applications and analogies Pictorial Analogies VII: Quantum Numbers and Orbitals
edited by RONDELORENZO Middle Georgia College Cochran. GA31014
with respect to size, shape, and orientation, they do lack the feature of clearly referring to different electrons about the same atom (building).
John J. Fortrnan Wright State University Dayton, OH 45435
1 Quantum Number
Analogies have been made between the quantum numbers of electron energy levels and a location such as a floor, apartment, and room in a building (1).Such analogies are limited, because they relate to identifring electron configurations but do not give very good wnnotations as to the size, shape, and orientation of the orbitals. Because the principle quantum number, n, relates to the size of the atomic orbital, why not relate it to the size of a house as illustrated in Figure 1,where larger values represent larger houses. The secondary quantum number, 1, gives the shape of the orbital so an analogy can be made to the shape of the house with larger values associated with houses with more structure. This is showninFigure 2. The third quantum number, ml has to do with the orientation of the orbital in a magnetic field. Therefore, relate its values to different directions the house may be facing as depicted in Figure 3. While these analogies have advantages
Shape of House
Figure 2. Analogy to the relationship of the /quantum number to the shape of an atomic orbital.
rnR Quantum Number
Part of a presentation at the 195th National ACS Meeting and 3rd Chemical Congress of North America, Toronto, Canada, June 9, 1988.
Orientation of the House
w
1
2
3
Figure 1. Analogy to the increasing size of atomic orbitals with increasing value of the nquantum number.
South
East
Figure 3. Analogy to the directional relationship of the rn,quantum number.
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Lone Pair
-__-_-
Delocalized
i
Localized
Figure 4. Analogy to a localized bonding orbital. Figure 5. Analogy to a less localized lone electron pair orbital. Another analogy can be made to bonding and lone pair orbitals about an atom in a molecule. Electrons in a bonding orbital are more localized because they are attracted by the nuclear charge of the two atoms bonded together. This can be associated with a horse tied to a line between two trees as shown in Figure 4. The lone pair of electrons contained in an orbital not involved in a bond are attracted to only one nucleus, so the orbital can be more delocalized or spread out. This is analogous to the greater freedom of a horse hitched to only one tree, as pictured in Figure 5.
Larger copies of these figures will be sent to those wishing them for making overhead trans~arencieswith ~hotocopiers or thermofai. Acknowledgment Bruce Stiver of WSU's Media Services drew these illustrations and the expenses were paid by the chemistry department. Literature Cited 1. Rleck, D. F. J. Chem. Educ. 1990, 67,398.
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