Download Chapter 6 Electronic Structure of Atoms

Chemistry, The Central Science, 11th edition
Theodore L. Brown; H. Eugene LeMay, Jr.;
and Bruce E. Bursten
Chapter 6
Electronic Structure
of Atoms
John D. Bookstaver
St. Charles Community College
Cottleville, MO
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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6.1 The Wave Nature of Light
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The electronic structure of an atom refers to the arrangement of electrons.
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Visible light is a form of electromagnetic radiation or radiant energy.
Radiation carries energy through space.
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Electromagnetic radiation is characterized by its wave nature.
All waves have a characteristic wavelength, (). (lambda), and amplitude, A.
The frequency, (). (nu), of a wave is the number of cycles which pass a point in one second.
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The units of (). are Hertz (1 Hz = 1 s–1).
The speed of a wave is given by its frequency multiplied by its wavelength.
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For light, speed, c
=
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Electromagnetic radiation moves through a vacuum with a speed of 3.00 x 108 m/s.
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Electromagnetic waves have characteristic wavelengths and frequencies.
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The electromagnetic spectrum is a display of the various types of electromagnetic radiation
arranged in order of increasing wavelength.
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•Example: visible radiation has wavelengths between 400 nm (violet) and 750 nm (red).
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Title:
Characteristics of water waves.
Caption:
(a) The distance between corresponding points on each wave is called the wavelength.
In this drawing, the two corresponding points are two peaks, but they could be any
other two corresponding points, such as two adjacent troughs.
(b) The number of times per second that the cork bobs up and down is called the
frequency of the wave.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Title:
Characteristics of electromagnetic waves.
Radiant energy has wave characteristics; it consists of electromagnetic waves. Notice that the
shorter the wavelength, λ, the higher the frequency, ν.
The wavelength in (b) is half as long as that in (a), and the frequency of the wave in (b) is
therefore twice as great as the frequency in (a).
The amplitude of the wave relates to the intensity of the radiation, which is the maximum extent of
the oscillation of the wave. In these diagrams amplitude is measured as the vertical distance from
the midline of the wave to its peak.
The waves in (a) and (b) have the same amplitude. The wave in (c) has the same frequency as
that in (b), but its amplitude is lower.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Waves
• To understand the electronic structure of
atoms, one must understand the nature of
electromagnetic radiation.
• The distance between corresponding points
Electronic
on adjacent waves is the wavelength ().
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Waves
• The number of waves
passing a given point per
unit of time is the
frequency ().
• 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 = 
Title:
The electromagnetic spectrum.
Wavelengths in the spectrum range from very
short gamma rays to very long radio waves.
Notice that the color of visible light can be
expressed quantitatively by wavelength.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Concepts of Wavelength and Frequency
Two electromagnetic waves are represented in the figure. (a) Which wave has the higher
frequency? (b) If one wave represents visible light and the other represents infrared radiation,
which wave is which?
(a) The lower wave has a longer wavelength (greater distance between peaks). The
longer the wavelength, the lower the frequency (v = c/λ). Thus, the lower wave has
the lower frequency, and the upper wave has the higher frequency.
(b) The electromagnetic spectrum (Figure 6.4) indicates that infrared radiation has a
longer wavelength than visible light. Thus, the lower wave would be the infrared
radiation.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Sample Exercise 6.2 Calculating Frequency from Wavelength
The yellow light given off by a sodium vapor lamp used for public lighting has a wavelength of
589 nm. What is the frequency of this radiation?
Analyze: We are given the wavelength, λ, of the radiation and asked to calculate its
frequency, v.
Plan: The relationship between the wavelength (which is given) and the frequency
(which is the unknown) is given by Equation 6.1. We can solve this equation for v and
then use the values of and c to obtain a numerical answer. (The speed of light, c, is a
fundamental constant whose value is 3.00 × 108 m/s.)
Solve: Solving Equation 6.1 for frequency gives v = c/λ. When we insert the values
for c and λ, we note that the units of length in these two quantities are different. We can
convert the wavelength from nanometers to meters, so the units cancel:
Check: The high frequency is reasonable because of the short wavelength. The units
are proper because frequency has units of “per second,” or s–1.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The wavelength of electromagnetic energy multiplied by
its frequency equals:
a. c, the speed of light
b. h, Planck’s constant
c. Avogadro’s number
d. 4.184
Practice Exercise
(a) A laser used in eye surgery to fuse detached retinas produces radiation
with a wavelength of 640.0 nm. Calculate the frequency of this radiation. (b)
An FM radio station broadcasts electromagnetic radiation at a frequency of
103.4 MHz (megahertz; MHz = 106 s–1). Calculate the wavelength of this
radiation. The speed of light is 2.998 × 108 m/s to four significant digits.
