this problem short of developing a backbone injection for the American educational system.
For n = 2, we obtain 9 = cas' (-1)= 180'
J.T. Maloy Seaton Hall University South Orange, NJ 07079
For n = 3, we find (-112) = 120'
(6)
(-113) = 109,4T
(7)
9 = eosl
Computing the Tetrahedral Angle
!lb the Editoc We were somewhat surprised to read in a recent article [Duffey, G. H. J. Chem. Educ. 1990, 67, 35361 a rather involved computation of the tetrahedral angle using vector algebra. We had assumed that the following three-line demonstration was widely known. Denote by ri (i = 1,2, 3,4) the vectors from the center to each apex of a tetrahedron. Obviously they are all of identical length, r, and by symmetry
(5)
For n = 4, we bave 0 = eas'
The method works when n = 2,3, and 4 because for these structures the acute anele between anv two of the vectors is the same. For larger ?s, this equality no longer holds. It is not sufficient merely to argue from symmetry and eq 1. George H. Duffey Department of Physics South Dakota Sfate University Brookings, SD 57007
Choose any of the vectors, say r2,and take the scalar product of it with eq 1. Names and Discoverers To the Editor:
Solving for the tetrahedral angle 13 gives immediately
Of course, we do not claim any originality for this approach, for we must have seen i t in a book somewhere; we simply think that it might be better known. 8. T. Sutcliffe S. J. Smith
University of York, Heslington York, United Kingdom
To the Editor: With respect to the letter by B. T. Sutcliffe and S. J. Smith, several comments are in order. Their approach is described in a Letter to the Editor by Snatzke [Snatzke, G. J. Chem. Educ. 1963,40, 941. Interestingly, it may be applied to digonal and trigonal structures also. For n equivalent ligands arranged symmetrically about a central atom, the net dipole moment is zero and one may write
Vivi Ringnes's excellent and comprehensive article "Origin of the Names of Chemical Elements" [J.Chem. Educ. 1989, 66, 7311 will undoubtedly stand as the definitive treatment of that subject. Riugnes's derivation of the name promethium for element 61, however, is unnecessarily strained. According to the discoverers, it was indeed named after the god Prometheus, giver of fire to humankind, but for a much simpler reason than Ringnes has inferred. Not occurring in nature, element 61 was discovered as a fission product of uranium. It could therefore be said to bave arrived on Earth along with nuclear energy, the "new kind of fire", that the gods had given to humankind. Also, a correction should be made to the paper of David W. Ball [J.Chem. Educ. 1985,62,7871, cited by Ringnes. Ball identifies Marie and Pierre Curie, a h r whom the element curium was named, as the discoverers of radioactivity. They were not. Radioactivity was discovered by Henri Becquerel; the Curies' work elucidated the phenomenon, among other things. Robeti L. Wolke Professor Emeritus
University of Pittsburgh Pittsburgh, PA 15260 Nonpolitical Science
Here rj is drawn from the center to thejth ligand. If each bond is equivalent, the magnitude of each radial vector is the same:
One recalls the deffition of the dot product between two vedors, as in the my earlier paper [ J. Chem. Educ. 1990, 67, 35-36]. One also assumes that the smallest angle between any two of the vectors is the same. One then dot multiplies both sides of eq 1 by vector r, to get r2 + (n -l)? cos 9 = 0
(3)
To the Editor: In recent vean. i t has been fashionable for scientific authors to wrltc univers~tyor college texts for nonspecialist students. Althounh this is to be applauded, these texts are written for a l o c i market and may be very parochial. Because of Emlish l a w a c e problems, authorities in developinficount& tendlo trarklate what is considered a suitable i.:naiish text "lock, stock and barrel". This introduces a form of scientific imperialism with the dominant scientific culture forcing its own values onto another country. Currently, I am responsible for helping an Indonesian University introduce a new text for a chemistry course to be given specifically to Agricultural Ewnomics students. The selected U S . text, like many others in this genre, had a n American emphasis, citing US. brand names, using western cultural values, and dealing with Volume 69 Number 2
February 1992
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