
of Atoms
= eq given
The Wave Nature of Matter
Problem: An electron has a mass of 9.06 x 10-25 kg and
is traveling at the speed of light. Calculate its
wavelength?
h
(6.63 x 10-34 J / s)
-18


2.44
x10
m
 = mv (9.06 x 10-25 kg ) x (3.00x 108 m/s)
Problem: What is the wavelength of a 70.0 kg skier
traveling down a mountain at 15.0 m/s?
h
 = mv
-34
(6.63 x 10 J / s)

 6.31x10-37 m
(70.0 kg) x (15.0m/s)
Electronic
Structure
of Atoms
J = Joule = kg.m2
The Nature of Energy
White Light’s Continuous Spectrum:
VIB G.Y O R
Electronic
Structure
of Atoms
The Nature of Energy
Substances both absorb and emit only certain Discrete Spectra
{Flame Tests.Li,Na,K} {Na,B}
{AtomicSpectra}
Electronic
Structure
of Atoms
The Bohr “Planetary” Model
of the Atom (1913)
•
Niels Bohr adopted Planck’s assumption and explained atomic phenomena
in this way:
1. Electrons in an atom can only occupy certain orbits (corresponding to
certain energies, frequencies and wavelengths, because E=h=h c/λ).
2. Electrons in permitted orbits have specific, “allowed” energies; these
energies will not be radiated from the atom.
1st
EL
f=4
2nd EL
f=5
3. Energy is only absorbed or emitted in such a way as
to move an electron from one “allowed” energy state
to another; the energy is defined by
E = h
Electronic
Structure
of Atoms
The Bohr Model of the Atom
Which series releases most energy?
{ExcitedElectrons*}
Electronic
Structure
of Atoms
The larger the fall
the
greater the energy
Atomic Spectra & Bohr Atom
The energy absorbed or emitted
from the process of electron
promotion or demotion can be
calculated by the
Rydberg formula for hydrogen (1885)
1


RH
(
1
1
- 2
nf2
ni
)
Rydberg formula for hydrogen-like
elements (He+, Li 2+, Be3+ etc., )
1


where RH is the Rydberg constant, 2.18 Electronic
10−18 J,
Structure
and ni and nf are the initial and final energy
levels
of Atoms
of the electron. Z is the atomic number
Atomic Spectra & Bohr Atom
Since energy and wavelength are mathematically
related, the Rydberg Equation can also be expressed
in terms of energy:
RH RH
1
1
1
= n2 - n2
 E = RH n 2 - n 2
f
i
f
i

(
)
(
)
 2.180 x 10 J   2.180 x 10 J 
 - 
  E f  Ei
E  
2
2
nf
ni

 

-18
-18
The energy possessed by an electron at a particular energy level
(En) can be expressed as:

-18
2.180 x 10 Joule
En 
n2
Electronic
 = eq
given
Structure
where RH is the Rydberg constant, 2.18  10−18 J, and ni and nf are the initial
of Atoms
and final energy levels of the electron.
Atomic Spectra and the Bohr Atom
Problem: How much energy (J) is liberated when an
electron changes from n = 4 to n = 2? What is the
wavelength (m) of the light emitted?
E  Ef  Ei
 2.180x 10-18 J 

2


nf



 2.180 x 10-18 J 
 2.180x 10-18 J 
 
  
2
2
2f
ni




 2.180 x 10-18 J 


2
4i


E  (0.545x 10 -18 J) - (0.1362x 10-18 J)  0.4088x 10-18 J
To convert energy to wavelength, we must employ the equations:
c
c
  h 
E

