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Wave Particle Duality – Light and Subatomic Particles In high school physics light was treated as having both wave like and particle like character. Diffraction and refraction of light both exemplify its wave like properties. Particle like properties of light can also be demonstrated readily. One way to do this is to consider the photoelectric effect (see text) which implies, surprisingly, that light photons have momentum.

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Subatomic Particles – Wave Character A number of experiments show that small particles have observable wave like properties. Such wave like properties become increasingly important as one moves to particles of smaller mass. The electron is the most important of these particles. Interesting diffraction and refraction experiments have been conducted with electrons.

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Mathematical Description of Electrons The fact that electrons exhibit wave like behavior suggested that equations used to describe waves, and light waves in particular, might be modified to describe electrons. We will see some familiar mathematical functions used to describe the electron (e.g. cos θ, sin θ, e iθ ). We will use so-called wave functions (Ψ ’s ) to gain insight into the behavior of electrons in atoms.

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De Broglie’s Contribution De Broglie used results/equations from classical physics to rationalize experimental results which proved that subatomic particles (and some atoms and molecules) had wave like properties. He proposed, in particular, that particles with a finite rest mass had a characteristic wave length – as do light waves.

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8-5 Two Ideas Leading to a New Quantum Mechanics Wave-Particle Duality – Einstein suggested particle-like properties of light could explain the photoelectric effect. – Diffraction patterns suggest photons are wave-like. deBroglie, 1924 – Small particles of matter may at times display wavelike properties. Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 8Slide 5 of 50 Louis de Broglie Nobel Prize 1918

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Wave-Particle Duality Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 8Slide 6 of 50 E = mc 2 h = mc 2 h /c = mc = p p = h/λ λ = h/p = h/mu

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Wave properties of electrons demonstrated FIGURE 8-16 Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 8Slide 7 of 50

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Probabalistic Description of Electrons Classical physics suggests that we should be able (given enough information) to describe the behaviour of any body – changes in velocity, kinetic energy, potential energy and so on over time. Classical physics suggests that all energies are continuously variable – a result which very clearly is contradicted by experimental results for atoms and molecules (line spectra/quantized energies).

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Uncertainty Principle The quantum mechanical description used for atoms and molecules suggests that for some properties only a probabalistic description is possible. Heisenberg suggested that there is a fundamental limitation on our ability to determine precise values for atomic or molecular properties simultaneously. The mathematical statement of Heisenberg’s so- called Uncertainty Principle is given on the next slide.

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The Uncertainty Principle Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 8Slide 10 of 50 FIGURE 8-17 The uncertainty principle interpreted graphically Δx Δp ≥ h 4π4π Heisenberg and Bohr

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Atomic “Diagrams” Many simple diagrams of atoms/atomic structure have limitations. In class we’ll consider some limitations of the C atom diagram shown on the next slide. Representations of molecules are even more challenging – at least if we want to consider the electrons!

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The “Carbon Atom” Limitations?

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A Molecular Model

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Wave Functions and Standing Waves If we wish to describe the behaviour of a system changing over time in three dimensional space we would need four variables - three coordinates and time. Classically, we might wish to describe the velocity of a satellite re-entering the Earth’s atmosphere and write, for example, v(x,y,z,t). Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 8Slide 14 of 50

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Form of Wave Functions For wave functions used to describe the behaviour of electrons in atoms we could, by analogy, write Ψ(x,y,z,t). For charged particles and Coulombic interactions, using spherical polar coordinates simplifies the mathematical work greatly. We then write wave functions as Ψ(r,ϴ,φ,t). It turns out that in many cases the properties of an electron, atom, or molecule do not change over time.

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Wave Functions and Time If the behaviour of an electron, atom or molecule does not change with time we can write simpler wave functions, such as Ψ(x,y,z) or Ψ(r,ϴ,φ). The classical analogy of a system with wave like behaviour not changing over time is any object that features standing waves. In such cases there is no destructive wave interference. Then wave like properties should be constant over time.

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Standing Waves in Newtonian Mechanics In macroscopic systems with “constant” wave like properties one sees nodes which do not move over time. An example would be a guitar string vibrating with, in the simplest case, two nodes occurring at each end of the string. More complex waves are possible for real systems – which again reflect constructive rather than destructive wave interference. Similar considerations apply to electrons.

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Wave Mechanics Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 8Slide 18 of 50 FIGURE 8-18 Standing waves in a string 2L n Standing waves. Nodes do not undergo displacement. λ =, n = 1, 2, 3…

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The electron as a matter wave FIGURE 8-19 Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 8Slide 19 of 50

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Dihydrogen Oxide Waves

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Sample Term Test 1 Example

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[2]A5.A 16.0 L tank contains a mixture of helium gas at a partial pressure of kPa and nitrogen gas at a partial pressure of 75.0 kPa. If neon gas is added to the tank, what must the partial pressure of neon be to reduce the mole fraction of nitrogen to 0.200?

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Sample Term Test 1 Example

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