### Atomic percent

**
**

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

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 (H_{2}O) is at.%_{H2O} = 2/3 x 100 ≈ 66.67%, while the *atomic ratio* of hydrogen to oxygen is *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

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

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 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****:****Yb**_{3}Al_{5}O_{12}is pure**Yb**_{3}Al_{5}O_{12}.

- The
*doping fraction*equals,

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

## See also

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