Determination of Atomic Weight
Modern atomic weights are calculated from measured values of atomic mass (for each nuclide) and isotopic composition. Highly accurate atomic masses are available for virtually all non-radioactive nuclides, but isotopic compositions are both harder to measure to high precision and more subject to variation between samples. For this reason, the atomic weights of the twenty-two mononuclidic elements are known to especially high accuracy – an uncertainty of only one part in 38 million in the case of fluorine, a precision which is greater than the current best value for the Avogadro constant (one part in 20 million).
| Isotope | Atomic mass | Abundance | |
|---|---|---|---|
| Standard | Range | ||
| 28Si | 27.976 926 532 46(194) | 92.2297(7)% | 92.21–92.25% |
| 29Si | 28.976 494 700(22) | 4.6832(5)% | 4.69–4.67% |
| 30Si | 29.973 770 171(32) | 3.0872(5)% | 3.10–3.08% |
The calculation is exemplified for silicon, whose atomic weight is especially important in metrology. Silicon exists in nature as a mixture of three isotopes: 28Si, 29Si and 30Si. The atomic masses of these nuclides are known to a precision of one part in 14 billion for 28Si and about one part in one billion for the others. However the range of natural abundance for the isotopes is such that the standard abundance can only be given to about ±0.001% (see table). The calculation is
- Ar(Si) = (27.97693 × 0.922297) + (28.97649 × 0.046832) + (29.97377 × 0.030872) = 28.0854
The estimation of the uncertainty is complicated, especially as the sample distribution is not necessarily symmetrical: the IUPAC standard atomic weights are quoted with estimated symmetrical uncertainties, and the value for silicon is 28.0855(3). The relative standard uncertainty in this value is 1×10–5 or 10 ppm. To further reflect this natural variability, in 2010, IUPAC made the decision to list the atomic weights of 10 elements as a range rather than a fixed number.
Read more about this topic: Relative Atomic Mass
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