Download Chapter 6 Electronic Structure of Atoms

Chapter 6
Electronic Structure of Atoms
Dr. Subhash C. Goel
South GA College
Douglas, GA
Electronic
Structure
of Atoms
A wave is a continuously repeating change or
oscillation in matter or in a physical field.
Light is an electromagnetic wave, consisting of
oscillations in electric and magnetic fields traveling
through space.
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A wave can be characterized by its wavelength
and frequency.
Wavelength, symbolized by the Greek letter
lambda, l, is the distance between any two
identical points on adjacent waves.
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Frequency, symbolized by the Greek letter nu, n,
is the number of wavelengths that pass a fixed
point in one unit of time (usually a second). The
unit is 1/S or s-1, which is also called the Hertz (Hz).
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Wavelength and frequency are related by the wave
speed. The speed of light, c, is 3.00 x 108 m/s.
c = nl
The relationship between wavelength and
frequency due to the constant velocity of light is
illustrated on the next slide.
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When the
wavelength is
reduced by a
factor of two,
the frequency
increases by
a factor of
two.
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Exercise:
1. What is the wavelength of blue light with a
frequency of 6.4  1014/s?
2. What is the frequency of light having a
wavelength of 681 nm?
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The range of frequencies and wavelengths of
electromagnetic radiation is called the
electromagnetic spectrum.
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The Nature of Energy
The wave nature of light
does not explain how
an object can glow
when its temperature
increases.
Also, The wave theory
could not explain the
photoelectric effect.
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Electronic
Structure
of Atoms
The Nature of Energy
Max Planck explained it by assuming that
energy comes in packets called quanta.
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Electronic
Structure
of Atoms
The Nature of Energy
• Einstein used this
assumption to explain the
photoelectric effect.
• He concluded that energy is
proportional to frequency:
E = hn
where h is Planck’s
constant, 6.626  10−34 J-s.
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Electronic
Structure
of Atoms
The Nature of Energy
• Therefore, if one knows the wavelength of
light, one can calculate the energy in one
photon, or packet, of that light:
c = ln
E = hn
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Electronic
Structure
of Atoms
Exercise Energy of a Photon
Calculate the energy of one photon of yellow light
that has a wavelength of 589 nm.
Chemistry, The Central Science, 12th Edition
Theodore L. Brown; H. Eugene LeMay, Jr.; Bruce E. Bursten; Catherine J. Murphy; and Patrick Woodward
© 2012 Pearson Education, Inc.
In the early 1900s, the atom was understood to
consist of a positive nucleus around which
electrons move (Rutherford’s model).
This explanation left a theoretical dilemma:
According to the physics of the time, an electrically
charged particle circling a center would continually
lose energy as electromagnetic radiation. But this
is not the case—atoms are stable.
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In addition, this understanding could not explain
the observation of line spectra of atoms.
A continuous spectrum contains all wavelengths
of light.
A line spectrum shows only certain colors or
specific wavelengths of light. When atoms are
heated, they emit light. This process produces a
line spectrum that is specific to that atom. The
emission spectra of six elements are shown on the
next slide.
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Emission of Energy
(2 Possibilities)
or
Continuous Energy Loss
Electronic
Quantized Energy Loss
Structure
of Atoms
Emission of Energy
Continuous Energy Loss
Quantized Energy Loss
• Any and all energy
values possible on way
down
• Implies electron can be
anywhere about
nucleus of atom
• Only certain, restricted,
quantized energy
values possible on way
down
• Implies an electron is
restricted to quantized
energy levels
 Continuous emission
spectra
 Line spectra
Electronic
Structure
of Atoms
Line Emission Spectrum of Hydrogen Atoms
Electronic
Structure
of Atoms
7.3
Line Spectra vs. Continuous Emission
Spectra
• The fact that the emission spectra of H2
gas and other molecules is a line rather
than a continuous emission spectra tells
us that electrons are in quantized
energy levels rather than anywhere
about nucleus of atom.
Electronic
Structure
of Atoms
In 1913, Neils Bohr, a Danish scientist, set down
postulates to account for
1. The stability of the hydrogen atom
2. The line spectrum of the atom
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Energy-Level Postulate
An electron can have only certain energy values,
called energy levels. Energy levels are quantized.
For an electron in a hydrogen atom, the energy is
given by the following equation:
E
RH
n2
RH = 2.179  10−18 J
n = principal quantum number
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Transitions Between Energy Levels
An electron can change energy levels by
absorbing energy to move to a higher energy
level or by emitting energy to move to a lower
energy level.
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For a hydrogen electron, the energy change is
given by
ΔE  E f  E i
 1

