Chemistry 101 : Chap. 6 Electronic Structure of Atoms (1) The Wave Nature of Light (2) Quantized...
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Transcript of Chemistry 101 : Chap. 6 Electronic Structure of Atoms (1) The Wave Nature of Light (2) Quantized...
Chemistry 101 : Chap. 6Chemistry 101 : Chap. 6
Electronic Structure of Atoms
(1) The Wave Nature of Light
(2) Quantized Energy and Photon
(3) Line Spectra and Bohr Models
(4) The Wave Behavior of Matter
(5) Quantum Mechanics and Atomic Orbitals
(6) Representations of Orbitals
(7) Many Electron Atoms
(8) Electron Configurations
(9) Electron Configurations and Periodic Table
Electronic StructureElectronic Structure
What is the electronic structure?
The way electrons are arranged in an atom
How can we find out the electronic structure experimentally ?
Analyze the light absorbed and emitted by substances
Is there a theory that explains the electronic structure of atoms?
Yes. We need “quantum mechanics” to explain the results from experiments
Wave Nature of LightWave Nature of Light
Electromagnetic Radiation :
Visible light is an example of electromagnetic radiation (EMR)
Electric Field
Magnetic Field
Wave Nature of LightWave Nature of Light
Properties of EMR
All EMR have wavelike characteristics
Wave is characterized by its wavelength, amplitude and
frequency
EMR propagates through vacuum at a speed of 3.00 108 m/s
(= speed of light = c)
Wave Nature of LightWave Nature of Light
Frequency () and wavelength ()
Frequency measures how many wavelengths pass through a point per second:
1 s
4 complete cycles pass
through the origin
= 4 s-1 = 4 Hz
Note that the unit of is m
= c
Wave Nature of LightWave Nature of Light
Example : What is the wavelength, in m, of radio wave transmitted
by the local radio station WHQR 91.3 MHz?
Wave Nature of LightWave Nature of Light
Example : Calculate the frequency of radio wave emitted by a
cordless phone if the wavelength of EMR is 0.33m.
Physics in the late 1800’sPhysics in the late 1800’s
Universe
Matter (particles) Wave (radiation)
F = ma
Newton’s equation
Isaac Newton (1643-1727)
0
BJt
EB
Et
BE
Maxwell’s equation
James C. Maxwell (1831-1879)
The Failure of Classical TheoriesThe Failure of Classical Theories
In the late 1800, there were three important phenomena that
could not be explained by the classical theories
Black body radiation
Photoelectric effect
Line Spectra of atoms
Black Body RadiationBlack Body Radiation
Black body :
An object that absorbs all electromagnetic radiations that falls
onto it. No radiation passes through it and none is reflected.
The amount and wavelength of electromagnetic radiation
a black body emits is directly related to their temperature.
Hot objects emit light.
The higher the temperature, the higher the emitted frequency
Black Body RadiationBlack Body Radiation
wavelength (nm)
inte
nsity
visible region
“Ultraviolet catastrophe” classical theory predictssignificantly higher intensityat shorter wavelengths thanwhat is observed.
Black Body RadiationBlack Body Radiation
Classical Theory :
Electromagnetic radiation has only wavelike characters.
Energy (or EMR) can be absorbed and emitted in any amount.
Planck’s Solution :
Max Planck (1858 - 1947)
He found that if he assumed that energy
could only be absorbed and emitted in
discrete amounts then the theoretical and
experimental results agree.
1exp
8)(
5
kThc
hcI
Quantization of EnergyQuantization of Energy
Energy Quanta : Planck gave the name ``quanta’’ to the smallest
quantity of energy that can be absorbed or emitted as EMR.
E = h
h = Planck Constant = 6.626 10-34 Js
Energy of a quantumof EMR with frequency
frequency of EMR
NOTE : Energy of EMR is related to frequency, not intensity
NOTE : When energy is absorbed or emitted as EMR with a frequency , the amount of energy should be a integer multiple of h
Quantization of EnergyQuantization of Energy
Example : Calculate the energy contained in a quantum of EMR
with a frequency of 95.1 MHz.
Photoelectric EffectPhotoelectric Effect
Photoelectric Effect : When light of certain frequency strikes a
metal surface electrons are ejected. The velocity of ejected
electrons depend on the frequency of light, not intensity.
e- e- e-
e-
K.E.of ejected electron =
Energy of EMR Energy needed to release an e-
Light of a certain minimum frequency
is required to dislodge electrons from
metals
Photoelectric EffectPhotoelectric Effect
Einstein’s Solution: In 1905, Einstein explained photoelectric
effect by assuming that EMR can behave as a stream of particles,
which he called photon. The energy of each photon is given by
Ephoton = h
e- e- e-
K.E.e = h
incident photon energy
binding energy Kinetic energyof ejected electrons
Einstein’s discovery confirmed Planck’snotion that energy is quantized.
