1.
Electronic Structure of Atom
Mr. Rumwald Leo G. Lecaros
School of Chemical Engineering and Chemistry
Mapua Institute of Technology
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2.
Outline
Quantum Theory
Photoelectric effect
Bohr’s Theory
Dual Nature of the Electrons
Quantum Mechanics
Quantum Numbers
Electronic Configuration (Part 2)
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3.
The Electromagnetic Spectrum
Visible light is a small portion of
the electromagnetic radiation
spectrum detected by our eyes.
Electromagnetic radiation
includes radio waves,
microwaves and X-rays.
Described as a wave traveling
through space.
There are two components to
electromagnetic radiation, an
electric field and magnetic field.
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4.
The Wave Nature of Light
Wavelength, , is the
distance between two
corresponding points
on a wave.
Amplitude is the size or
“height” of a wave.
Frequency, , is the
number of cycles of the
wave passing a given
point per second,
usually expressed in Hz.
5.
Planck’s Quantum Theory
Higher T = shorter λ (higher E) maximum.
Couldn’t explain with classical physics
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6.
Electromagnetic Radiation
In 1900 Max Planck studied black body
radiation and realized that to explain the
energy spectrum he had to assume that:
1. energy is quantized
2. light has particle character
Planck’s equation is
6
sJ10x6.626constantsPlanck’h
hc
or EhE
34-
7.
The Wave Nature of Light
The fourth variable of light is velocity.
All light has the same speed in a vacuum.
c = 2.99792458 x 108 m/s
The product of the frequency and wavelength is the
speed of light.
Frequency is inversely proportional to wavelength.
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c
8.
The Wave Nature of Light
Refraction is the bending of light when it passes
from one medium to another of different density.
Speed of light changes.
Light bends at an angle depending on its wavelength.
Light separates into its component colors.
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9.
The Wave Nature of Light
Electromagnetic radiation can be categorized in terms of
wavelength or frequency.
Visible light is a small portion of the entire electromagnetic
spectrum.
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10.
Example Problem 6.1
Neon lights emit an orange-red colored
glow. This light has a wavelength of 670 nm.
What is the frequency of this light?
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11.
The Particulate Nature of Light
Photoelectric effect: light striking a metal
surface generates photoelectrons.
The light’s energy is transferred to electrons in
metal.
With sufficient energy, electrons “break free” of the
metal.
Electrons given more energy move faster (have
higher kinetic energy) when they leave the metal.
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12.
The Particulate Nature of Light
Photoelectric effect is
used in photocathodes.
Light strikes the
cathode at frequency .
Electrons are ejected if
exceeds the threshold
value 0.
Electrons are collected
at the anode.
Current flow is used to
monitor light intensity.
13.
Photoelectric Experiments
a) For > 0, the number of electrons
emitted is independent of frequency.
Value of 0 depends on metal used.
b) As light intensity increases, the
number of photoelectrons increases.
c) As frequency increases, kinetic energy
of emitted electrons increases linearly.
d) The kinetic energy of emitted electrons
is independent of light intensity.
14.
The Particulate Nature of Light
The photoelectric effect is not explained using a wave
description but is explained by modeling light as a particle.
Wave-particle duality - depending on the situation, light is best
described as a wave or a particle.
Light is best described as a particle when light is imparting
energy to another object.
Particles of light are called photons.
Neither waves nor particles provide an accurate description
of all the properties of light. Use the model that best
describes the properties being examined.
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15.
The Particulate Nature of Light
The energy of a photon (E) is proportional
to the frequency ( ).
and is inversely proportional to the wavelength
( ).
h = Planck’s constant = 6.626 x 10-34 J s
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E h
hc
16.
Example Problem 6.2
The laser in a standard laser printer emits
light with a wavelength of 780.0 nm. What is
the energy of a photon of this light?
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17.
The Particulate Nature of Light
Binding Energy - energy holding an electron to a
metal.
Threshold frequency, o - minimum frequency of light
needed to emit an electron.
For frequencies below the threshold frequency, no
electrons are emitted.
For frequencies above the threshold frequency, extra
energy is imparted to the electrons as kinetic energy.
Ephoton = Binding E + Kinetic E
This explains the photoelectric effect.
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18.
Example Problem 6.3
In a photoelectric experiment, ultraviolet
light with a wavelength of 337 nm was
directed at the surface of a piece of
potassium metal. The kinetic energy of the
ejected electrons was measured as 2.30 x
10-19 J. What is the electron binding energy
for potassium?
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19.
Atomic Spectra
Atomic Spectra: the particular pattern of
wavelengths absorbed and emitted by an element.
Wavelengths are well separated or discrete.