1
ΔE  RH  2  2 
n

n
i 
 f
RH = 2.179  10−18 J, Rydberg constant
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The energy of the emitted or absorbed photon is
related to DE:
E photon  ΔE electron  hn
h  Planck' s constant
We can now combine these two equations:
 1

1
hn   R H  2  2 
n

n
i 
 f
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Light is absorbed by an atom when the electron
transition is from lower n to higher n (nf > ni). In this
case, DE will be positive.
Light is emitted from an atom when the electron
transition is from higher n to lower n (nf < ni). In this
case, DE will be negative.
An electron is ejected when nf = ∞.
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ni = 3
ni = 3
ni = 2
nf = 2
Ephoton = DE = Ef - Ei
1
Ef = -RH ( 2
nf
1
Ei = -RH ( 2
ni
1
DE = RH( 2
ni
)
)
1
n2f
)
nnf f==11
Electronic
Structure
of Atoms
7.3
Exercise: Calculate the wavelength (in nm)
of a photon emitted by a hydrogen atom
when its electron drops from the n = 5
state to the n = 3 state.
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Electronic
Structure
of Atoms
The Nature of Energy
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Electronic
Structure
of Atoms
The Nature of Energy
•
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)
2. Electrons in permitted orbits have specific, “allowed”
energies; these energies will not be radiated from the
atom.
2. 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 = hn
Electronic
© 2012 Pearson Education, Inc.
Structure
of Atoms
In 1923, Louis de Broglie, a French physicist,
reasoned that particles (matter) might also have
wave properties.
The wavelength of a particle of mass, m (kg), and
velocity, v (m/s), is given by the de Broglie relation:
h
λ
mv
34
h  6.626  10 J  s
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Building on de Broglie’s work, in 1926, Erwin
Schrödinger devised a theory that could be used to
explain the wave properties of electrons in atoms
and molecules.
The branch of physics that mathematically
describes the wave properties of submicroscopic
particles is called quantum mechanics or wave
mechanics.
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Quantum mechanics alters how we think about the
motion of particles.
In 1927, Werner Heisenberg showed how it is
impossible to know with absolute precision both
the position, x, and the momentum, p, of a particle
such as electron.
h
(Δx )(Δp) 
4π
Because p = mv this uncertainty becomes more
significant as the mass of the particle becomes
smaller.
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Quantum Mechanics
• The wave equation is
designated with a lowercase
Greek psi (). No direct
physical meaning.
• 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.
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Electronic
Structure
of Atoms
Quantum Numbers
• 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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Electronic
Structure
of Atoms
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.
• For Hydrogen atom:
En= -(2.18X10-18)(1/n2) as in Bohr Model
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Electronic
Structure
of Atoms
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.
Electronic
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Structure
of Atoms
Angular Momentum Quantum
Number (l)
Value of l
0
1
2
3
Type of orbital
s
p
d
f
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Electronic
Structure
of Atoms
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, and so forth.
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Electronic
Structure
of Atoms
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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Electronic
Structure
of Atoms
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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Electronic
Structure
of Atoms
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
Electronic
electron.
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Structure
of Atoms
p Orbitals
• The value of l for p orbitals is 1.
• They have two lobes with a node between
them.
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Electronic
Structure
of Atoms
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.
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Electronic
Structure
of Atoms
Energies of Orbitals
• For a one-electron
hydrogen atom,
orbitals on the same
energy level have
the same energy.
• That is, they are
degenerate.
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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.
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Electronic
Structure
of Atoms
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.
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Electronic
Structure
of Atoms
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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Electronic
Structure
of Atoms
An electron configuration of an atom is a
particular distribution of electrons among available
subshells.
An orbital diagram of an atom shows how the
orbitals of a subshell are occupied by electrons.
Orbitals are represented with a circle or squares;
electrons are represented with arrows up for ms=
+½ or down for ms= -½.
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The Pauli exclusion principle summarizes
