Chemical Education Today
Letters Units We May Never (or Rarely) See In 1991 the 19th Conférence Générale des Poids et Mesures (General Conference on Weights and Measures), the periodically held conference that adopts standards that become part of the SI system of units (������������������������������������������ le Système International d’Unités)�������� , recom� mended some new multiplicative prefixes to be used with the base units: zetta- (Z, 1021), yotta- (Y, 1024), zepto- (z, 10‒21), and yocto- (y, 10‒24). These prefixes are derived from the Latin word septum, meaning seven (because the power of 21 is represented by seven groups of three zeros), and the Greek octo, meaning eight (for a similar reason). With the definition of these prefixes, we have reached a point where some combinations of prefix and unit are highly unlikely to have any real significance. Consider the yoctocou� lomb, yC. It equals 1 × 10‒24 C. However, the fundamental unit of charge is 1.602 × 10‒19 C, or 160.2 zeptocoulombs. Because no chemically relevant charged particle can have less than the fundamental unit of charge, we will likely never have need to use the yoctocoulomb as a unit of absolute charge. (We may, however, be able to use it to represent a charge density, as in yoctocoulomb per cubic meter.) Similarly, a yoctomole may also be the limit as a worthwhile unit for quantity. A single atom or molecule is 1/(6.022 × 1023) of a mole, or 1.66 ymol. Any less than that is a chemically irrel� evant quantity, as we would be talking about less than a single atom or molecule. Again, the unit may be useful for express� ing very small values of amount density, but not for absolute amounts of, well, amount. Even some densities may be limited, however. For example, consider computer memory. A larger absolute capacity can always be achieved by using a larger disk, but the memory den� sity may be limited. Assuming that a single Si atom is 234 pm
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across, a square meter of Si has 1.83 × 1019 atoms on its surface. If we assume that at its limit, one byte of computer memory will reside on eight silicon atoms (using the standard that there are 8 bits in a byte), memory density has an absolute limit of 0.00000228 YBy/m2. It is likely that one byte will need more than eight silicon atoms, so yottabytes per square meter may never be used in any case. On this end of the scale, there are other combinations that are equally unlikely to be experienced. With an estimated age of 13.6 billion years, the estimated maximum volume of the universe is 8.92 × 1078 m3, or 8.92 × 106 Ym3. However, astrono� mers typically use light-years (ly) as a more convenient unit of distance (where 1 ly = 9.46 × 1015 m). Using this measuring stick, the universe’s volume is 1.054×10‒41 Yly3. It seems doubt� less, then, that the cubic yottalight-year will become a popular unit. Similarly, with a lifetime of 4.29 × 1017 s, any unit beyond an exasecond (1018 s; 1 es) like zettasecond (Zs) or yottasecond (Ys) will only be useful in the remotely distant future. It would make an interesting class exercise (and indeed, a good learning tool) to see what other combinations of extreme numerical prefix and unit would lack significance. Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2009/Nov/abs1270_2.html Full text (HTML and PDF) David W. Ball Department of Chemistry Cleveland State University Cleveland, OH 44115
[email protected] Journal of Chemical Education • Vol. 86 No. 11 November 2009 • www.JCE.DivCHED.org • © Division of Chemical Education
