classes%5Cfall08%5C20A-1ID10%5CNotesonminimumsizeofhydrogen

classes%5Cfall08%5C20A-1ID10%5CNotesonminimumsizeofhydrogen...

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Notes on minimum size of hydrogen. Often in science we have simple models that give us qualitatively correct (and often near-quantitatively correct) information which we will, without the simple models, need complicated methods. One such case is the size of hydrogen (or hydrogenic systems, such as He+, Li++, etc.). Formally, to get the size of H we need to solve the Schrödinger equation, get the lowest energy orbital (the 1s orbital, which we will see later) and see what its size is. Instead, we can use a very qualitative idea. Let’s approximate the lowest orbital of hydrogen as it is a single blub, of shape, e.g., Let’s call the center of the wavefunction: xcenter, where xcenter is the position of the proton; and the extent of the wavefunction L. We also define the uncertainty in the position of the wavefunction as DeltaX. The wavefunction will extend essentially from Xcenter-DeltaX to Xcenter+ DeltaX , i.e., the extent of the wavefunction is L=2*DeltaX. Next we need the wavelength, Lambda, of the wave; the wave has about ½ an oscillation (a full oscillation requires

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This note was uploaded on 06/15/2009 for the course CHEM 20A taught by Professor Neuhauser during the Fall '08 term at Mt. SAC.

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