Download Chapter 6: Electronic Structure of Atoms Recommended Text

Chapter 6: Electronic
Structure of Atoms
Recommended Text
Problems
„
5, 8, 15, 17, 19, 21, 25, 29ab,
„
31, 49, 51, 53, 55ab, 57ac, 59,
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63, 65, 67abcd, 71, 73, 90
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The Nature of Light
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Case 1
„
„
„
Stand outside in the sun.
The shadow your body makes in sunlight
suggests that light travels in straight lines from
the sun and is blocked by your body.
In this, light behaves like
The Nature of Light
„
Case 2
„
„
„
Place two sheets of glass together with a little
water between them.
With care, you will see fringes.
These are formed by
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The Nature of Light
„
Light is a electromagnetic radiation
„
It contains 2 components
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Electric and magnetic components
Waves
„
The wavelength (λ)
„
The frequency (ν)
„
For waves traveling at the
same velocity, the longer the
wavelength, the smaller the
frequency.
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Electromagnetic Radiation
„
„
All electromagnetic radiation travels at the
same velocity: the speed of light (c),
3.00 × 108 m/s.
Therefore,
Example:
„
What is the wavelength of yellow light with a
frequency of 5.09 x 1014 s-1? (Note: s-1,
commonly referred to as Hertz (Hz) is defined
as “cycles or waves per second”.)
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More Example:
„
What is the frequency of violet light
with a wavelength of 408 nm?
Photoelectric Effect
„
„
In 1905, Albert Einstein proposed that
light had both wave and particle
properties as observed in the
photoelectric effect.
He concluded that energy is proportional
to frequency:
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Photoelectric Effect
„
„
„
The photoelectric effect is the ejection of
electrons from the surface of a metal
when light shines on it.
Electrons are ejected only if the light
exceeds a certain “threshold” frequency.
Violet light, for example, will cause
potassium to eject electrons, but no
amount of red light (which has a lower
frequency) has any effect.
Example
„
What is the energy of a photon
corresponding to radio waves of
frequency 1.255 x 10 6 s-1?
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Line Spectrum
„
„
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.
Line Spectrum
„
Niels Bohr adopted Planck’s assumption and
explained:
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Line Spectrum
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The Energy of an allowed orbital in a hydrogen
atom is
Line Spectrum
„
The energy absorbed or emitted from the
process of electron promotion or demotion can
be calculated by the equation:
„
Lyman series:
„
Balmer :
„
Paschen
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Example:
Predict which of the following
electronic transitions produces the
spectral line having the longest
wavelength: n = 2 to n = 1, n = 3 to
n = 2, or n = 4 to n = 3.
Example:
„
Calculate the energy of a photon of light
emitted from a hydrogen atom when an
electron falls from level n = 3 to level n = 1.
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The Wave Nature of Matter
„
„
Louis de Broglie proposed that if light
can have material properties, matter
should exhibit wave properties.
He demonstrated that the relationship
between mass and wavelength was
Example
„
The de Broglie relation shows that a baseball
(0.145 kg) moving at about 60 mph (27 m/s)
has a wavelength of about 1.7 x 10-34 m.
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Practice
„
What is the wavelength of an electron moving
with a speed of 5.97 × 106 m/s? The mass of
the electron is 9.11 × 10–31 kg.
The Uncertainty Principle
„
Heisenberg showed that the more
precisely the momentum of a particle is
known, the less precisely is its position
known:
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Quantum Mechanics
„
Although we cannot precisely define an electron’s
orbit, we can obtain the probability of finding an
electron at a given point around the nucleus.
„
„
Erwin Schrodinger defined this probability in a
mathematical expression called a wave function,
denoted ψ (psi).
ψ2
Quantum Mechanics
„
„
„
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.
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Principal Quantum Number (n)
„
The principal quantum number, n,
describes the
on which
the orbital resides.
Angular Momentum Quantum
Number (l)
„
This quantum number defines the
of the orbital.
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Magnetic Quantum Number
(ml)
„
The magnetic quantum number
describes the
of the orbital.
Magnetic Quantum Number
(ml)
„
„
Orbitals with the same value of n form a shell.
Different orbital types within a shell are
subshells.
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Example:
a.
b.
c.
Predict the number of subshells in the
fourth shell, that is, for n = 4.
Give the label for each of these subshells.
How many orbitals are in each of these
subshells?
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.
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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.
p Orbitals
„
„
The value of l for p orbitals is 1.
They have two lobes with a node between
them.
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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.
Energies of Orbitals
„
„
For a one-electron hydrogen atom,
Degenerate.
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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.
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.
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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.
Electron Configurations
„
„
This shows the distribution of
all electrons in an atom.
Each component consists of
4p 5
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Orbital Diagrams
„
„
„
Each box in the diagram
represents
Half-arrows represent
The direction of the
arrow represents the
Hund’s Rule
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Orbital Energy Levels in Multielectron Systems
3d
4s
Energy
3p
3s
2p
2s
1s
Electron Configuration
„
Here are a few examples.
„
Using the abbreviation [He] for 1s2, the
configurations are
Z=4 Beryllium
Z=3 Lithium
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Electron Configuration
„
With boron (Z=5), the electrons begin
filling the 2p subshell.
Z=5 Boron
Z=6 Carbon
Z=7 Nitrogen
Z=8 Oxygen
Z=9 Fluorine
Z=10 Neon
1
s
2
2
s
2
2
p
2
Electron Configuration
„
Note that elements within a given family have
similar configurations.
„
The Group IIA elements are sometimes called the
alkaline earth metals.
Beryllium
Magnesium
Calcium
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Electron Configuration
„
Note that elements within a given family have
similar configurations.
Helium
Neon
Argon
Krypton
Example
„
Draw the orbital diagram for the electron
configuration of oxygen, atomic number 8.
How many unpaired electrons does an
oxygen atom possess?
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More Example
„
What is the characteristic valence
electron configuration of the group 7A
elements, the halogens?
Practice Makes Perfect
„
(a) Write the electron configuration for
bismuth, element number 83. (b) Write the
condensed electron configuration for this
element. (c) How many unpaired electrons
does each atom of bismuth possess?
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Some Anomalies
„
„
Some irregularities occur when there are
enough electrons to
This occurs because
Example
„
Boron, atomic number 5, occurs naturally as two isotopes,
and 11B, with natural abundances of 19.9% and 80.1%,
respectively.
a.
b.
c.
d.
e.
f.
10B
In what ways do the two isotopes differ from each other? Does the
electronic configuration of 10B differ from that of 11B?
Draw the orbital diagram for an atom of 11B. Which electrons are
the valence electrons?
Indicate three major ways in which the 1s electrons in boron differ
from its 2s electrons.
Elemental boron reacts with fluorine to form BF3, a gas. Write a
balanced chemical equation for the reaction of solid boron with
fluorine gas.
ΔHof for BF3(g) is –1135.6 kJ mol–1. Calculate the standard
enthalpy change in the reaction of boron with fluorine.
When BCl3, also a gas at room temperature, comes into contact
with water, the two react to form hydrochloric acid and boric acid,
H3BO3, a very weak acid in water. Write a balanced net ionic
equation for this reaction.
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Definitions/Principals
„
„
„
„
„
„
wavelength (λ)
frequency (ν)
the photoelectric effect.
The uncertainty
principle
principal quantum
number, n
angular momentum
quantum number, l
„
„
„
„
„
„
magnetic quantum
number, ml
spin quantum number,
ms
degenerate.
spin quantum number,
ms
Hund’s rule
Pauli exclusion principle
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