c


c
E  h  h   
 

8
3
.
0
x
10
m/s 

Electronic
-34
-7
 6.63 x 10 J.s 

4.865
x
10
m

Structure
-18
of Atoms
 0.4088 x 10 J 
Atomic Spectra and the Bohr Atom
Notice that the wavelength calculated from
the Rydberg equation matches the wavelength
of the green colored line in the H spectrum.
  4.865 x 10-7 m
E  0.4088 x 10-18 J
Electronic
Structure
of Atoms
2006 (B)
Ele 1
Electronic
Structure
of Atoms
Ele 2
Heisenberg’s Uncertainty Principle
• Heisenberg showed that the more
precisely the momentum of a particle
is known, the less precisely is its
position known:
h
(x) (mv) 
4
• In many cases, our uncertainty of the
whereabouts of an electron is greater
than the size of the atom itself!
Electronic
Structure
of Atoms
Quantum Model of the Atom
•
•
•
•
•
•
Max Planck (energy quanta, Planck’s constant)
Albert Einstein (energy and frequency)
Niels Bohr (electrons and Spectra)
Louis de Broglie (particle-wave duality of matter)
Werner Heisenberg (electron uncertainty)
Erwin Schrödinger (probability wave function, the four
quantum numbers)
Prof. Alonso
• Jörge L. Alônsø (diagrammatic quantum mechanical
atomic model)
Solvay Conference in
Brussels 1911
Electronic
Structure
of Atoms
1
Energy
Levels =
1, 2, 3, etc
2 Sublevel
Orbital
types =
s, p, d, f
3dyz
3s
3pz
3px
2pz
3dxy
2s
2px
3dxz
1s
2py
3 Orbital cloud
orientation
(x, y, z, etc)
3dx
3dx2y2
2
3py
Electronic
4 Electron
pair
spin inStructure
of Orbital
Atoms
cloud (2e- ea)
1
Energy
Levels =
1, 2, 3, etc
2 Sublevel
Orbital
types =
s, p, d, f
3dyz
3s
3pz
3px
2pz
3dxy
2s
2px
3dxz
1s
2py
3 Orbital cloud
orientation
(x, y, z, etc)
3dx
3dx2y2
2
3py
Electronic
4 Electron
pair
spin inStructure
of Orbital
Atoms
cloud (2e- ea)
Quantum Numbers
• Describe the location of electrons within atoms.
• There are four quantum numbers:
 Principal = describes the energy level (1,2,3,etc)
Azimuthal = energy sublevel, orbital type (s2, p6,
d10, f14)
Magnetic = orbital orientation or cloud (2
electrons on each cloud) Example: three p clouds:
px, py, pz
Electronic
Spin = which way the electron is spinning (↑↓) Structure
of Atoms
Electron Configuration, Orbital Notation
and Quantum Numbers
Principal (n)= energy level
Azimuzal () = sublevel
orbital type
1s2 2s2 2p6 3s23p63d10 4s24p64d104f14
Magnetic (ml) = orbital
cloud orientation (2eper orbital)
Spin (ms) =
electron + or Electronic
Structure
of Atoms
Electron Configuration
Two issues:
(1)Arrangement of electrons within an atom
1s2 2s2 2p6 3s23p63d10 4s24p64d104f14
(2) Order in which electrons fill the orbitals
1s22s22p63s23p64s23d104p65s24d105p66s24f14
Aufbau Process:
Using Periodic Table Sub-blocks:
Electronic
Structure
of Atoms
Historic Development of Atomic Theory
Bohr (1913)
Schrödinger (1926)
Electronic
Structure
of Atoms
The Schrödinger Equation
i
• is the imaginary unit, (complex number whose square is a negative real
number)
t
• is time,
• is the partial derivative with respect to t,
• is the reduced Planck's constant (Planck's constant divided by 2π),
ψ(t) • ψ(t) is the wave function,
Electronic
• is the Hamiltonian (a self-adjoint operator acting on the state
Structure
space).
of Atoms
Quantum Mechanics
• Developed by Erwin Schrödinger, it
is a mathematical model
incorporating both the wave &
particle nature of electrons.
• The wave function is designated
with a lower case Greek psi ().
• The square of the wave function, 2,
gives a probability density map of
where an electron has a certain
statistical likelihood of being at any
given instant in time.
Electronic
Structure
of Atoms
{QuantumAtom}
The Schrödinger Equation
• Solving the wave equation gives a set of
wave functions ψ(t ,) 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
Principal Quantum Number, n
1
2
3
• The principal quantum number, n, describes the
energy level on which the orbital resides.
Electronic
• The values of n are integers ≥ 0.
Structure
of Atoms
Azimuthal Quantum Number, 
• This quantum number defines the shape of the orbital.
• Allowed values of  are integers ranging from 0 to n − 1.
• We also use letter designations:
Value of 
0
1
2
3
Type of orbital
s
p
d
f
=0
=1
=2
=3
Electronic
Structure
of Atoms
Magnetic Quantum Number, ml
• Describes the three-dimensional orientation of the
orbital.
• Values 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.
0
+1
0
Electronic
Structure
of Atoms
-1
Values of Quantum Numbers
• Principal Quantum #: values of n are integers ≥ 0.
• Azimuthal Quantum #: values of  are integers ranging from 0 to n − 1.
• Magnetic Quantum #: values are integers ranging from -  to  :
−  ≤ ml ≤  .
Electronic
Structure
of Atoms
s Orbitals ( = 0)
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
{RadialElectronDistribution}
s Orbitals ( = 0)
• Spherical in shape.
• Radius of sphere
increases with
increasing value of n.
{1s}
{2s}
{3s}
Electronic
Structure
of Atoms
p Orbitals ( = 1)
• Have two lobes with a node between them.
+1 {px}
0 {py}
-1 {pz}
Electronic
Structure
{www.link}
of Atoms
2
2
6
Orbital Overlap: 1s 2s 2p
1s

