Atomic ratio

 ( Physical Chemistry ) 

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

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Atoms Mathematically, the atomic percent is

$\backslash mathrm\{atomic\; \backslash \; percent\}\; \backslash \; (\backslash mathrm\{i\})\; =\; \backslash frac\{N\_\backslash mathrm\{i\}\}\{N\_\backslash mathrm\{tot\}\}\; \backslash times\; 100\; \backslash$ %

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

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

For example, the atomic percent of hydrogen in water (H₂O) is , while the atomic ratio of hydrogen to oxygen is .

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

$\backslash mathrm\{isotopic\; \backslash \; abundance\}\; \backslash \; (\backslash mathrm\{i\})\; =\; \backslash frac\{N\_\backslash mathrm\{i\}\}\{N\_\backslash mathrm\{tot\}\}\; \backslash \; ,$

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

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

For example, the isotopic ratio of deuterium (D) to hydrogen (H) in heavy water is roughly (corresponding to an isotopic abundance of 0.00014%).

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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 Ytterbium : Y₃Al₅O₁₂ is pure Yb₃Al₅O₁₂.
• The doping fraction equals,

:::::::$\backslash mathrm\; \backslash frac\{N\_\backslash mathrm\{atoms\; \backslash \; of\; \backslash \; dopant\}\}\{N\_\backslash mathrm\{atoms\; \backslash \; of\; \backslash \; solution\; \backslash \; which\; \backslash \; can\; \backslash \; be\; \backslash \; substituted\; \backslash \; with\; \backslash \; the\; \backslash \; dopant\}\}$

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See also

• Table of concentration measures

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