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Theatomic ratio is a measure of theratio of atoms of one kind (i) to another kind (j). A closely related concept is theatomic percent (orat.%), which gives the percentage of one kind of atom relative to the total number of atoms.^[1] Themolecular equivalents of these concepts are themolar fraction, ormolar percent.

Mathematically, theatomic percent is

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

whereN_i are the number of atoms of interest andN_tot are the total number of atoms, while theatomic ratio is

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

For example, theatomic percent ofhydrogen inwater (H₂O) isat.%_H2O = 2/3 x 100 ≈ 66.67%, while theatomic ratio of hydrogen to oxygen isA_H:O = 2:1.

Another application is inradiochemistry, where this may refer toisotopic ratios orisotopic abundances. Mathematically, theisotopic abundance is

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

whereN_i are the number of atoms of the isotope of interest andN_tot is the total number of atoms, while theatomic ratio is

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

For example, theisotopic ratio ofdeuterium (D) tohydrogen (H) inheavy water is roughlyD:H = 1:7000 (corresponding to anisotopic abundance of 0.00014%).

Inlaser physics however, theatomic ratio may refer to thedoping ratioor thedoping fraction.

• For example, theoretically, a 100%doping ratio ofYb:Y₃Al₅O₁₂ is pureYb₃Al₅O₁₂.
• Thedoping fraction equals,

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

• Table of concentration measures

• Physical chemistry

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