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Quantum Numbers

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A Covert Search

With their inherently unpredictable nature, how can electrons even be located?

Credit: Anonymous9000
Source: http://www.flickr.com/photos/anonymous9000/2662486337/sizes/o/in/photolist-54gWqR-54gWBP-54gWEk-54gWWV-54gXea-54gXkt-54gXQ8-54gXSD-54gY58-54gY8p-54gYgz-54gYJr-54gYU4-54gZqD-54gZug-54gZBk-54gZGX-54gZPD-54m7hw-54m7k7-54m7q9-54m7t5-54m7FS-54m7Sf-54m82o-54m85E-54m8zf-54m91o-54m9vw-54m9Ao-54m9Gu-54ma7W-54maeL-54masN-54maxJ-54maFu-54maHs-54maLf-54maUf-54mb11-54mbbC-54mbyq-54mbUf-54mbXL-54mc7d-54mcmS-54mctq-54mcZq-54mddf-54mdxJ-54mdLW/
License: CC BY-NC 3.0

[Figure1]

Let’s say you are a spy for the CIA, and you have recently been assigned a covert mission which you have 48 hours to complete. If you fail all hope is lost. You have just been contacted by a potential informer, who has told you to meet them at a luxury hotel in San Francisco. However, there’s a problem: you don’t know what room they are in, what their name is, or how they look. So arriving with style but proceeding with caution, you begin to weigh the possibilities.

First of all, you consider that the more floors there are in the hotel, the harder it will be to track your informer, both location-wise and effort-wise. Searching 30 floors in and out would take a lot of energy! Also, there are a variety of room sizes: some smaller, some larger. The larger ones are sure to be occupied by more people right? Not quite -- the rich live for luxury and probably wouldn’t mind a little extra space. Another challenge: where are the larger rooms located, or the smaller ones? To the north of the building? To the south? And last but not least, is our informer a male or a female? Well then, here goes!

Much like the key people in a spy case, electrons are very elusive. We cannot know for sure where they are located in an atom, but we can consider the possibilities, using quantum numbers. The quantum numbers -- n, l, ml, and ms -- each give the likely areas of electron density in which the electron might be located, the likely shapes of the area, the likely orientations of the area, and the spin direction of the electron (up or down).                                                                

Creative Applications

  1. True or False: An electron with principal quantum number n = 6 cannot be located in the first principal energy level. Explain your answer.
  2. Give one correct set of quantum numbers for neon (Ne) in its ground state.
  3. Identify the error in this set of quantum numbers for gallium (Ga), and give a plausible replacement: 4, 1, 3, ½.

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