valence_bond - Waves This wave created by a water droplet...

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Waves This wave created by a water droplet hitting the surface of water will have features that are similar to our electron’s wavefunction: tall in the middle, then dropping below the level of the undisturbed water surface, to climb again, and drop again in a series of concentric hills and valleys, frozen (standing still) by the camera to be examined in detail. And, if we trace the water surface on a graph paper representing height of the water surface on the vertical axis and the separation from the center on the horizontal axis, we get a mathematical function looking like a wave Waves and Electrons Electrons have a split personality. Luckily, they make waves or rather, behave like waves and they can behave as particles. We describe the behavior of electrons with a wavefunction, whose most important property is that when squared, represents the probability of finding an electron in space. [three functions are plotted below vs. distance from the nucleus]. The 3 s orbital Red-wavefunction Blue-wavefunction 2 to give the probability Green- Ψ 2 multiplied by volume—to see most probable location for an electron (volume corrected plot) [scales are different for each function]
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The wavefunction (a 3D function) has a certain value in each point of space (x, y, z, if you like Cartesian coordinates). The square of this function represents probability of finding an electron in a minuscule amount of space around that point (the point itself has no volume, so we use this volume element, dx, dy, dz, for those mathematically inclined). Thus orbitals, as represented by wavefunctions' squares, are places (volumes of space) where probabilities of finding an electron are non-zero, i.e. places where the electrons are allowed to be. The probability of finding an electron in a volume of space is called electron density; it is a fraction of an electron per unit volume.
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This note was uploaded on 03/01/2011 for the course CHEM 030.205 taught by Professor Klein during the Fall '09 term at Johns Hopkins.

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valence_bond - Waves This wave created by a water droplet...

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