Energy, Frequency and Wavelength
Energy, Frequency and Wavelength
Example : Calculate the energy of a photon of EMR with a
wavelength of 2.00 m.
EMR: Is it wave or particle?EMR: Is it wave or particle?
Einstein’s theory of light poses a dilemma:
Is light a wave or does it consist of particles?
When conducting experiments with EMR using wave measuring
equipment (like diffraction), EMR appear to be wave
When conducting experiments with EMR using particle techniques
(like photoelectric effect), EMR appear to be a stream of particles
EMR actually has both wavelike and particle-like characteristics.
It exhibits different properties depending on the methods used
to measure it.
Continuous SpectrumContinuous Spectrum
Many light sources, including light bulb, produce light containing many different wavelengths
continuous spectrum
Line SpectrumLine Spectrum
When gases are placed under low pressure and high voltage,
they produces light containing a few wavelengths.
Line SpectrumLine Spectrum
Rydberg equation: The positions of all line spectrum () can be
represented by a simple equation.
22
21
111
nnRH
RH (Rydberg Constant) = 1.096776 107 m-1 (for hydrogen)
n1 and n2 are integer numbers (n1 < n2)
Line SpectrumLine Spectrum
Example : Identify the locations of first three lines of hydrogen
line spectrum
Bohr Model of Hydrogen AtomBohr Model of Hydrogen Atom
(1) The electron is permitted to be in orbits of certain radii,
corresponding to certain definite energies.
(2) When the electron is in such permitted orbits, it does not
radiate and therefore it will not spiral into the nucleus.
(3) Energy is emitted or absorbed by the electron only as the
electron changes from one allowed state (or orbit) to another.
This energy is emitted or absorbed as a photon, E=h
Bohr Model of Hydrogen AtomBohr Model of Hydrogen Atom
n = 1n = 2n = 3n = 4n = 5n = 6
nucleus
Bohr model proposed in 1913Niels Bohr (1885 – 1962)
principal quantum number
ground state
excited states
Bohr Model of Hydrogen AtomBohr Model of Hydrogen Atom
Question #1 : What is the energy of electron associated with each orbit?
218
2
1)1018.2(
1)(
nJ
nhcRE H
n = 6n = 5n = 4
n = 3
n = 2
n = 1
4
11018.2 18 JE
JE 181018.2
9
11018.2 18 JE
n = 6n = 5n = 4
n = 3
n = 2
n = 1
Energy
Ground State
e
Ground State e
Bohr Model of Hydrogen AtomBohr Model of Hydrogen Atom
h = | Einit - Efinal |
Question #2 : How much energy will be absorbed or emitted when the
electron changes it orbit between n1 and n3?
n3 n1 : Einit > Efinal emission n1 n3 : Einit < Efinal absorption
Bohr Model of Hydrogen AtomBohr Model of Hydrogen Atom
Example : How much energy will be absorbed or emitted for
an electron transition from n=1 to n=3 ? What is the
frequency of light associated with such transition?
Is this result consistent with the Rydberg equation?
Bohr Model of Hydrogen AtomBohr Model of Hydrogen Atom
Why the hydrogen line spectra (above)
shows only Balmer series, involving n=2?
What happens to the transitions
involving n=1?
Balmer series
Energy gap decreases as n increases
What is the meaning of n = and E = 0?
Limitations of Bohr ModelLimitations of Bohr Model
(1) Bohr model does not work for atoms with more than
one electron
Check out http://jersey.uoregon.edu/vlab/elements/Elements.htmlfor emission and absorption spectra all elements in periodic table
(2) There are more lines buried under the line spectrum of
hydrogen. Bohr model of hydrogen can not explain such
fine structure of hydrogen atom, which was discovered later.
The Wave Behavior of Matter The Wave Behavior of Matter
Electrons in Bohr model are treated as particles. In order to
explain the electronic structure of atom, we need to incorporate
the wave-like nature of electron into the theory.
Louis de Broglie (1892-1987)
vm
hDe Broglie Wavelength
For a particle of mass m, moving with a velocity v,
The Wave Behavior of Matter The Wave Behavior of Matter
Example : What is the wavelength of an electron traveling at 1% of the
speed of light? Repeat the calculation for a baseball moving at 10 m/s.
(mass of electron = 9.11 10-31 kg, mass of baseball = 145 g)
Quantum MechanicsQuantum Mechanics
Schrodinger developed a theory incorporating wave-like nature of particles
(1) The motions of particles can be described by wavefunction, (r).
