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Ch 7: Quantum Theory and Atomic Structure

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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 Pauli Exclusion ... – PowerPoint PPT presentation

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Title: Ch 7: Quantum Theory and Atomic Structure


1
Ch 7 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
2
Electromagnetic Radiation
  • WAVELENGTH - The distance between identical
    points on successive waves. ( ? )
  • FREQUENCY - The number of waves that pass through
    a particular point per second. (?)
  • AMPLITUDE - The vertical distance from the
    midline to a peak, or trough in the wave.

v c
???
3
(No Transcript)
4
Relationship between ? and ?
  • c ??

5
Light has wave characteristics
  • Refraction
  • Diffraction

6
Figure 7.4
Different behaviors of waves and particles.
7
The diffraction pattern caused by light passing
through two adjacent slits.
Figure 7.5
8
Light has wave characteristics
  • Refraction
  • Diffraction

c speed of light 3.00 x 108 m/s
Wavelength (meters)
1
Visible
Radio
TV
X-rays
Infrared
Microwaves
700 nm
400 nm
600 nm
500 nm
9
Two-minute problem
  • How does the wavelength of a cell phone microwave
  • (3 GHz) compare to a 10 m radio wave?
  • A. 100 times longer
  • B. 10 times longer
  • C. 10 times shorter
  • D. 100 times shorter

10
Light has particle characteristics
  • Photoelectric effect
  • Threshold frequency

11
Light particles are called photons
  • E hn
  • c ln
  • High energy
  • frequency high
  • wavelength short (small)
  • Low Energy
  • frequency low
  • wavelength long (large)
  • Sample problem The lower wavelength limit of
    visible light is about 400 nm. What is the
    energy of this radiation?

12
Matter has particle characteristics
  • Defined trajectory
  • At least on macroscopic level!

13
Matter has wave characteristics
  • De Broglie wavelength
  • ? h/mv
  • Electron microscopy, neutron diffraction
  • Observed only for tiny objects (why?)

14
Matter has wave characteristics
The diffraction pattern caused by a beam of
electrons passing through two adjacent slits.
15
Two-minute problem
  • How does the wavelength of a neutron compare to a
    electron of the same speed?
  • A. 2000 times longer
  • B. 20 times longer
  • C. 20 times shorter
  • D. 2000 times shorter

16
Worksheet break
17
Quantization of Energy
  • Max Planck (1900)
  • Proposed that energy can be released or absorbed
    by atoms in chunks of some minimum size
  • quantum smallest quantity of energy that can be
    emitted or absorbed as electromagnetic radiation
  • Energy is quantized
  • values of energy are restricted to certain
    quantities
  • E h?
  • where E Energy (J)
  • h Plancks constant
  • 6.63 x 10-34 Js
  • ? frequency (Hz or 1/s)

18
Continuous and Line Spectra
  • Continuous spectrum
  • a spectrum containing light of all wavelength
  • examples rainbow, prism
  • Line spectrum
  • a spectrum showing only certain colors or
    specific wavelength of light

19
Bohrs Model of Hydrogen
  • Niels Bohr (1913)
  • Offered a theoretical explanation of line spectra
  • combined classical physics and quantum theory
  • proposed that only orbits of certain radii,
    corresponding to certain definite energies, are
    permitted
  • an electron in a permitted orbit has a specific
    energy and is said to be in an allowed energy
    state

20
Bohr Model (cont.)
  • Energy Level Postulate
  • electrons can have only specific energy values
  • where E Energy (J)
  • RH Rydberg constant
  • 2.18 x 10-18 J
  • n energy level
  • note energy is negative!

