Atomic ratio

{{short description|Measure of the ratio of atoms of one kind (i) to another kind (j)}} {{Refimprove|date=August 2015}}

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.<ref>{{cite book|title=McGraw-Hill Dictionary of Chemistry|date=27 January 2003|url=https://archive.org/details/dictionaryofchem00mcgr_1|url-access=registration|publisher=McGraw-Hill|isbn=0-07-141046-5|pages=[https://archive.org/details/dictionaryofchem00mcgr_1/page/31 31]|ref=1}}</ref> The molecular equivalents of these concepts are the '''molar fraction''', or '''molar percent'''.

==Atoms== Mathematically, the ''atomic percent'' is

:<math> \mathrm{atomic \ percent} \ (\mathrm{i}) = \frac{N_\mathrm{i}}{N_\mathrm{tot}} \times 100 \ </math> % where ''N''_i are the number of atoms of interest and ''N''_tot are the total number of atoms, while the ''atomic ratio'' is :<math> \mathrm{atomic \ ratio} \ (\mathrm{i:j}) = \mathrm{atomic \ percent} \ (\mathrm{i}) : \mathrm{atomic \ percent} \ (\mathrm{j}) \ .</math>

For example, the ''atomic percent'' of hydrogen in water (H₂O) is {{nowrap|at.%_H₂O {{=}} 2/3 x 100 ≈ 66.67%}}, while the ''atomic ratio'' of hydrogen to oxygen is {{nowrap|''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 :<math> \mathrm{isotopic \ abundance} \ (\mathrm{i}) = \frac{N_\mathrm{i}}{N_\mathrm{tot}} \ ,</math> 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 :<math> \mathrm{isotopic \ ratio} \ (\mathrm{i:j}) = \mathrm{isotopic \ percent} \ (\mathrm{i}) : \mathrm{isotopic \ percent} \ (\mathrm{j}) \ .</math>

For example, the ''isotopic ratio'' of deuterium (D) to hydrogen (H) in heavy water is roughly {{nowrap|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''' '''<big>:</big>''' '''Y'''₃Al₅O₁₂ is pure '''Yb'''₃Al₅O₁₂. *The ''doping fraction'' equals,

::::::::<math>\mathrm \frac{N_\mathrm{atoms \ of \ dopant}}{N_\mathrm{atoms \ of \ solution \ which \ can \ be \ substituted \ with \ the \ dopant}}</math>

==See also== *Table of concentration measures

==References== {{Reflist}}

Category:Physical chemistry