Download Chapter 7 The Quantum- Mechanical Model of the Atom

Chapter 7 Lecture
Lecture Presentation
Chapter 7
The QuantumMechanical Model
of the Atom
----Revised by Wang
Sherril Soman
Grand Valley State University
© 2014 Pearson Education, Inc.
The Nature of Light: Its Wave Nature
• Light: a form of electromagnetic radiation
Composed of perpendicular oscillating waves,
one for the electric field, and
one for the magnetic field
• All electromagnetic waves move through
space at the same, constant speed.
3.00 × 108 m/s = the speed of light
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Speed of Energy Transmission
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Characterizing Waves
• The amplitude is the height of the wave.
– The amplitude is a measure of light intensity.
The larger the amplitude, the brighter the light.
crest
trough
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Characterizing Waves
• The wavelength (l) is a measure of the
distance covered by the wave.
Wavelength (l)
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Characterizing Waves
• The frequency (n) is the number of waves (the
number of cycles) that pass a point in a given
period of time.
– Units are hertz (Hz) or cycles/s = s−1 (1 Hz = 1 s−1).
• The total energy is proportional to,
the amplitude of the waves, and
the frequency.
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The Relationship Between
Wavelength and Frequency
speed, m/s
frequency,
/s (or Hz)
wavelength, m
Example 7.1 Wavelength and Frequency
Calculate the wavelength (in nm) of the red light emitted by a
barcode scanner that has a frequency of 4.62 × 1014 s–1.
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Color
• The color of light is determined by its
wavelength or frequency.
• White light is a mixture of all the colors
of visible light.
– A spectrum
– Red Orange Yellow Green Blue Indigo
Violet
• When an object absorbs some of the
wavelengths of white light and reflects
others, it appears colored. The observed
color is predominantly the colors
reflected.
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Amplitude and Wavelength
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The Electromagnetic Spectrum
• Visible light comprises only a small fraction of
all the wavelengths of light, called the
electromagnetic spectrum.
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Continuous Spectrum
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Thermal Imaging using Infrared Light
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Using High-Energy Radiation
to Kill Cancer Cells
During radiation therapy, a tumor is
targeted from multiple directions in order to
minimize the exposure of healthy cells, while
maximizing the exposure of cancerous cells.
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Electromagnetic wave – particles or
waves ?
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Electromagnetic wave – particles or
waves ?
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Einstein’s Explanation
• 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.
– Inversely proportional to its wavelength
– The proportionality constant is called Planck’s
Constant, (h), and has the value 6.626 × 10−34 J ∙ s.
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Einstein’s Explanation
Example 7.2 Photon Energy
A nitrogen gas laser pulse with a wavelength of 337 nm contains
3.83 mJ of energy. How many photons does it contain?
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Spectra
• When atoms or molecules absorb energy, that
energy is often released as light energy,
– Fireworks, n
– eon lights, etc.
Na
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K
Li
Ba
Emission Spectra
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Indication of energy level of electrons
 Electrons in atoms are at discrete energy
levels.
 The energy difference between the high
level and the low level equals to the emitted
photon energy.
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Rydberg’s Spectrum Analysis
Johannes Rydberg (1854–1919)
• Rydberg analyzed the spectrum of
hydrogen and found that it could be
described with an equation that involved an
inverse square of integers.
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Rutherford’s Nuclear Model
• The atom contains a tiny dense center called the
nucleus.
• The nucleus is essentially the entire mass of
the atom.
• The nucleus is positively charged .
• The electrons move around in the empty space of
the atom surrounding the nucleus.
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Problems with Rutherford’s Nuclear Model
of the Atom
• Electrons are moving charged particles.
• According to classical physics, moving charged
particles give off energy.
• Therefore, electrons should constantly be giving
off energy.
– This should cause the atom to glow!
• The electrons should lose energy, crash into the
nucleus, and the atom should collapse!
– But it doesn’t!
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The Bohr Model of the Atom
Neils Bohr (1885–1962)
• Bohr’s major idea was that the energy of the atom
was quantized, and that the amount of energy in
the atom was related to the electron’s position in
the atom.
– Quantized means that the atom could only have very
specific amounts of energy.
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Bohr Model of H Atoms
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Bohr Model of H Atoms
photonener gy  E  E final  Einitial
 1

1

hn  2.18 10 J 

2
2
n

n
final
initial


 1
c
1 
18 
h  2.18 10 J

2
2 

l
n
n
initial 
 final
18
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Bohr Model of H Atoms
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Bohr Model of H Atoms
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Bohr Model of H Atoms
Example 7.7 Wavelength of Light for a Transition in the Hydrogen Atom
Determine the wavelength of light emitted when an electron in a
hydrogen atom makes a transition from an orbital in n = 6 to an
orbital in n = 5.
photonener gy   E  Einitial  E final
hn  2.18  10
h
c
l
18
 2.18  10
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 1

1

J

2
2
n

n
final
initial


18
 1
1 

J

n 2 n 2 
initial 
 final
Wave Behavior of Electrons
Louis de Broglie (1892–1987)
• de Broglie proposed that particles could have
wavelike character.
v, speed
Electron Diffraction
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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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Schrödinger’s Equation
• Schrödinger’s equation allows us to
calculate the probability of finding an
electron with a particular amount of energy
at a particular location in the atom.
• Solutions to Schrödinger’s equation
produce many wave functions, Y.
• A plot of distance versus Y 2 represents an
orbital, a probability distribution map of a
region where the electron is likely to be found.
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Solutions to the Wave Function, Y
• Calculations show that the size, shape, and
orientation in space of an orbital are
determined to be three integer terms in the
wave function.
– Added to quantize the energy of the electron.
• These integers are called quantum
numbers.
– Principal quantum number, n
– Angular momentum quantum number, l
– Magnetic quantum number, ml
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Principal Quantum Number, n
• Characterizes the energy level of the electron in
a particular orbital.
– Corresponds to Bohr’s energy level
• n can be any integer  1.
• n is also called principal shell.
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Angular Momentum Quantum Number, l
• The angular momentum quantum number
determines the shape of the orbital. It is
also called subshell.
• 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.
–
–
–
–
I =0, s,
I =1, p,
I =2, d,
I =3, f.
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Energy Levels and Sublevels
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?
Energy Levels and Sublevels
Example 7.5 Quantum Numbers I
What are the quantum numbers and names (for example, 2s, 2p) of
the orbitals in the n = 4 principal level?
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Magnetic Quantum Number, ml
• The magnetic quantum number is an integer
that specifies the orientation of the orbital.
– The direction in space the orbital is aligned
relative to the other orbitals
• Values are integers from −l to +l
– Including zero
– Gives the number of orbitals of a particular shape
• When l = 2, the values of ml are −2, −1, 0, +1, +2,
which means there are five orbitals with l = 2.
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Magnetic Quantum Number, ml
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n, l, ml
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n, l, ml
Example 7.6 Quantum Numbers II
These sets of quantum numbers are each supposed to specify an
orbital. One set, however, is erroneous. Which one and why?
a.n = 3; l = 0; ml = 0 b. n = 2; l = 1; ml = –1
c. n = 1; l = 0; ml = 0 d. n = 4; l = 1; ml = –2
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Describing an Orbital
• Each set of n, l, and ml describes one
orbital.
• Orbitals with the same value of n are in the
same principal energy level.
– Also called the principal shell
• Orbitals with the same values of n and l are
said to be in the same sublevel.
– Also called a subshell
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l = 0, the s Orbital
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l =1, p Orbitals
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l =2, d Orbitals
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l=3, f Orbitals
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