Atomic ratio

Mathematically, the atomic percent is

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

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

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

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 A_H:O = 2:1.

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

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

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

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

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%).

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,

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

• Table of concentration measures