(2) Wavefunction, (r), can tell us only the probability to locate
the particle at the position r
Erwin Schrodinger (1887-1961)
Schrodingerequation
Werner Heisenberg (1901-1976)
Hydrogen Atom in Quantum Mechanics
Hydrogen Atom in Quantum Mechanics
• The denser the stippling, the higher the probability of finding the electron
Probability to find a electron
Bohr model vs. Quantum Mechanics
Bohr model vs. Quantum Mechanics
or
n = 1
n = 1
orbit
orbitalz
x
y
Bohr’s model:
Quantum Mechanics:
electron circles around nucleus
electron is somewherewithin that spherical region
Bohr model vs. Quantum Mechanics
Bohr model vs. Quantum Mechanics
Probability to find the electron at a distance r from the nucleus(green = Bohr model, Red = Quantum Mechanics)
n = 1 n = 2
distance from nucleus (10-10 m) distance from nucleus (10-10 m)
Bohr model vs. Quantum Mechanics
Bohr model vs. Quantum Mechanics
Bohr’s model:
Quantum Mechanics:
requires only the principal quantum number (n) to describe an orbit
n : principal quantum numberl : azimuthal quantum numberml : magnetic quantum number
needs three different quantum numbers to describe an orbital
Bohr model vs. Quantum Mechanics
Bohr model vs. Quantum Mechanics
Energy level diagam
n=1
n=2
n=3
Energy
Bohr model Quantum Mechanics
l = 1
l = 0
l = 2
Principal Quantum NumberPrincipal Quantum Number
Principal quantum number, n, in quantum mechanics is
analogous to the principal quantum number in Bohr model
The higher n, the higher the energy of the electron
Energy of electron in a given orbital :
2
1n
RchE H
n is always a positive integer: 1, 2, 3, 4 ….
n describes the general size of orbital and energy
Azimuthal Quantum NumberAzimuthal Quantum Number
l takes integer values from 0 to n-1
for n = 3 l = 0, 1, 2e.g.
l is normally listed as a letter:
Value of l: 0 1 2 3 letter: s p d f
l defines the shape of an electron orbital
Azimuthal Quantum NumberAzimuthal Quantum Number
z
x
y
l = 0s-orbital
l =1p-orbital(1 of 3)
l = 2 d-orbital(1 of 5)
l = 3f-orbital(1 of 7)
Magnetic Quantum NumberMagnetic Quantum Number
ml takes integral values from -l to +l, including 0
for l = 2 ml = -2, -1, 0, 1, 2e.g.
ml describes the orientation of an electron orbital in space
2Pz2Px
2Py
Example : Which of the following combinations of quantum numbers is possible?
n=1, l=1, ml= -1
n=3, l=2, ml= 1
n=2, l=1, ml= -2
n=3, l=0, ml= -1
Quantum NumbersQuantum Numbers
Atomic OrbitalsAtomic Orbitals
Shell:
A set of orbitals with the same principal quantum number, n
Subshells:
Orbitals of one type (same l) within the same shell
A shell of quantum number n has n subshells
Total number of orbitals in a shell is n2
Atomic Orbitals in H AtomAtomic Orbitals in H Atom
n=1 shell : It has 1 subshell (1s)
n=2 shell : It has 2 subshells (2s, 2p)
n=3 shell : It has 3 subshells (3s,3p,3d)
There are 5 orbitals in this subshell
Each orbital in this subshell hasthe same n and l quantum number,but different ml quantum number
Atomic OrbitalsAtomic Orbitals
Example: Fill in the blanks in the following table
Principal quantum Type of orbitals Total Number Number (n) (subshell) of orbitals
1
2
3
4
Electron Spin Quantum NumberElectron Spin Quantum Number
Spin magnetic quantum number (ms) : A fourth quantum number
that characterizes electrons:
ms can only take two values, +1/2 or -1/2
Many-Electron AtomsMany-Electron Atoms
For the same type of orbitals (i.e same l),
the energy of an orbital increases with n.
For a given value of n, the energy of an
orbital increases with l.