+
2s
2p
“P” orbital electrons are
repelled by the “S” orbital
electrons and so spend more
time further from the
nucleus.
“P” orbital electrons also
repel from each others’
sublevels, so they runElectronic
along
Structure
of Atoms
the axes.
d Orbitals ( = 2)
-1
2
-2
•Four of the five orbitals
have 4 lobes; the other
resembles a p orbital
with a doughnut around
the center.
Electronic
1
0
Structure
of Atoms
{*Orbitals.s.p.d} {www.link}
f Orbitals ( = 3)
0
• There are seven f
orbitals per n level.
1
2
3
-1
-2
-3
 The f orbitals have
complicated names.
 They have an  = 3
 m = -3,-2,-1,0,+1,+2,
+3
7 values of m
 The f orbitals have
important effects in the
lanthanide and actinide
elements.
Electronic
Structure
of Atoms
{www.link.f}
Energies of Orbitals
• For a one-electron
hydrogen atom, orbitals
on the same energy
level have the same
energy.
• That is, they are
degenerate (collapsed).
Electronic
Structure
of Atoms
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
{E.L. vs FillingOrder}
Structure
of Atoms
Electron Configuration & Periodic Table
Electronic
Structure
of Atoms
Spin Quantum Number, ms
• 1920s: it was discovered that two electrons in the
same orbital do not have exactly the same energy.
{e-spin}
The “spin” of
an electron
describes its
magnetic
field, which
Electronic
affects
its
Structure
energy.
of Atoms
Electron Configurations
• Distribution of all
electrons in an atom.
• Consist of
 Number denoting the
energy level.
 Letter denoting the type
of orbital.
 Superscript denoting the
number of electrons in
those orbitals.
Electronic
Structure
of Atoms
Orbital Diagrams
• Each box represents
one orbital.
• Half-arrows represent
the electrons.
• The direction of the
arrow represents the
spin of the electron.
Electronic
Structure
of Atoms
Basic Principles of Electron
Configuration Notations
• Pauli Exclusion Principle
• Hund’s Rule of Maximum Multiplicity
• Alonso’s Rules of the Stability of Degenerate Orbitals
Electronic
Structure
of Atoms
Pauli Exclusion Principle
Only two electrons can occupy an orbital and
they must have opposite spins.
Electronic
• No two electrons in the same atom can have exactly the same
Structure
of Atoms
energy (identical sets of quantum numbers)
Hund’s Rule of Maximum Multiplicity
One electron fills each orbital before a second of
opposite spin accompanies it.
“For degenerate orbitals, the lowest energy is
attained when the number of electrons with the same
spin is maximized.”
{Electron Configuration}
{Electron Configuration2}
Electronic
Structure
of Atoms
Alonso’s Rules of the Stability of
Degenerate Orbitals
s
d
Completely Filled Completely Filled
Completely Filled Half Filled
Most Stable
Electron
Configuration
Half Filled
Half Filled
Completely Filled Not even Half Filled
Phenomenon also occurs between degenerate s and f orbitals
Electronic
Structure
of Atoms
Periodic Table and
Electron
Configuration
{e- filling order}
Electronic
Structure
of Atoms
Nitrogen
1s22s22p3
Electronic configuration :
4s
3d
3p
3s
2p
Hund’s Rule
2s
1
1s
2
GROUP
3
4
5
6
7
0
He
1
H
2
Li
Be
B
C
N
O
F
Ne
3
4
Na Mg
Al
Si
P
S
Cl
Ar
Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br
Kr
K
Ca Sc
Ti
V
Electronic
Structure
of Atoms
Neon
1s22s22p6
Electronic configuration:
4s
3d
3p
3s
2p
Hund’s Rule
2s
1
1s
2
GROUP
3
4
5
6
7
0
He
1
H
2
Li
Be
B
C
N
O
F
Ne
3
4
Na Mg
Al
Si
P
S
Cl
Ar
Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br
Kr
K
Ca Sc
Ti
V
Electronic
Structure
of Atoms
Vanadium
1s22s22p6 3s2 3p6 4s2 3d3