Answers: (a) 4.688 × 1014 s–1, (b) 2.901 m
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
6.2 Quantized Energy and Photons
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The wave nature of light does not
explain how an object can glow
(shine) when its temperature
increases.
Heated solids emit radiation (black
body radiation)
The wavelength distribution depends
on the temperature (i.e., “red hot”
objects are cooler than “white hot”
objects).
Max Planck proposed that energy can
only be absorbed or released from
atoms in certain amounts.
These amounts are called quanta
He explained it by assuming that
energy comes in packets called
Electronic
quanta.
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
A quantum is the smallest amount of energy that can be emitted or
absorbed as electromagnetic radiation.
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Einstein used this assumption to explain the
photoelectric effect.
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Einstein assumed that light traveled in
energy packets called photons.
The energy of one photon is
• E = h
He concluded that energy is proportional to
frequency:
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where h is Planck’s constant, 6.626  10−34 J-s.
Title:
The photoelectric effect.
Caption:
When photons of sufficiently
high energy strike a metal
surface, electrons are
emitted from the metal.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Sample Exercise 6.3 Energy of a Photon
Calculate the energy of one photon of yellow light with a wavelength of 589 nm.
If one photon of radiant energy
supplies 3.37 × 10–19 J, then one
mole of these photons will supply
(a) A laser emits light with a frequency of 4.69 × 1014 s–1. What is the energy of one photon of the
radiation from this laser?
(b) If the laser emits a pulse of energy containing 5.0 × 1017 photons of this radiation, what is the
total energy of that pulse?
(c) If the laser emits 1.3 × 10–2 J of energy during a pulse, how many photons are emitted during
the pulse?
Answers: (a) 3.11 × 10–19 J, (b) 0.16 J, (c) 4.2 × 1016 photons
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The energy of a photon of
electromagnetic energy divided
by its frequency equals:
a.
b.
c.
d.
c, the speed of light
h, Planck’s constant
Avogadro’s number
4.184
Electronic
Structure
of Atoms
6.3 Line Spectra and the Bohr Model
• Line spectra : a particular source of radiant
energy may emit a single wavelength as in the
light of laser.
• Radiation composed of a single wavelength is
said to be monochromatic
• However most common radiation sources
including light bulbs and stars produce
radiation containing many different wave
length
• Therefore, if one knows the wavelength of
light, one can calculate the energy in one
photon, or packet, of that light:
c = 
E = h
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
• A spectrum is produced when
radiation from light sources is
separated into different
wavelength component as
shown in the figure which is
called continues spectrum
• For atoms (Na) (H) figure
below and molecules one does
not observe a continuous
spectrum, as one gets from a
white light source.
• Only a line spectrum of specific
wavelengths is observed. As
shown
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
The emission spectra observed from energy
emitted by atoms and molecules.
Not all radiation sources produce a continuous
spectrum when a high voltage is applied to
tubes that contain different gases.
The light emitted by neon gases is the familiar
is the red orange glow as shown in figure
A formula that calculate the wavelengths of all
the spectral lines of hydrogen is called
Rydberg equation
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Energy state of the hydrogen atom
•
Niels Bohr adopted Planck’s assumption
and explained these phenomena in this
way:
1. Electrons in an atom can only occupy
certain orbits (corresponding to certain
energies).
The energy that the electron will be
depending on which orbit it is in. page
220
The lower the energy the more stable the
atom will be
n=1 ,2, 3,…….
The lowest energy state n=1 is called the
ground state
When the electron is in a higher energy state
n=2 or higher the atom is said to be I an
excited state
Electronic
Structure
As shown in figure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this
way:
2. Electrons in permitted orbits
have specific, “allowed”
energies; these energies will
not be radiated from the atom.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this
way:
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
Electronic
Structure
E = h
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
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.
Light that contains colors of all
wavelengths is called:
a.
b.
c.
d.
a continuous spectrum.
monochromatic.
a line spectrum.
a Balmer series.
Electronic
Structure
of Atoms
The Wave Nature of Matter
• Louis de Broglie posited that if light can
have material properties, matter should
exhibit wave properties.
• He demonstrated that the relationship
between mass and wavelength was
h
 = mv
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Uncertainty Principle
• Heisenberg showed that the more precisely
the momentum of a particle is known, the less
precisely is its position known:
(x) (mv) 
h
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
© 2009, Prentice-Hall, Inc.
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
mechanics.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Quantum Mechanics
• The wave equation is
designated with a lower
case Greek psi ().
• The square of the wave
equation, 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
© 2009, Prentice-Hall, Inc.
Quantum Numbers
• Solving the wave equation gives a set of
wave functions, called 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. n, l, and m
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. as
1,2,3,……
• As n increases the orbital becomes
larger
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 orbitals.
Value of l
Type of orbital
0
s
1
p
2
d
3
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
copper 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.