Orbitals in a given subshell (same n, l)
have the same energy (degenerate)
Many-Electron AtomsMany-Electron Atoms
Aufbau Principle helps you to remember the order of energy levels
1s
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d 6f
7s 7p 7d 7f
Many-Electron AtomsMany-Electron Atoms
Electron configuration: The way in which electrons are distributed
among the various orbitals of an atom
(1) The orbitals are filled in order of increasing energy
(2) Pauli exclusion principle : No two electrons in an atom can have
the same set of four quantum numbers (n, l, ml, ms)
Maximum 2 electrons can occupy a single orbital. These two
electrons have the same (n, l, ml) quantum numbers, but different
ms quantum number: one has ms = +1/2 (spin-up) and the other has
ms = -1/2 (spin-down)
1s
or
1s
or 1s2
Many-Electron AtomsMany-Electron Atoms
Electron configurations of H, He, Li, Be, B
H :
1s
He :
1s
Li :1s 2s
Be :
1s 2s
B :
1s 2s 2p
1s1
1s2
1s22s1
1s22s2
1s22s22p1
2s
2s
2p
2p
2p
2p
Many-Electron AtomsMany-Electron Atoms
Electron configuration of C :
1s 2s 2p 1s 2s 2p
Or
(3) Hund’s Rule : For degenerate orbitals, the lowest energy is attained
when the number of electrons with the same spin is maximized.
Which configuration has the lower energy?
Sum of ms value has to be maximized
Total ms value = +1/2 – 1/2 = 0
Total ms value = +1/2 + 1/2 = 1 Lower Energy!
Many-Electron AtomsMany-Electron Atoms
Electron configurations of C, N, O, F, N
C :
N :
O:
F :
Ne :
1s 2s 2p
1s22s22p2
1s 2s 2p
1s22s22p3
1s 2s 2p
1s22s22p4
1s 2s 2p
1s22s22p5
1s 2s 2p
1s22s22p6
Many-Electron AtomsMany-Electron Atoms
[Ne]
14Si 1s22s22p63s23p2 Line notation
orbital diagram(no energy info)
s
p
d
1
2
3
Condensed line notation
“core electrons”
3s23p2
Electron configurations of 14Si
Valence Electrons
Example : What is the electronic structure of Ca? Which electrons are core electrons and which are valence electrons?
Many-Electron AtomsMany-Electron Atoms
valence electrons (2)
core electrons = electron configuration
of the preceding noble gas
s
p
d
1
2
3
20Ca : 4s2
4
f
(4s orbital is filled before 3d !)[Ar]
Many-Electron AtomsMany-Electron Atoms
Example : What is the electronic structure of Br? Which electrons are core electrons and which are valence electrons?
valence electrons (7)
core electrons = electron configuration
of the preceding noble gas
s
p
d
1
2
3
35Br : 3d104s24p5
4
f
(4s orbital is filled before 3d !)[Ar]
For main group elements,electrons in a filled d-shell(or f-shell) are not valenceelectrons
Many-Electron AtomsMany-Electron Atoms
Example : What is the electronic structure of V? Which electrons are core electrons and which are valence electrons?
s
p
d
1
2
3
4
f
23V: [Ar] 3d34s2
core electron = electron configuration
of the preceding noble gas
valence electrons (5)
(4s orbital is filled before 3d !)
Many-Electron AtomsMany-Electron Atoms
Example : What is the electronic structure of Cr? Which electrons are core electrons and which are valence electrons?
s
p
d
1
2
3
4
f
24Cr: [Ar] 3d54s1
[Ar] 3d44s2 is less stable than [Ar] 3d54s1
A half-filled or completely filled d-shell is a preferred configuration
Electronic Structure of IonsElectronic Structure of Ions
Atoms form ions in order to achieve more stable electron
configurations
Metals : ALWAYS LOSE electrons to become
positive ions (cation)
Non-metals: USUALLY GAIN electrons to become
negative ions (anion)
Generally, atoms form ions by loosing or gaining electrons
to achieve the electron configuration of nearest noble gas
Electronic Structure of IonsElectronic Structure of Ions
Electron configurations of 11Na ion :
[Ne]11Na :
s
p
d
1
2
3
“core electrons” = [Ne]
3s1
Valence Electrons
[Ne]11Na+ :
Electronic Structure of IonsElectronic Structure of Ions
valence electrons (7)
core electrons = [Ar]s
p
d
1
2
3
35Br : 3d104s24p5
4
f
[Ar]
Electron configurations of 35Br ion :
35Br : 3d104s24p6 [Ar] = [Kr]
Electronic Structure of IonsElectronic Structure of Ions
Example : What is the electron configuration of Fe and the ions
formed by Fe?
s
p
d
1
2
3
4
f
26Fe: [Ar] 4s23d6
4s electrons (higher n) are removed before 3d electrons
26Fe2+ : [Ar]3d626Fe3+ : [Ar]3d5
Electronic Structure of IonsElectronic Structure of Ions
Example : What is the electron configuration of ion formed by Sc?
s
p
d
1
2
3
4
f
21Sc: [Ar] 4s23d121Sc3+ : [Ar]