Physics:Atomic ratio
The atomic ratio is a measure of the ratio of atoms of one kind (i) to another kind (j). A closely related concept is the atomic percent (or at.%), which gives the percentage of one kind of atom relative to the total number of atoms.[1] The molecular equivalents of these concepts are the molar fraction, or molar percent.
Atoms
Mathematically, the atomic percent is
- [math]\displaystyle{ \mathrm{atomic \ percent} \ (\mathrm{i}) = \frac{N_\mathrm{i}}{N_\mathrm{tot}} \times 100 \ }[/math] %
where Ni are the number of atoms of interest and Ntot are the total number of atoms, while the atomic ratio is
- [math]\displaystyle{ \mathrm{atomic \ ratio} \ (\mathrm{i:j}) = \mathrm{atomic \ percent} \ (\mathrm{i}) : \mathrm{atomic \ percent} \ (\mathrm{j}) \ . }[/math]
For example, the atomic percent of hydrogen in water (H2O) is at.%H2O = 2/3 x 100 ≈ 66.67%, while the atomic ratio of hydrogen to oxygen is AH:O = 2:1.
Isotopes
Another application is in radiochemistry, where this may refer to isotopic ratios or isotopic abundances. Mathematically, the isotopic abundance is
- [math]\displaystyle{ \mathrm{isotopic \ abundance} \ (\mathrm{i}) = \frac{N_\mathrm{i}}{N_\mathrm{tot}} \ , }[/math]
where Ni are the number of atoms of the isotope of interest and Ntot is the total number of atoms, while the atomic ratio is
- [math]\displaystyle{ \mathrm{isotopic \ ratio} \ (\mathrm{i:j}) = \mathrm{isotopic \ percent} \ (\mathrm{i}) : \mathrm{isotopic \ percent} \ (\mathrm{j}) \ . }[/math]
For example, the isotopic ratio of deuterium (D) to hydrogen (H) in heavy water is roughly D:H = 1:7000 (corresponding to an isotopic abundance of 0.00014%).
Doping in laser physics
In laser physics however, the atomic ratio may refer to the doping ratio or the doping fraction.
- For example, theoretically, a 100% doping ratio of Yb : Y3Al5O12 is pure Yb3Al5O12.
- The doping fraction equals,
- [math]\displaystyle{ \mathrm \frac{N_\mathrm{atoms \ of \ dopant}}{N_\mathrm{atoms \ of \ solution \ which \ can \ be \ substituted \ with \ the \ dopant}} }[/math]
See also
References
- ↑ McGraw-Hill Dictionary of Chemistry. McGraw-Hill. 27 January 2003. pp. 31. ISBN 0-07-141046-5. https://archive.org/details/dictionaryofchem00mcgr_1.
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