Chapter 6 Electronic Structure of Atoms

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Chapter 6Electronic Structure of Atoms
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The Wave Nature of Light
Properties of waves
All waves have a characteristic wavelength, ?,
and amplitude, A
Wind-generated ocean waves frequency 5-20
s wavelength 100-200 m Tsunami-generated
waves frequency 10-120 min wavelength gt500
km
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The frequency, ?, of a wave is the number of
cycles which pass a point in one second
Speed, v, frequency, ?, and wavlength, ?, are
related by the wave equation
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For light and other electromagnetic radiation
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All electromagnetic radiation (X-rays, UV,
visible, infrared, radio waves, etc)
-does not require a medium -travels at the same
speed, c
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Quantized Energy and Photons
Max Planck (1858-1947) and the study of radiation
from hot bodies energy can only be absorbed or
released from atoms in certain amounts called
quanta, i.e. energy is quantized.
"A new scientific truth does not triumph by
convincing its opponents and making them see the
light, but rather because its opponents
eventually die, and a new generation grows up
that is familiar with it."-Max Planck, A
Scientific Autobiography and Other Papers , 1949
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Light is quantized and has particle-like
properties.
Common analogy to explain quantization. Consider
walking up a ramp versus walking up stairs.
So, energy is always emitted or absorbed in
whole-number multiples
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First experimental evidence for quantization The
Photoelectric Effect and Photons (Einstein, 1905)
Albert Einstein 1921 Nobel Prize in physics for
photoelectric effect
Max Planck 1918 Nobel Prize in physics for
quantum theory
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If light shines on the surface of a metal
electrons may be ejected from the metal. This is

. The electrons will only be ejected if the
frequency of the light is greater than a certain
minimum frequency (the threshold frequency).
Below the threshold frequency, no electrons are
ejected. Above the threshold frequency, the
number of electrons ejected increases as the
intensity of the light increases. The kinetic
energy of the emitted electrons increases
as .
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Einsteins explanation
Energy is quantized each quantum called a .
Energy of each quantum given by the Planck
equation
Minimum energy needed to release an e- from
metal work function, wo, of metal
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Let wo h?o
If E lt wo, i.e. if ? lt ?o each photon does not
have enough energy to release e- ?
If light did not have particle properties, then
increasing intensity of light should transfer
enough energy to release e- (light would be a
continuous energy stream)
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Some properties of light can only be explained
using a wave model (e.g., diffraction).
Light has a dual nature
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Line spectra and the Bohr Model
Monochromatic Radiation that
spans a whole array of different
wavelengths White light can be separated
into a continuous spectrum of colors.
Max Planck (right) with Neils Bohr, 1922 Nobel
Prize in physics.
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simple gas like Na or H2
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To calculate the wavelengths of the spectral
lines of the hydrogen atom, the Rydberg equation
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Line spectra used by Neils Bohr as basis for a
model of the atom
In a stationary state, e- can circle nucleus
without losing energy
Between stationary states, e- loses energy as
photons (hv) until it enters a new stationary
state.
Therefore e- in an atom can have only particular
energies!
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The first orbit in the Bohr model has n 1,
closest to the nucleus, and has negative energy
by convention.
The furthest orbit in the Bohr model has n
(quantum number) close to infinity and
corresponds to zero energy, i.e., the electron
has escaped from the influence of the nucleus.
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Electrons in the Bohr model can only move between
orbits by absorbing and emitting energy in quanta
(h?).
Does this diagram show absorption or emission of
quanta?
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Electrons in the Bohr model can only move between
orbits by absorbing and emitting energy in quanta
(h?).
Does this diagram show absorption or emission of
quanta?
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Electrons in the Bohr model can only move between
orbits by absorbing and emitting energy in quanta
(h?).
The amount of energy absorbed or emitted on
movement between states is given by
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Example
What is the wavelength of the energy that must be
absorbed for an electron to be promoted from the
n1 to the n3 level in a hydrogen atom?
Note n is called the Principal Quantum Number
nf gt ni if energy is absorbed.
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Now c ??
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The Wave Behavior of Matter
Planck, Einstein light has particle properties
de Broglies proposal
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Example
What is the wavelength of an electron (m 9.11 x
10-31 kg) traveling with a velocity of 0.01 c,
compared to that of a golfball (m 100 g, v 30
m s-1)?
l
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But wavelength of a golf ball (m 100 g v 30
m s-1)
x
l
The wavelength property of matter is only
important for very small particles traveling at
very high speed.