Wavelengths vary from one element to the next.
Atoms can only exist in a few states with very
specific energies.
When light is emitted, the atom goes from a higher
energy state to a lower energy state.
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20.
Atomic Spectra
Electrical current dissociates molecular
H2 into excited atoms which emit light
with 4 wavelengths.
21.
Atomic Spectra and the Bohr Atom
Every element has a unique spectrum.
Thus we can use spectra to identify
elements.
This can be done in the lab, stars, fireworks, etc.
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22.
Example Problem 6.4
When a hydrogen atom undergoes a transition from E3 to
E1, it emits a photon with = 102.6 nm. Similarly, if the
atom undergoes a transition from E3 to E2, it emits a
photon with = 656.3 nm. Find the wavelength of light
emitted by an atom making a transition from E2 to E1.
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23.
The Bohr Atom
Bohr model - electrons orbit the
nucleus in stable orbits.
Although not a completely
accurate model, it can be used to
explain absorption and emission.
Electrons move from low
energy to higher energy
orbits by absorbing energy.
Electrons move from high
energy to lower energy orbits
by emitting energy.
Lower energy orbits are
closer to the nucleus due to
electrostatics.
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24.
The Bohr Atom
Excited state: grouping of electrons that is
not at the lowest possible energy state.
Ground state: grouping of electrons that is
at the lowest possible energy state.
Atoms return to the ground state by emitting
energy as light.
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25.
Atomic Spectra and the Bohr Atom
The Rydberg
equation is an
empirical equation
that relates the
wavelengths of the
lines in the
hydrogen
spectrum.
25
hydrogenofspectrumemission
in thelevelsenergytheof
numberstherefer tosn’
nn
m101.097R
constantRydbergtheisR
n
1
n
1
R
1
21
1-7
2
2
2
1
26.
Atomic Spectra and the Bohr Atom
Example 4-8. What is the
wavelength of light
emitted when the
hydrogen atom’s energy
changes from n = 4 to n =
2?
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2 1
2 2
1 2
7 -1
2 2
7 -1
7 -1
7 -1
6 -1
n 4 and n 2
1 1 1
R
n n
1 1 1
1.097 10 m
2 4
1 1 1
1.097 10 m
4 16
1
1.097 10 m 0.250 0.0625
1
1.097 10 m 0.1875
1
2.057 10 m
27.
Atomic Spectra and the Bohr Atom
In 1913 Neils Bohr incorporated Planck’s
quantum theory into the hydrogen
spectrum explanation.
Here are the postulates of Bohr’s theory.
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1. Atom has a number of definite and discrete
energy levels (orbits) in which an electron
may exist without emitting or absorbing
electromagnetic radiation.
As the orbital radius increases so does the energy
1<2<3<4<5......
28.
Atomic Spectra and the Bohr Atom
2. An electron may move from one discrete
energy level (orbit) to another, but, in so
doing, monochromatic radiation is
emitted or absorbed in accordance with
the following equation.
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EE
hc
hEE-E
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12
Energy is absorbed when electrons jump to higher orbits.
n = 2 to n = 4 for example
Energy is emitted when electrons fall to lower orbits.
n = 4 to n = 1 for example
29.
Atomic Spectra and the Bohr Atom
3. An electron moves in a circular orbit about the
nucleus and it motion is governed by the
ordinary laws of mechanics and electrostatics,
with the restriction that the angular
momentum of the electron is quantized (can
only have certain discrete values).
angular momentum = mvr = nh/2
h = Planck’s constant n = 1,2,3,4,...(energy levels)
v = velocity of electron m = mass of electron
r = radius of orbit
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30.
Atomic Spectra and the Bohr Atom
Light of a characteristic wavelength (and
frequency) is emitted when electrons move from
higher E (orbit, n = 4) to lower E (orbit, n = 1).
This is the origin of emission spectra.
Light of a characteristic wavelength (and
frequency) is absorbed when electrons jump from
lower E (orbit, n = 2) to higher E (orbit, n= 4)
This is the origin of absorption spectra.
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31.
Atomic Spectra and the Bohr Atom
Bohr’s theory correctly explains the H
emission spectrum.
The theory fails for all other elements
because it is not an adequate theory.
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32.
The Wave Nature of the Electron
In 1925 Louis de Broglie published his Ph.D.
dissertation.
A crucial element of his dissertation is that electrons
have wave-like properties.
The electron wavelengths are described by the de
Broglie relationship.
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particleofvelocityv
particleofmassm
constantsPlanck’h
mv
h
33.
The Wave Nature of the Electron
Example 4-9. Determine the wavelength, in m, of an
electron, with mass 9.11 x 10-31 kg, having a velocity of 5.65
x 107 m/s.
