A Time Scale for Fast Events David Onwood Indiana-Purdue University, Fort Wayne, IN 46805
0 2 4 6 FLOW METHODS P-JUMP T-JUMP
As the technology for determiningrates of rapid inter- and intraatomic events continues to advance,' the phrase "very fast reactions" must be understood in the context of the year in which it was written or spoken. Scientific vocabulary has not grown so as to afford a single means that is uniform, succinct, and accurate to describe the characteristic times of ranid events. There is not a middle around nor an easy trmsi~ionbetween semiqusntitntiw phraies like "this reariono occurs in milliseronds" Iwhirhcould be applied to times differing by almost two orders of magnitudi) on the one hand, and precise statements like "half-time of 1.748 X seconds" on the other. S I subunits provide order but are restrictive. Various disciplines generate their own terms: cycle times are expressed in "megaflops" for modern computers, while the frequency of electromagnetic radiation is indicated by various units, some of frequency, some of reciprocal length, for different ranges. These mixed units tend to obscure the underlying unity of our science and make it more difficult for students to grasp connections between related quantities. While an unjustified proliferation of units is undesirable, it is clear that an alternative, derived, time descriptor is in order. In order to obtain one with the widest possible application, we may consider the set of all significant durations: from cosmological time to the shortest which is physically possible. Now, as others have done for a t least
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ULTRASONIC METHOOS
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Figure 2. A prscale tor fast reaction methods. parts of the range,',2 we place every member of the set in an open-ended scale of decadic logarithms of times expressed in, say, seconds. Figure 1shows some members of the set. We see two points of interest: 1) For very large times, values are less well-defined and may depend on the method used to measure them. 2) The regions of most interest to chemists, and many other scientists, contain negative values (and cover a wider span than that allotted to geologists).
' Caldin, E. F. "Fast Reactions in Solution": Wiley: New York. 1964. ~
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'See almost any introductow earth science text. In a chemical context, a very u d e selection is mown in. Fried. V.; Hameka H. F.; Blukis. U "Pnysica. Chem stry"; Macrndlan: New York. 1977;p 696.
I'FAST' KINETICS 'SLOW' KINETICS] UNIVERSE
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TIME FOR FASTEST ELECTRON TRANSFER REACTION
HUMAN PULSE PERIOD
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Figure 1. A logarithmic time scale for all possible events and durations 880
Journal of Chemical Education
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FASTEST NUCLEAR PROCESSES
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These characteristics are strikingly similar to those of hydronium ion activity in aqueous solutions, for which we have an established3formalism in the well-known pH scale. Following that, we may define as a convenient expression for the description and discussion
of rapid events: the cycle time for radiation of frequency f Hz has p T = log(f). This expression has several advantages, in many scientific and pedagogic application^.^ I t provides a continuous scale for rapid events and is capable of providing as manv or as few sienificant figures as are aopropriate. Figure 2 shows the dei/nmtion ot'lhe limits of ~lst;ful"ess of fast reaction methods t ~ yrelating the time range3ofdit'ferent
techniques to the physical processes involved in each. The investigation and understanding of fast processes will surely continue to grow in volume of work and in importance, both within our discipline and without. The adoption of the p T scale, which is formally similar t o a scale now inuse in the experimental sciences, could aid us and our students in organizing this corpus of knowledge and may he useful t o research workers.
S#rensen,S.P. L. Biochem. 2.1909, 2L 131, 201; Compt. Rend. Trav. Lab. Carisberg 1909, 8. I . 4 A list of examples will be provided by the author upon wrilten request.
Volume 63 Number 8 August 1966
661