21
Energy Levels
22
Bohr Equation
  • Used to describe the energy that is absorbed or
    emitted when an electron moves from one energy
    level to another
  • negative ?E light is emitted
  • positive ?E light is absorbed

23
Two-minute problem
  • which of the four electron transitions shown in
    the figure to the right produces the shortest
    wavelength line in the hydrogen emission spectrum

24
The Heisenberg Uncertainty Principle
D x m D u
25
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)
26
Quantum Mechanics and Atomic Orbitals
  • Schrodinger (1926) proposes a theory that
    incorporates the wavelike and particle-like
    behavior of the electron
  • provides information about the electrons
    location in an allowed energy state
  • probability wavefunction ?2
  • atomic orbitals describe the distribution of
    electrons in space
  • defined by four quantum numbers

27
Quantum Numbers
  • Principle quantum number (n)
  • Defines the size and energy of an orbital
  • Positive integral values
  • as n increases, the size and energy increases
  • Angular momentum quantum number (l)
  • Defines the shape of an orbital
  • Integral values from 0 to n-1
  • Value of l is designated by a letter
  • Value of l 0 1 2 3
  • Letter used s p d f

28
Quantum Numbers (cont.)
  • Magnetic quantum number (ml)
  • describes the orientation of the orbital in space
  • Values range from -l to l
  • Spin quantum number (ms)
  • describes the direction the electron is spinning

29
Sample Problem
  • Considering the limitations on values for the
    various quantum numbers, state whether an
    electron can be described by each of the
    following sets. If a set is not possible, state
    why.
  • n 2, l 1, ml -1
  • n 1, l 1, ml 1
  • n 3, l 1, ml -3

30
Relationship between Quantum Numbers
  • electron shell
  • a collection of orbitals with the same value of n
  • subshell
  • one or more orbitals with the same set of n and l
    values
  • Pattern
  • each shell is divided into the number of
    subshells equal to the principle quantum number,
    n.
  • each subshell is divided into orbitals equal to
    the number of ml values

31
Electron Probability and Shape of Orbitals s
orbitals
32
Electron Probability and Shape of Orbitals p
orbitals
33
Orbital Diagrams
  • diagram used to show how the electrons are
    distributed among the orbitals of a subshell
  • orbital is represented by a circle or square
  • electrons represented by an arrow
  • Example Hydrogen

34
Pauli Exclusion Principle
  • An orbital can hold at most two electrons, and
    then only if the electrons have opposite spin
  • each electron is an atom has a unique set of
    quantum numbers
  • Example Helium

35
Sample Problem
  • Based on the Pauli exclusion principle, which of
    the following orbital diagrams are possible?

36
Magnetic Properties
  • paramagnetic
  • diamagnetic

37
Diagonal Rule (Aufbau Principle)
1s 2s 2p 3s 3p 3d 4s 4p 4d
4f 5s 5p 5d 5f... 6s 6p 6d
6f... 7s 7p 7d 7f...
38
Hunds Rule
  • the lowest energy arrangement is obtained by
    putting e- in separate orbital of a subshell with
    parallel spin before pairing e-
  • Example Carbon
  • Z 6 1s2 2s2 2p2
  • You try Oxygen
  • Z 8

39
Sample Problem
  • Electron Configuration of Vanadium
  • Quantum Numbers
  • n
  • l
  • ml
  • ms

1s 2s 2p
3s 3p 4s
3d
40
Exceptions
  • Some transition metals do not follow the diagonal
    rule!
  • Example chromium
  • Z 24
  • diagonal rule
  • 1s2 2s2 2p6 3s2 3p6 4s2 3d4
  • -filled and half-filled orbitals are more stable
    than unevenly filled orbitals.
  • true electron configuration
  • 1s2 2s2 2p6 3s2 3p6 4s1 3d5

41
The Periodic Table
  • Dmitri Mendeleev
  • designed periodic table in which the elements
    were arranged in order of increasing atomic mass
  • Henry Moseley
  • designed periodic table in which the elements
    were arranged in order of increasing atomic
    number
  • Periodic law
  • the physical and chemical properties of the
    elements are periodic functions of their atomic
    numbers

42
Periodic Trends
  • Atomic Radius
  • Why?
  • Ionization Energy
  • Why?
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