Edited by RALPHK. BlRDWHlSlELL
textbook forum
University ol Wesl Florida Pensacola. FL 32504
Another QuantumNumber? Charles 1.Penino and Donald L. Peterson California State University, Hayward, CA 94542 The presentation of the concept of "spin" in general chemistry, organic chemistry, and physical chemistry textbooks is inconsistent and misleading tostudents and in some cases even incorrect. The problem appears to lie in the reluctance of authors to designate or admit to five quantum numbers. Nearly all texts name, define, and assign a value to two quantities associated with the intrinsic angular momentum of an electron: s. the snin. and m.. a comoonent of s in an assigned direction ~ o w e v &authors , appear to be reluctant to desienate both s and m, as auantum numbers and utilize that a; pedagogical tool.~wo.ofthe most popular physical chemistrv textbooks differ simificantlv in their treatments. ~ 1 b e r t ~ ' b a srather good Geatmentthat refers to s as a quantum number initially, but retreats from this position, subsequently referring to s as the "spin." He designates m, as the quantum number for spin without actually naming it so. In an accompanying table, he refers to s as a "quantum' numher for spin angular momentum" and m, as the "quantum number for the z-component of the spin angular momentum." This listing correctly generates a total of five quantum numbers, but no reference is ever made to this in the text. The quantum number, s, simply disappears from sight and, in a description accompanying a figure, m, is referred to as the spin quantum number. To the experienced reader, the treatment by Atkins2 appears to be the same; however, his wording is significantly different. This text refers to s as the spin angular momentum quantum number, differing from Alberty in maintaining that designation but avoiding direct reference in the text to m, as a quantum numberwith an appropriate name. In a table accompanying the text, both s and m, are referred to as quantum numbers; however. no useful name for m. is ~resented.These authors. and others, resist the bf defining five quantum numbers as the total needed in order to make a correct presentation of the concepts of spin. Furthermore, it would be advantageous to have universally accepted names for s and m, in order that astudent fully understand what is being taught. Other textbooks perform similarly to these two, and in some unusual instances go all wrong, such as several that identify s as the fourth quantum number with values of ill2. Obviously, if s is the fourth quantum number, then m, is the fifth by the present methodology we are using for instruction in physical chemistry. The most likely reason for
avoiding the notion of five quantum numbers is that the value o i s as 112 does not change, unlike the other quantum numbers (n, 1, mi, and m,). Why bother specifying a quantum fornumber whose value remainsconstant? W; ariuethat " the sake of consistent pedagogical progress, parallel symbols. names. and definitions are necessarv for s and m." as are presently assigned to 1 and ml, the angular and magnetic quantum numbers for orbital angular momentum. In this latter case, the emphasis on the modifier "orbital" would benefit understanding there as well. A complete set of the five quantum numbers consistent with the approach of most authors but more complete than usual would he: ~~~
n-principal quantum number I-angular quantum number (for orbital angular momentum) ml-magnetic quantum number (z-axis component of 1) s-spin quantum number (for intrinsic angular momentum) m,-spin magnetic quantum number (z-axiscomponent) The assignment of spin magnetic quantum number for m, differs from some authors who prefer mametic spin auan. . tum number, but our suggestion follows the original assignment of Pauling%ecaure it emphasizes that both ml and m. are magnetic numbers, one for orbital angular mo: mentum and the other for spin angular momentum. This might mean that ml could be better named as the orbital magnetic quantum number rather than the magnetic quantum number. which is most often found. We submit that the physical chemistry student is very oftennot able to distinguish an author's intent upon reading the words "spin", "spin quantum number", and "spin angular momentum quantum numher" especiallv when different authors refer toboth s and m, in those v e j same ways. An improved understanding of the quantum numbers, spedroscopy, termsymbols, and other advanced concepts could possibly result from the teaching of five quantum numbers with appropriate definitions.
' Alberly. R. A. Physlcal Chemistry. 7th d . ; Wiley: New Yo*,
1983:.-aa 381483. -- - - ~ Atkins, P. W. Physical Chemistry. 3rd York, 1986: pp 336-338. ~
~
ed.; W. H. Freeman: New
Pauling. L. me Nature of the Chernlcal Bond, 3rd d . ; Cornell University: lthaca. NY. 1960: p 47. :
Volume 66
Number 8
August 1989
623