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Proof diffraction of a beam of electrons
Diffraction is a property of waves
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The Uncertainty Principle
Because of wave nature of matter, cannot
determine precisely the momentum (mv) or the
position of a small particle moving at high
speed. Called the Heisenberg Uncertainty
Principle If ?x is the uncertainty in position
and ?mv is the uncertainty in momentum, then
Werner Heisenberg (1901-1976) 1933 Nobel Prize
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Quantum Mechanics and Atomic Orbitals
If an electron has wave properties it can be
described by a wave equation.
Developed by Schrödinger for the H atom.
Greek psi
Electron in an atom described by a wave function,
?.
? has no physical meaning but ?2 ? probability
of finding an electron in a region of space
probability density
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Schrödingers quantum mechanical description of
atomic structure
Allowed energy levels of an electron in an atom
(quantized)
Hamiltonian operator describes electrons Ek
and Ep
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Orbitals and Quantum Numbers
Allowed energy levels
Described by three quantum numbers
n principal quantum number
l azimuthal quantum number
ml magnetic quantum number
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Example
n 3 (3rd energy level of atom)
? l 0, 1, 2
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n 3 (3rd energy level of atom)
? l 0, 1, 2
one s orbital
three p orbitals
five d orbitals
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Representations of Orbitals
All s-orbitals are spherical
As n increases, the s-orbitals
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A node is .
node
At a node, ?2 0
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As n increases, the number of nodes increases.
For an s-orbital, the number of nodes is given by
(n - 1).
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Chapter 6, Fig 18
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n 3 (3rd energy level of atom)
? l 0, 1, 2
one s orbital
three p orbitals
five d orbitals
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Fig. 6.20, 9th Ed. Fig. 6.22, 10th Ed.
There are three p-orbitals
. The three p-orbitals lie along
the x-, y- and z- axes of a Cartesian system.
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There are three p-orbitals px, py, and pz. The
three p-orbitals lie along the x-, y- and z- axes
of a Cartesian system.
The letters correspond to allowed values of ml of
-1, 0, and 1.
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.
The orbitals are shaped. As
n increases, the p-orbitals
. All p-orbitals have
(and other nodes for n ? 3)
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n 3 (3rd energy level of atom)
? l 0, 1, 2
one s orbital
three p orbitals
five d orbitals
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n must be 3 or greater ml numbers are -2, -1, 0,
1, 2
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Effective Nuclear Charge (Chapter 7.2)
All s orbitals have ?2 ? 0 at the nucleus.
Therefore electrons in s orbitals feel the full
effect of the nuclear charge.
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In the case of p, d and f orbitals, there is a
node at the nucleus.
Electrons in these orbitals feel the nuclear
charge less.
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In fact, electrons in p and d orbitals are
screened from the nucleus by the s electrons, and
by electrons in inner shells.
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As the effective nuclear charge on an electron
decreases, the electron moves further from the
nucleus and its energy increases (less coulombic
attraction by nucleus).
Hence for a given shell the energy of the
orbitals becomes
s lt p lt d lt f
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In the H atom, all orbitals in a shell have the
same energy.
This is called an .
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This energy level diagram is for one electron
atoms only H, He, Li2, etc
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Many-Electron Atoms
For multi-electron atoms (He, Li, Li, etc.) the
orbital energy level diagram is different
And
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Stern-Gerlach experiment Evidence for Electron
Spin
Beam of Ag atoms with an odd number of electrons
focusing slit
detector
magnetic field
Led to the ms spin quantum number
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Electrons have a property called spin.
Spin is a quantized property governed by a spin
quantum number S. The possible values are called
ms.
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The Pauli Exclusion Principle
. Determined from observing two
very distinct lines in line spectra that first
appeared to be one single line.
Result of this
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The Exclusion Principle governs the way that
electrons can be accommodated in the orbitals of
an atom.
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Examples
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Examples
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Examples
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Examples
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Examples
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Examples
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Mg
is written for convenience as
Mg
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The periodic table reflects the electron
configuration of the elements
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Ga
Ga
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Pb
Pb
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End of Chapter 6Electronic Structure of Atoms