Physics:Atomic ratio

Short description: Measure of the ratio of atoms of one kind (i) to another kind (j)

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. The molecular equivalents of these concepts are the molar fraction, or molar percent.

Atoms

Mathematically, the atomic percent is

$\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{c}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}(\mathrm{i})=\frac{N_{\mathrm{i}}}{N_{\mathrm{t}\mathrm{o}\mathrm{t}}}\times 100$ %

where N_i are the number of atoms of interest and N_tot are the total number of atoms, while the atomic ratio is

$\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{c}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}(\mathrm{i}\mathrm{:}\mathrm{j})=\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{c}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}(\mathrm{i}):\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{c}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}(\mathrm{j}).$

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 A_H:O = 2:1.

Isotopes

Another application is in radiochemistry, where this may refer to isotopic ratios or isotopic abundances. Mathematically, the isotopic abundance is

$\mathrm{i}\mathrm{s}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{b}\mathrm{u}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}(\mathrm{i})=\frac{N_{\mathrm{i}}}{N_{\mathrm{t}\mathrm{o}\mathrm{t}}},$

where N_i are the number of atoms of the isotope of interest and N_tot is the total number of atoms, while the atomic ratio is

$\mathrm{i}\mathrm{s}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}(\mathrm{i}\mathrm{:}\mathrm{j})=\mathrm{i}\mathrm{s}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}(\mathrm{i}):\mathrm{i}\mathrm{s}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{p}\mathrm{i}\mathrm{c}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}(\mathrm{j}).$

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,

$\frac{N_{\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{d}\mathrm{o}\mathrm{p}\mathrm{a}\mathrm{n}\mathrm{t}}}{N_{\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{w}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{h}\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{d}\mathrm{o}\mathrm{p}\mathrm{a}\mathrm{n}\mathrm{t}}}$

See also

• Table of concentration measures