Atomic ratio

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

Atoms[edit]

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[edit]

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[edit]

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}}

See also[edit]