Ammonia multiplication table

For another simple, but more general, example of a symmetry group, let us recall our earlier examination of the ammonia molecule. We were able to discover six and only six symmetry operations that could be performed on this molecule. If this is indeed a complete list, they should constitute a group. The easiest way to see if they do is to attempt to write a multiplication table. This will contain 36 products, some of which we already know how to write. Thus we know the result of all multiplications involving E, and we know that... 

Inspection of Table 13-2 reveals that it is not symmetric across its principal diagonal. For example, CF = B, and EC = A, this is not an abelian group. One might inquire whether this group is the smallest that we can set up for the ammonia model. Inspection of the multiplication table should convince the reader that the following subsets meet the requirements for a group E, D, F E, A E, B E, C. These subgroups can be... 

The multiplication table for the ammonia model is given in Table 13-7 in terms of the symmetry symbols just described. (A, B,C we taken to be [Pg.440]

TABLE 13-7 Multiplication Table for the Ammonia Molecule First operation... 

Applying each pair of operations in turn gives the full multiplication table shown in Table 2.4. This table is considerably more complex than that for the examples of water and ammonia used earlier because the number of individual operations is greater. However, the rules set out for the products of the principal axis with vertically orientated mirror planes can also be seen to apply to the dihedral planes in this case. 

A study performed in Iowa City, Iowa, USA (a major agricultural area), of patients admitted to a specialized bum center, 94 of a total of 2,762 had chemical skin injuries (3.3 %) [32]. Involved chemicals included anhydrous ammonia (31/94, 34 %), acids (14), alkaline caustic substances (68), organic chemical agents (6), and undetermined chemical agents (5 cases). The majority were occupationally related. There was one fatality and 36/94 patients required skin grafting surgical procedures, some of whom required multiple such procedures. Complications that occurred include wound infections, pneumonitis, cardiac dysrhythmias, and myocardial infarction (overall, 24/94,25.5 %). Sequelae occurred in 27/94 cases (28.7 %). Early and copious potable water decontamination did not prevent some serious chemical skin injuries from develop-ing[32] (see also Sect. 4.4.1.2) (Tables 1.4and 1.5). 

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