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Chapter 7 Lecture
Lecture Presentation
Chapter 7
The QuantumMechanical Model
of the Atom
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The Beginnings of Quantum Mechanics
 Quantum-mechanical model: A model that
explains the behavior of absolutely small particles
such as electrons and photons.
– Until the beginning of the twentieth century it was
believed that all physical phenomena were
deterministic.
– Work done at that time by many famous physicists
discovered that for sub-atomic particles, the present
condition does not determine the future condition.
• Albert Einstein, Neils Bohr, Louis de Broglie, Max Planck,
Werner Heisenberg, P. A. M. Dirac, and Erwin
Schrödinger
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Continuous
 Quantum mechanics forms the foundation of
chemistry
– Explaining the periodic table
– The behavior of the elements in chemical bonding
– Provides the practical basis for lasers, computers, and
countless other applications
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The Nature of Light
(1) Its Wave Nature
1) Definition
• Light: a form of electromagnetic radiation
– composed of perpendicular oscillating waves, one for the
electric field and one for the magnetic field.
– require no medium for their propagation
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2) Characterizing Waves
*****
• Amplitude: the height of the wave, a measure of light
intensity—the larger the amplitude, the brighter the light.
• Wavelength (l, lambda): a measure of the distance
covered by the wave.
• Frequency (n, nu): the number of waves that pass a point
in a given period of time. Unit = cycles/s or s–1 (Hz, hertz).
• The relationship between wavelength and frequency:
c = 3.00 × 108 m/s (speed of light)
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3) Electromagnetic Spectrum
*****
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Continuous
• The main regions of the electromagnetic spectrum ranging
in wavelength from 10-15 m (gamma rays) to 105 m (radio
waves).
• The shorter wavelength (high-frequency) light has
higher energy. (high-energy electromagnetic radiation
can potentially damage biological molecules-Ionizing
radiation)
• The electromagnetic spectrum is largely invisible to the
eye.
• White light is a mixture of all the colors of visible light:
– Red Orange Yellow Green Blue Indigo Violet
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4) Interference and Diffraction
(characteristics of wave)
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The Nature of Light
(2) Its Particle Nature
The Photoelectric Effect
The metals emit electrons when a light shines on their
surface called photoelectric effect.
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Continuous
*****
• A minimum frequency, called
threshold frequency, was
needed before electrons
would be emitted regardless
of the intensity.
• Einstein proposed that the
light energy was delivered to
the atoms in packets, called
quanta or photons.
• The energy of a photon of light is directly proportional to
its frequency:
hc
E  hn 
l
Planck’s Constant h = 6.626 × 10−34 J ∙ s.
• Energy can be absorbed or emitted only as whole
multiples of a quantum, that is, 1 hv, 2 hv, 3 hv etc.
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Continuous
*****
• One photon at the threshold frequency gives the electron
just enough energy for it to escape the atom - Binding
energy, f.
• When irradiated with a shorter wavelength photon, the
electron absorbs more energy than is necessary to
escape. This excess energy becomes kinetic energy of
the ejected electron.
Kinetic Energy = Ephoton – Ebinding
KE = hn − f
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Suppose a Metal Will Eject Electrons from Its Surface
When Struck by Yellow Light. What Will Happen If the
Surface Is Struck with Ultraviolet Light?
1. No electrons would be ejected.
2. Electrons would be ejected, and they would have the
same kinetic energy as those ejected by yellow light.
3. Electrons would be ejected, and they would have
greater kinetic energy than those ejected by yellow
light.
4. Electrons would be ejected, and they would have lower
kinetic energy than those ejected by yellow light.
Ans: 3
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Atomic Spectroscopy
• When atoms absorb energy, that energy is often released
as energy as light.
• When that emitted light is passed through a prism, a
pattern of particular wavelengths of light is seen that is
unique to that type of atom
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The Bohr Model of the Atom
• Bohr’s major idea: The energy of the atom was quantized,
the amount of energy in the atom was related to the
electron’s position in the atom (particle like behavior).
– Quantized means that the atom could only have very
specific amounts of energy.
• The electrons travel in orbits that are at a fixed distance
from the nucleus-stationary states, the energy of the
electron in a particular orbit was proportional to the
distance from the nucleus.
• Electrons emit radiation when they “jump” from an orbit
with higher energy down to an orbit with lower energy.
• The emitted radiation was a photon of light and the
distance between the orbits determined the energy of the
photon of light produced.
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Bohr’s Hydrogen Atom: A Planetary Model
 Bohr proposed the electron energy of hydrogen atom is
quantized
 Each specified electron energy value, called an energy
level (En), of the atom:
1
E n   RH 2
n
n: an integer, RH = 2.18 x 10–18 J (Rydberg constant)


When the electron is located infinitely far from
nucleus: En = 0
The “–” sign : represents attraction forces
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Bohr Model of H Atoms
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Bohr’s Explanation of H atom Line Spectra
*****
 Bohr’s Equation:
ΔE  E final  E initial
1
1
  RH ( 2  2 )
n f ni
E:
energy change of an electron from initial energy
level to final energy level
Efinal: final energy level
Einitial: initial energy level
RH: 2.18 x 10–18 J