experimental observations that no two electrons in
one atom can have the same four quantum
numbers.
That means that within one orbital, electrons must
have opposite spin. It also means that one orbital
can hold a maximum of two electrons (with
opposite spin).
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An s subshell, with one orbital,
can hold a maximum of 2 electrons.
A p subshell, with three orbitals,
can hold a maximum of 6 electrons.
A d subshell, with five orbitals,
can hold a maximum of 10 electrons.
An f subshell, with seven orbitals,
can hold a maximum of 14 electrons.
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In 1927, Friedrich Hund discovered, by
experiment, a rule for determining the lowestenergy configuration of electrons in orbitals of a
subshell.
Hund’s rule states that the lowest-energy
arrangement of electrons in a subshell is obtained
by putting electrons into separate orbitals of the
subshell with the same spin before pairing
electrons.
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The lowest-energy configuration of an atom is
called its ground state.
Any other allowed configuration represents an
excited state.
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The building-up principle (or aufbau principle)
is a scheme used to reproduce the ground-state
electron configurations by successively filling
subshells with electrons in a specific order (the
building-up order).
This order generally corresponds to filling the
orbitals from lowest to highest energy. Note that
these energies are the total energy of the atom
rather than the energy of the subshells alone.
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1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
7p
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3d
4d
5d
6d
4f
5f
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This results in the following order:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p,
6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p
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Another way to learn the building-up order is to
correlate each subshell with a position on the
periodic table.
The principal quantum number, n, correlates with
the period number.
Groups IA and IIA correspond to the s subshell;
Groups IIIA through VIIIA correspond to the p
subshell; the “B” groups correspond to the d
subshell; and the bottom two rows correspond to
the f subshell. This is shown on the next slide.
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There are a few exceptions to the building-up
order prediction for the ground state.
Chromium (Z=24) and copper (Z=29) have been
found by experiment to have the following groundstate electron configurations:
Cr:
Cu:
1s2 2s2 2p6 3s2 3p6 3d5 4s1
1s2 2s2 2p6 3s2 3p6 3d10 4s1
In each case, the difference is in the 3d and 4s
subshells.
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There are several terms describing electron
configurations that are important.
The complete electron configuration shows every
subshell explicitly.
Br:
1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p5
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The noble-gas configuration substitutes the
preceding noble gas for the core configuration and
explicitly shows subshells beyond that.
Br:
[Ar]3d104s24p5
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The valence configuration consists of the
electrons outside the noble-gas or pseudo-noblegas core.
Br: 4s24p5
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For main-group (representative) elements, an s or
a p subshell is being filled.
For d-block transition elements, a d subshell is
being filled.
For f-block transition elements, an f subshell is
being filled.
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?
Write the complete electron
configuration of the arsenic atom, As,
using the building-up principle.
For arsenic, As, Z = 33.
1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p3
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?
What are the electron configurations for
the valence electrons of arsenic and
zinc?
Arsenic is in period 4, Group VA.
Its valence configuration is 4s24p3.
Zinc, Z = 30, is a transition metal in
the first transition series.
Its noble-gas core is Ar, Z = 18.
Its valence configuration is 4s23d10.
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For nitrogen, the orbital diagram would be
1s
2s
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2p
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?
Write an orbital diagram for the ground
state of the nickel atom.
For nickel, Z = 28.
1s
2s
3s
4s
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2p
3p
3d
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Magnetic Properties of Atoms
Although an electron behaves like a tiny magnet,
two electrons that are opposite in spin cancel each
other. Only atoms with unpaired electrons exhibit
magnetic susceptibility.
This allows us to classify atoms based on their
behavior in a magnetic field.
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A paramagnetic substance is one that is weakly
attracted by a magnetic field, usually as the result
of unpaired electrons.
A diamagnetic substance is not attracted by a
magnetic field generally because it has only paired
electrons.
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