Electronic configuration:
4s
3d
3p
[Ar]
2p
[Ne]
3s
2s
1
1s
2
GROUP
3
4
5
6
7
0
He
1
H
2
Li
Be
B
C
N
O
F
Ne
3
4
Na Mg
Al
Si
P
S
Cl
Ar
Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br
Kr
K
Ca Sc
Ti
V
Electronic
Structure
of Atoms
Chromium
1s22s22p6 3s2 3p6 4s1 3d5
Electronic configuration:
4s
3d
3p
[Ar]
2p
[Ne]
3s
Notice that one of the 4s electrons
has been transferred to 3d so that 3d
is now a half filled shell with extra
stability. 4s and 3d contain only
unpaired electrons.
2s
1
1s
2
GROUP
3
4
5
6
7
0
He
1
H
2
Li
Be
B
C
N
O
F
Ne
3
4
Na Mg
Al
Si
P
S
Cl
Ar
Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br
Kr
K
Ca Sc
Ti
V
Electronic
Structure
of Atoms
Nickel
1s22s22p6 3s2 3p6 4s2 3d8
Electronic configuration:
4s
3d
3p
[Ar]
2p
[Ne]
3s
2s
1
1s
2
GROUP
3
4
5
6
7
0
He
1
H
2
Li
Be
B
C
N
O
F
Ne
3
4
Na Mg
Al
Si
P
S
Cl
Ar
Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br
Kr
K
Ca Sc
Ti
V
Electronic
Structure
of Atoms
Copper
1s22s22p6 3s2 3p6 4s13d10
Electronic configuration:
4s
3d
3p
Notice that again one of the 4s electrons
has been promoted to 3d so that 3d
is now a completely filled shell with extra
stability.
3s
2p
2s
1
1s
2
GROUP
3
4
5
6
7
0
He
1
H
2
Li
Be
B
C
N
O
F
Ne
3
4
Na Mg
Al
Si
P
S
Cl
Ar
Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br
Kr
K
Ca Sc
Ti
V
Electronic
Structure
of Atoms
Some Anomalies
Some irregularities occur when there are enough Electronic
Structure
of Atoms
electrons to half-fill s and d orbitals on a given row.
Some Anomalies
Electron configuration for copper is
[Ar] 4s1 3d5
rather than the expected
[Ar] 4s2 3d4.
Electronic
•This occurs because the s and d orbitals are very close in energy.
Structure
of Atoms
Some Anomalies
• These anomalies also occur in f-block atoms, as well.
Electronic
Structure
of Atoms
Electron Configuration
Identify elements which posses the following
electron configurations:
1s2 2s2 2p6 3s2 3p6 4s2 3d6 Fe
2
2
6
2
6
0
6
2
6
6
1s 2s 2p 3s 3p 3d 4s
[Ar] 4s 3d
[Ar] 4s 3d
Fe
2+
Fe
2
Fe
{Aufbau order of filling}
{Energy level order}
{Previous Nobel Gas Abbreviation}
{Cations formed by removal of outermost
electrons}
2-
Write Elect-Config for S
[Ne] 3s2 3p6
Electronic
Structure
of Atoms
Electronic
Structure
of Atoms
Periodic Table and
Electron
Configuration
{e- filling order}
Electronic
Structure
of Atoms
Uses dots to represent
Valence Electrons = those in
outermost Energy Level
1
2
3
4
5
6
7
Transition Metals
Have additional electrons, but
they are in an energy level that is
lower than the valence electrons.
Electronic
Structure
of Atoms
Electronic
Structure
of Atoms
Electrons behave as waves (like standing waves above) and particles.
Electron position cannot be pinned down.
Electronic
Structure
of Atoms
Electons don’t follow orbits, but rather orbitals describe their paths.
The Energy of Electromagnetic Waves
Einstein concluded that energy (E) is proportional to
frequency():
E  h 
where h is Planck’s constant, 6.63  10−34 J-s.
Electronic
Energy from electrons comes in whole number multiples ofStructure
h.
of Atoms
 = eq given
The Bohr Model of the Atom (1913)
Electronic
Structure
of Atoms
The Nature of Energy
• 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
Electronic
Structure
of Atoms
Atoms and Electromagnetic Radiation
•To understand the electronic structure of atoms, one must
understand the nature of waves.
Atoms absorb and emit energy, often in the form of electromagnetic radiation
(light, microwaves, radio & TV waves, u.v., infrared,etc)
Electronic
Structure
of Atoms