Energy of H(g) from n = 1 to n = ∞, E = 2.18 x 10–18
J/atom, It is the ionization energy of the H(g)
The emitted photon E = hn
Bohr’s theory is limited for one-electron species,
such as H, He+, and Li2+
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Hydrogen Energy Transitions and Radiation
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Wave Behavior of Electrons
*****
• de Broglie proposed that particles could have wavelike
character just like light
• The wavelength of a particle (such as an electron) given
by:
h
l
mv
λ:
wavelength
h: Planck’s constant
m: mass of the particle
v: moving speed of the particle
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Electron Diffraction
• Proof that the electron had wave nature came a few years
later with the demonstration that a beam of electrons
would produce an interference pattern the same as waves
do.
Electrons actually
present an
interference pattern,
demonstrating they
behave like waves.
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Uncertainty Principle
• Heisenberg stated that the product of the uncertainties in
both the position and speed of a particle was inversely
proportional to its mass.
– x = position, x = uncertainty in position
– v = velocity, v = uncertainty in velocity
– m = mass
• This means that the more accurately you know the
position of a small particle, such as an electron, the less
you know about its speed, and vice versa.
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Trajectory versus Probability
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Quantum Mechanics (Wave Mechanics)

Schrödinger (wave) equation:
• An acceptable solution to Schrödinger equation that
states the location of an electron at a given point in
space and each wave function  is associated with a
particular energy E.
• A plot of distance versus 2 represents an orbital, a
probability distribution map of a region where the
electron is likely to be found.
• Quantum mechanics is applied to explain the waveparticle duality behavior for many-electron atoms
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Quantum Numbers and Atomic Orbitals
 Quantum Numbers
•
Solving a Schrödinger equation, in other words, a wave
function contain three parameters that have specific
integral values called quantum numbers (n, l, and ml).
•
A wave function with a given set of three quantum
numbers is called an atomic orbital.
•
These orbitals allow us to visualize a three-dimension
region which describe the probability of finding an
electron.
•
A fourth quantum number, called electron spin
quantum number (ms), describe the orientation of the
spin of the electron.
•
Each electron in a atom is described by its unique set
of four quantum number.
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*****

The Principal Quantum Number (n)
•
•
n = 1, 2, 3, .....(positive integer)
Determines the size and the energy level of the atomic
orbital
All orbitals with same value of n constitute a principal
level (shell)
•

The Angular Momentum Quantum Number (ι)
•
•
•
ι = = 0, 1, 2,...., n–1
Determines the shape of the orbital
All orbitals with the same value of n and the same value
of ι constitute a sublevel (subshell)
•
Value of ι :
0
1 2
3
Orbital (subshell) designation:
s
p d
f
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
•
•
The Magnetic Quantum Number (mι )
*****
mι = –ι , –ι+1, ..., 0, ..., ι–2, ι–1, ι
Determines the orientation in space of the orbitals of
any given type in a sublevel
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Energy Levels and Sublevels
*****
• the number of sublevels within
a principal level = n.
• the number of orbitals within a
sublevel = 2l + 1.
• the number of orbitals in a
principal level = n2.
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Quantum Mechanical Explanation of Atomic
Spectra
• Each wavelength in the spectrum of an atom corresponds
to an electron transition between orbitals.
• When an electron is excited, it transitions from an orbital
in a lower energy level to an orbital in a higher energy
level.
• When an electron relaxes, it transitions from an orbital in
a higher energy level to an orbital in a lower energy level.
• Electrons in high energy states are unstable, a photon of
light is released whose energy equals the energy
difference between the orbitals.
• Each line in the emission spectrum corresponds to the
difference in energy between two energy states.
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Quantum Leaps
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Probability Density Function (1s for example)
The probability density function
represents the total probability of
finding anlectron at a particular
point in space.
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Radial Distribution Function (1s for example)
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2s and 3s
•
•
The S Orbitals (l = 0,
mι= 0)
Node: the region of
zero electron
probability
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
The Three p Orbitals (l = 1, mι= –1, 0, +1)
mι= –1
•
mι= 0
mι= +1
First principal shell to have p
subshell correspond to n = 2.
Three values of
mι gives three p
orbitals in the p
subshell
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
The Five d Orbitals (l = 2, mι= –2, –1, 0, +1, +2)
Five values of
mι gives five d
orbitals in the
d subshell

First principal shell to have d
subshell correspond to n = 3.
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
The Seven f Orbitals (l = 3, mι= –3, –2, –1, 0, +1, +2, +3)
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The Shapes of Atomic Orbitals
• The l quantum number primarily determines
the shape of the orbital.
• l can have integer values from 0 to (n – 1).
• Each value of l is called by a particular letter
that designates the shape of the orbital.
– s orbitals are spherical.
– p orbitals are like two balloons tied at the knots.
– d orbitals are mainly like four balloons tied at
the knots.
– f orbitals are mainly like eight balloons tied at
the knots.
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End of Chapter 7
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