Ch 7: Quantum Theory and Atomic Structure

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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
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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
???
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(No Transcript)
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Relationship between ? and ?

• c ??

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Light has wave characteristics

• Refraction
• Diffraction

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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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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
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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

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Light has particle characteristics

• Photoelectric effect
• Threshold frequency

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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?

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Matter has particle characteristics

• Defined trajectory
• At least on macroscopic level!

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Matter has wave characteristics

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

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Matter has wave characteristics
The diffraction pattern caused by a beam of
electrons passing through two adjacent slits.
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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

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Worksheet break
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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)

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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

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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

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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!

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Energy Levels
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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

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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

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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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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

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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

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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

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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

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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

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Electron Probability and Shape of Orbitals s
orbitals
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Electron Probability and Shape of Orbitals p
orbitals
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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

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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

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Sample Problem

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

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Magnetic Properties

• paramagnetic
• diamagnetic

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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...
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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

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Sample Problem

• Electron Configuration of Vanadium
• Quantum Numbers
• n
• l
• ml
• ms

1s 2s 2p
3s 3p 4s
3d
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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

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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

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Periodic Trends

• Atomic Radius
• Why?
• Ionization Energy
• Why?