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

\( {\mathrm {atomic\ percent}}\ ({\mathrm {i}})={\frac {N_{{\mathrm {i}}}}{N_{{\mathrm {tot}}}}}\times 100\ \) %

where Ni are the number of atoms of interest and Ntot are the total number of atoms, while the atomic ratio is

\( {\mathrm {atomic\ ratio}}\ ({\mathrm {i:j}})={\mathrm {atomic\ percent}}\ ({\mathrm {i}}):{\mathrm {atomic\ percent}}\ ({\mathrm {j}})\ \) .

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 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

\( {\mathrm {isotopic\ abundance}}\ ({\mathrm {i}})={\frac {N_{{\mathrm {i}}}}{N_{{\mathrm {tot}}}}}\ , \)

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

\( {\mathrm {isotopic\ ratio}}\ ({\mathrm {i:j}})={\mathrm {isotopic\ percent}}\ ({\mathrm {i}}):{\mathrm {isotopic\ percent}}\ ({\mathrm {j}})\ . \)

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,

\( {\mathrm {\frac {N_{{\mathrm {atoms\ of\ dopant}}}}{N_{{\mathrm {atoms\ of\ solution\ which\ can\ be\ substituted\ with\ the\ dopant}}}}}} \)