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Wed. Oct. 2, 2019

Today’s Lecture

• Quantum Mechanics and Atomic Theory

• 12.1 Electromagnetic Radiation

• 12.2 The Nature of Matter

Lecture 13

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Quantum Mechanics and

Atomic Theory (Ch. 12)

• 12.1 Electromagnetic Radiation

• 12.2 The nature of matter

• 12.3 The atomic spectrum of hydrogen

• 12.4 The Bohr model

• 12.5 Quantum Mechanical Description of atom

• 12.6 Particle in a box (not for exam)

• 12.7 Wave Equation for the Hydrogen atom

• 12.8 Physical Meaning of a Wave Function

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• Electromagnetic radiation:
  • visible light, x-rays, infrared, ultraviolet, etc.
  • one way energy can travel through space
  • has wavelike behavior and travels at the

speed of light in vacuum

Fig. 12.

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• waves have 3 characteristics:
  • wavelength (λ: lambda): meters
    • distance between 2 consecutive peaks

    • ---

  • frequency (ν: nu): s-1^ (Hz)

    • of waves (cycles) / second

07_93 (^) λ 1 second 1

ν 1 = 4 cycles/second = 4 hertz

ν 2 = 8 cycles/second = 8 hertz

λ 2

λ 3

Fig. 12.2 ν 3 = 16 cycles/second = 16 hertz

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• Classical physics (late 1800s):
  • matter was thought to consist of particles with a specific position/mass in space
  • electromagnetic radiation was described as a wave, treated with wave theory; massless and positionless

Nature of Matter

BUT: Radiation from solid bodies that had been heated red- hot -- _________________was inconsistent. The theory requires that intensity goes to infinity for very short wavelengths – the __________________

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• The observed energy profiles are consistent with the proposal that energy can be gained or lost from only in discrete amounts.
• energy can be gained or lost only in integer numbers of h ν (experimental observation in 1901)
• h = Planck ’ s constant = 6.626 x 10-^34 J s (or Kg m^2 /s)
  • ∆ E = nhν (n = integer)
    • ∆ E is the change in energy of a system
    • Previously, it was believed any amount of energy could be transferred between entities in a system
    • Planck suggested: » energy is ________ and can only occur in discrete units of size h ν

» each small “packet” of energy: _________ Energy of matter is not continuous Physics 1918^ Energy has^ ________^ behaviour

Max Planck (1858-1947)

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Einstein’s Particle Theory of Light

• electromagnetic radiation:
  • has particle behaviour
  • is quantized
  • is made up of a stream of particles called photons

 Energy of a photon:

• the minimum energy required to remove the bound electron is the threshold energy, Eo

E (^) photon

hc

h ν

Eo = h νo

Albert Einstein (1879-1955)

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The Photoelectric Effect Deciphered

• When ν < νo , the energy of the photon, E < Eo and an electron will not be emitted
• When ν > νo , energy of the photon E > Eo an electron will be emitted and excess energy goes into kinetic energy of the emitted electron

KEelectron = 1/2mv^2 = h ν - h νo

 intensity of light is a measure of the number of photons in a given part of the light beam

 the more photons of νo or greater, the more electrons that can be released

Energy of the incident photon (^) Energy required to remove the electron

Mass of the electron

(Velocity of the electron)^2 Albert Einstein (1879-1955)

Physics 1921

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If waves have particle properties, do

particles have wave properties?

“ The only phenomena involving integers in Physics were those of interference and of normal modes of vibration. This fact suggested to me the idea that electrons too could not be regarded simply as corpuscles, but that periodicity must be assigned to them ." de Broglie, doctoral thesis 1924

de Broglie proposed that the relationship between the wavelength of the electron and its momentum is:

mv

h λ =

Louis de Broglie (1892-1987)

Speed of Physics 1929 electron

mass of electron

relates wavelength to mass: “___________”

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• electromagnetic radiation behaves a wave and as a particle. A “particle” of EM radiation is a photon.
• matter also has wavelike properties
• ______________________
• this gives the wavelength of a moving particle
• Wavelength of an electron on the same order of magnitude as chemical bonds

mv

h λ =

Dual nature of light

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10 -12^10 -10^10 -8^ 4 x 10-

Gamma rays

X rays Ultraviolet Infrared Microwaves Radio waves FM Shortwave AM

4 x 10-

Wavelength in meters

5 x 10-7^ 6 x 10-7^ 7 x 10-

7 x 10-7^10 -4^10 -2^1 102

Visible

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X-Ray Pattern of key enzyme of the pathogen for African sleeping sickness in a living cell

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A full 3D set of x-ray structure factors (from Photosystem I)