Quantum Theory and Atomic Structure

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Chapter 7
Quantum Theory and Atomic Structure
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Quantum Theory and Atomic Structure
7.1 The Nature of Light
7.2 Atomic Spectra
7.3 The Wave-Particle Duality of Matter and
Energy
7.4 The Quantum-Mechanical Model of the Atom
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Figure 7.1
Frequency and Wavelength
c l n
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Figure 7.2
Amplitude (Intensity) of a Wave
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Regions of the Electromagnetic Spectrum
Figure 7.3
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Sample Problem 7.1
Interconverting Wavelength and Frequency
SOLUTION
PLAN
Use c ln
1.00x10-10m
wavelength in units given
3x108m/s
3x1018s-1
n
1.00x10-10m
325x10-2m
3x108m/s
wavelength in m
n
9.23x107s-1
325x10-2m
473x10-9m
frequency (s-1 or Hz)
6.34x1014s-1
n
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Figure 7.4
Different behaviors of waves and particles.
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The diffraction pattern caused by light passing
through two adjacent slits.
Figure 7.5
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Figure 7.6
DE h n
Blackbody Radiation
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Figure 7.7
Demonstration of the photoelectric effect
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Sample Problem 7.2
Calculating the Energy of Radiation from Its
Wavelength
PLAN
After converting cm to m, we can use the energy
equation, E hn combined with n c/l to find
the energy.
SOLUTION
E hc/l
6.626X10-34Js
3x108m/s
x
E
1.66x10-23J
1.20cm
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Figure 7.8
The line spectra of several elements
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R
Rydberg equation
-
R is the Rydberg constant 1.096776 m-1
Three series of spectral lines of atomic hydrogen
Figure 7.9
for the visible series, n1 2 and n2 3, 4, 5,
...
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Figure 7.10
Quantum staircase
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Figure 7.11
The Bohr explanation of the three series of
spectral lines.
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Figure B7.1
Flame tests
strontium 38Sr
copper 29Cu
Figure B7.2
Emission and absorption spectra of sodium atoms.
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Figure B7.3
The main components of a typical spectrophotometer
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Figure 7.13
Wave motion in restricted systems
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Table 7.1 The de Broglie Wavelengths of
Several Objects
Substance
Mass (g)
Speed (m/s)
l (m)
slow electron
9x10-28
1.0
7x10-4
fast electron
9x10-28
5.9x106
1x10-10
alpha particle
6.6x10-24
1.5x107
7x10-15
one-gram mass
1.0
0.01
7x10-29
baseball
142
25.0
2x10-34
Earth
6.0x1027
3.0x104
4x10-63
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Sample Problem 7.3
Calculating the de Broglie Wavelength of an
Electron
PLAN
Knowing the mass and the speed of the electron
allows to use the equation l h/mu to find the
wavelength.
SOLUTION
6.626x10-34kgm2/s
l
7.27x10-10m
9.11x10-31kg
x
1.00x106m/s
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Figure 7.14
Comparing the diffraction patterns of x-rays and
electrons
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CLASSICAL THEORY
Figure 7.15
Matter particulate, massive
Energy continuous, wavelike
Summary of the major observations and theories
leading from classical theory to quantum theory.
Observation
Theory
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Figure 7.15 continued
Observation
Theory
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The Heisenberg Uncertainty Principle
D x m D u
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Sample Problem 7.4
Applying the Uncertainty Principle
PLAN
The uncertainty (Dx) is given as 1(0.01) of
6x106m/s. Once we calculate this, plug it into
the uncertainty equation.
SOLUTION
Du (0.01)(6x106m/s) 6x4m/s
6.626x10-34kgm2/s
Dx
10-9m
4p (9.11x10-31kg)(6x104m/s)
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The Schrödinger Equation
HY EY
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Figure 7.16
Electron probability in the ground-state H atom
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Quantum Numbers and Atomic Orbitals
An atomic orbital is specified by three quantum
numbers.
n the principal quantum number - a positive
integer
l the angular momentum quantum number - an
integer from 0 to n-1
ml the magnetic moment quantum number - an
integer from -l to l
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Table 7.2 The Hierarchy of Quantum Numbers for
Atomic Orbitals
Name, Symbol (Property)
Allowed Values
Quantum Numbers
Principal, n (size, energy)
Positive integer (1, 2, 3, ...)
1
2
3
Angular momentum, l (shape)
0 to n-1
0
0
1
0
0
Magnetic, ml (orientation)
-l,,0,,l
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Sample Problem 7.5
Determining Quantum Numbers for an Energy Level
PLAN
Follow the rules for allowable quantum numbers
found in the text.
l values can be integers from 0 to n-1 ml can
be integers from -l through 0 to l.
SOLUTION
For n 3, l 0, 1, 2
For l 0 ml 0
For l 1 ml -1, 0, or 1
For l 2 ml -2, -1, 0, 1, or 2
There are 9 ml values and therefore 9 orbitals
with n 3.
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Sample Problem 7.6
Determining Sublevel Names and Orbital Quantum
Numbers
(a) n 3, l 2
(b) n 2, l 0
(c) n 5, l 1
(d) n 4, l 3
PLAN
Combine the n value and l designation to name the
sublevel. Knowing l, we can find ml and the
number of orbitals.
SOLUTION
n
l
sublevel name
possible ml values
of orbitals
(a)
2
3d
-2, -1, 0, 1, 2
3
3
(b)
2
0
2s
0
1
(c)
5
1
5p
-1, 0, 1
3
(d)
4
3
4f
-3, -2, -1, 0, 1, 2, 3
7
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Figure 7.17
1s
2s
3s
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Figure 7.18
The 2p orbitals
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Figure 7.19
The 3d orbitals
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Figure 7.19 continued
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Figure 7.20
One of the seven possible 4f orbitals