Qualitative introduction to quantum theory

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Qualitative introduction to quantum theory
BS1030, Chemistry for Life Scientists November
11, 2008

• Prof. Judith Klein-Seetharaman
• School of Biological Sciences
• j.klein-seetharaman_at_rhul.ac.uk

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Overview

• Today Study of atomic structure - from classical
  mechanics to quantum theory
• Energy is quantized
• Wave-particle duality
• Next week Application of quantum theory to
  describe atomic structure
• The uncertainty principle
• The Schroedinger equation
• Quantum numbers
• Atomic orbitals
• Third week Bonding and shapes of molecules
• Types of bonds
• MO theory

Atkins Jones Chapter 1.1-1.6
Atkins Jones Chapter 1.7-1.22
Atkins Jones Chapter 23
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Atomic Structure

• Dalton

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Atomic Structure

• Dalton featureless spheres
• J.J. Thomson discovery of the electron as the
  first sub-atomic particle (neg. charge)
• Robert Millikan determined the charge of the
  electron
• But atom is neutral
• J.J. Thomson atom is a blob of a positively
  charged jelly with electrons like raisins
• Ernest Rutherford shoot positive charges from
  atoms against a thin platinum foil
• What do you expect to find? In JJ Thomsons
  model? In alternative models?

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Shooting alpha particles on a thin foil
1 in 20,000 is deflected with very large angle
Most go through
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Rutherfords Atom Model

• Nucleus many times smaller than itself with
  electrons occupying the rest of the space
• What are the electrons doing in the atom?

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The answer came from
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(No Transcript)
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The answer came from

• The study of light emitted by heated atoms

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The answer came from

• The study of light emitted by heated atoms

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What is light?

• electromagnetic radiation
• Oscillating electric and magnetic fields
  traveling at the speed of light
• of cycles is frequency
• 1Hz s-1
• One cycle per second
• Amplitude
• Wavelength

l v c
Wavelength x Frequency speed of light
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What is the speed of light

• In vacuum 2.998 108 m/s
• Radar waves leave earth, bounce off the moon and
  come back in 2.5 seconds (478,000 miles)

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Short or long wavelength?
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What is the wavelength of red?of blue?which
frequency?other waves?
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Continuous Spectrum
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Atomic spectra

• are LINE spectra

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There are patterns in the lines

• First Joseph Balmer, a swiss school teacher in
  1885
• Then Johann Rydberg, a swedish spectroscopist

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What does it mean?
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What does it mean?

• The electrons in an atom can only have certain
  energies.
• Energy is quantized.

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Next puzzle black body radiation
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Next puzzle black body radiation

• With increasing temperature, the total energy
  emitted increases and the maximum intensity
  shifts to shorter wavelengths.

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Stefan-Boltzmann Law
Wiens Law
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Can you determine the temperature on the surface
of the sun?

• Max intensity at 490nm

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A red giant is a late stage in the evolution of a
star. The average wavelength maximum is 700nm.

• What is the temperature of the star?

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What is the wavelength emitted by the human body?
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Why does the wavelength shift with T?

• Classical physics puts no restriction on how
  small a quantum can be transferred between matter
  and radiation
• Thus, classical physics says any hot body should
  emit any wavelength
• Even a human body would glow in the dark
• There would be no darkness
• Something is wrong! Ultraviolet catastrophe

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Plancks answer
E hn

• Energy exchange between matter and radiation is
  quantized
• Low frequencies, not enough energy to stimulate
  oscillations
• hPlanck constant
• Can reproduce Wiens and Stefan-Boltzmann laws
  perfectly

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The nail in the coffin Photoelectric effect

• No electrons are ejected if the frequency of the
  radiation is below a threshold value
  characteristic of the metal.
• Immediate ejection of electrons however low the
  intensity of the radiation.
• The kinetic energy of the ejected electrons
  increases linearly with the frequency of the
  incident radiation.

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Einsteins explanation

• Einstein proposed that electromagnetic radiation
  consists of particles, which were later called
  photons
• Each photon is a packet of energy
• Questions
• A. What is the energy of a photon e.g. of blue
  light?
• B. Why kinetic energy linear?

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Bohr Frequency Condition

• The frequency in a line spectrum of an atom
  arises from transition between two energy levels

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Light is also waves

• Best evidence Diffraction

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From waves to particles back to waves

• Line spectrum of atoms
• Bohrs frequency condition
• Black body radiation
• Plancks quantization of energy
• Photoelectric effect
• Einsteins particle interpretation
• Diffraction
• Clearly a wave-related property

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Wave-Particle Duality

• In the wave model, the intensity of the radiation
  is proportional to the square of the amplitude of
  the wave.
• In the particle model, the intensity is
  proportional to the number of photons present.

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Generalization to all particles

• French scientist Louis de Broglie proposed that
  all particles should have wavelike properties

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The wave-like behavior of electrons can be
experimentally observed
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Electron Microscope

• Electrons have wavelengths suitable to image
  biological samples down to near-atomic resolution

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The Dr. Jekyll Mr. Hyde of Physics
The Electron Wave Particle
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Crime Scene Investigators
Ernest Rutherford New Zealand Physicist
(1871-1937) Nobel Prize in Chemistry 1908
Max Planck German Physicist (1858-1947) Nobel
Prize in Physics 1918
Albert Einstein German Physicist
(1879-1955) Nobel Prize in Physics 1921
Robert Millikan American Physicist
(1868-1953) Nobel Prize in Physics 1923
Niels Bohr Danish Physicist (1885-1962) Nobel
Prize in Physics 1922
Joseph John Thomson British Physicist
(1856-1949) Nobel Prize in Physics 1906
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Now you (should) know

• Why we need quantum mechanics
• That Energy is quantized
• That matter shows particle/wave duality
• What are characteristics of particles
• What are characteristics of waves
• How to calculate energies, frequencies,
  wavelengths