Remember Planck’s constant is 6.626 x 10-34 Js which is also
equal to 6.626 x 10-34 kg m2/s.
33m1029.1
m/s1065.5kg109.11
ss/mkg10626.6
mv
h
11
731-
2234
34.
The Quantum Mechanical
Picture of the Atom
Werner Heisenberg in 1927 developed the
concept of the Uncertainty Principle.
It is impossible to determine simultaneously
both the position and momentum of an
electron (or any other small particle).
Detecting an electron requires the use of
electromagnetic radiation which displaces the
electron!
Electron microscopes use this phenomenon
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35.
The Quantum Mechanical Model of the Atom
Quantum mechanical model replaced the Bohr
model of the atom.
Bohr model depicted electrons as particles in circular
orbits of fixed radius.
Quantum mechanical model depicts electrons as waves
spread through a region of space (delocalized) called an
orbital.
The energy of the orbitals is quantized like the Bohr
model.
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36.
The Quantum Mechanical Model of the Atom
Diffraction of electrons shown in 1927.
Electrons exhibit wave-like behavior.
Wave behavior described using a wave
function, the Schrödinger equation.
H is an operator, E is energy and is the wave
function.
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H E
37.
Potential Energy and Orbitals
Total energy for electrons includes potential and
kinetic energies.
Potential energy more important in describing atomic
structure; associated with coulombic attraction
between positive nucleus and negative electrons.
Multiple solutions exist for the wave function for
any given potential interaction.
n is the index that labels the different solutions.
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H n E n
38.
Potential Energy and Orbitals
n can be written in terms of two
components.
Radial component, depends on the distance
from the nucleus.
Angular component, depends on the direction
or orientation of electron with respect to the
nucleus.
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39.
Potential Energy and Orbitals
The wave function may have positive and
negative signs in different regions.
Square of the wave function, 2, is always positive
and gives probability of finding an electron at any
particular point.
Each solution of the wave function defines an
orbital.
Each solution labeled by a letter and number
combination: 1s, 2s, 2p, 3s, 3p, 3d, etc.
An orbital in quantum mechanical terms is actually
a region of space rather than a particular point.
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40.
Quantum Numbers
Quantum numbers - solutions to the
functions used to solve the wave equation.
Quantum numbers used to name atomic
orbitals.
Vibrating string fixed at both ends can be used
to illustrate a function of the wave equation.
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41.
Quantum Numbers
When solving the Schrödinger equation,
three quantum numbers are used.
Principal quantum number, n (n = 1, 2, 3, 4, 5,
…)
Secondary quantum number, l
Magnetic quantum number, ml
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42.
Quantum Numbers
The principal quantum number, n, defines the
shell in which a particular orbital is found.
n must be a positive integer
n = 1 is the first shell, n = 2 is the second shell, etc.
Each shell has different energies.
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43.
Quantum Numbers
The secondary quantum number, l, indexes energy
differences between orbitals in the same shell in an atom.
l has integral values from 0 to n-1.
l specifies subshell
Each shell contains as many l values as its value of n.
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44.
Quantum Numbers
The energies of orbitals are specified
completely using only the n and l quantum
numbers.
In magnetic fields, some emission lines split
into three, five, or seven components.
A third quantum number describes splitting.
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45.
Quantum Numbers
The third quantum number is the magnetic
quantum number, ml.
ml has integer values.
ml may be either positive or negative.
ml’s absolute value must be less than or equal to l.
For l = 1, ml = -1, 0, +1
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46.
Quantum Numbers
Note the relationship between number
of orbitals within s, p, d, and f and ml.
47.
Example Problem 6.5
Write all of the allowed sets of quantum
numbers (n, l, and ml) for a 3p orbital.
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48.
Visualizing Orbitals
s orbitals are spherical
p orbitals have two lobes separated by a nodal
plane.
A nodal plane is a plane where the probability of finding
an electron is zero (here the yz plane).
d orbitals have more complicated shapes due to the
presence of two nodal planes.
49.
Visualizing Orbitals
Nodes are explained using the Uncertainty Principle.
It is impossible to determine both the position and
momentum of an electron simultaneously and with
complete accuracy.
An orbital depicts the probability of finding an electron.
The radial part of the wave function describes how
the probability of finding an electron varies with
distance from the nucleus.
Spherical nodes are generated by the radial portion of
the wave function.
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50.
Visualizing Orbitals
Cross sectional views of the 1s, 2s, and 3s orbitals.
51.
Visualizing Orbitals
Electron density plots
for 3s, 3p, and 3d
orbitals showing the
nodes for each
orbital.
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