Ch02Su08

Ch02Su08 - Structure and Properties of Organic Molecules...

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Structure and Properties of Organic Molecules Electrons exhibit wave-particle duality. 1) The particle property gives a meaning of “here at this spot at this time and going off in a particular direction with a certain speed (billiard ball)”. Localized desription 2) The wave property comes from diffraction (constructive and destructive interference) and can only be described by a mathematical function. Delocalized description Diffraction patterns: Light or surface of ‘ripple tank’ Diffraction pattern of X-rays on Ni surface The pattern only appears if the two holes are placed n∙ λ apart ( λ wavelength, n integer) or if X-ray λ corresponds to internuclear distance in Ni crystal. There are 2 types of wave: travelling (ripples on a pond) standing waves (guitar string). An electron in an atomic orbital can be described like a bound, stationary vibration – a standing wave. Consider a guitar string being plucked in the middle 3b49a2edfd1b5a458968f1625e99ae11a5fda7a9.doc 1
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We get a standing wave, which at one moment has all of the string up, and then the next moment, all of the string down. When electrons move they set up electromagnetic radiation Velocity v = Wavelength λ times frequency ν v = λ ν An instantaneous picture of the waveform would show the string in a smooth curve either displaced above or below the horizontal rest position. The amplitude of the wave is the square of the displacement. Imagine the amplitude being 3 dimensional – this is the shape of a 1s orbital. An orbital is described by its wave function, ψ , (psi), which is a mathematical description. The electron density at any point is equal to ψ 2 . (The +ve and –ve signs are not charges, just phases). A 1s orbital is spherically symmetrical, and is often represented as a circle (meaning a sphere). This corresponds to the Fundamental frequency of the wave / guitar string. If we place our finger exactly half way along the string and pluck again, the string vibrates, we observe a standing wave but the midpoint does not move. Figure 1-2 Function = e -|x| (can be plotted on graphing calculator) 3b49a2edfd1b5a458968f1625e99ae11a5fda7a9.doc 2
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Figure on board The amplitude at the midpoint is zero – a Node. When one half of the string is up, the other is down, the two halves vibrate out of phase with one another. This is the first Harmonic of the wave. Imagine the amplitude (square of the displacement) in three dimensions – two out of phase lobes, separated by a nodal plane: a 2p orbital. 3b49a2edfd1b5a458968f1625e99ae11a5fda7a9.doc 3
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Linear Combinations of Atomic Orbitals (LCAO) 1s, 2s, 2p,… orbitals are atomic orbitals. Atomic orbitals can combine and overlap to give more complex standing waves (i.e. more complex orbitals). This process is called linear combinations of atomic orbitals.
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This note was uploaded on 02/23/2010 for the course CHEM 202 taught by Professor Smith during the Spring '10 term at Duke.

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Ch02Su08 - Structure and Properties of Organic Molecules...

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