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Atoms

Mathematically, the atomic percent is

a t o m i c   p e r c e n t   ( i ) = N i N t o t × 100   {\displaystyle \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

a t o m i c   r a t i o   ( i : j ) = a t o m i c   p e r c e n t   ( i ) : a t o m i c   p e r c e n t   ( j )   . {\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 AH:O = 2:1.

Isotopes

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

i s o t o p i c   a b u n d a n c e   ( i ) = N i N t o t   , {\displaystyle \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

i s o t o p i c   r a t i o   ( i : j ) = i s o t o p i c   p e r c e n t   ( i ) : i s o t o p i c   p e r c e n t   ( j )   . {\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%).

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

N a t o m s   o f   d o p a n t N a t o m s   o f   s o l u t i o n   w h i c h   c a n   b e   s u b s t i t u t e d   w i t h   t h e   d o p a n t {\displaystyle \mathrm {\frac {N_{\mathrm {atoms\ of\ dopant} }}{N_{\mathrm {atoms\ of\ solution\ which\ can\ be\ substituted\ with\ the\ dopant} }}} }

See also

• Table of concentration measures

References

1. McGraw-Hill Dictionary of Chemistry. McGraw-Hill. 27 January 2003. pp. 31. ISBN 0-07-141046-5. 0-07-141046-5 ↩