Atomic units: Difference between revisions
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</ref> In the a.u. system any four of the five quantities charge ''e'', mass ''m<sub>e</sub>'', action ℏ, length ''a<sub>0</sub>'', and energy ''E<sub>h</sub>'' may be taken as base quantities, and other quantities are derived. In particular, ''time'' is a derived quantity, ℏ''/E<sub>h</sub>''. Because ''length'' is a basic unit, the [[speed of light]] is a measured quantity in a.u., ''c=1/α'' where the [[fine structure constant]] ''α'' = 1/137.035 999 11(46). | </ref> In the a.u. system any four of the five quantities charge ''e'', mass ''m<sub>e</sub>'', action ℏ, length ''a<sub>0</sub>'', and energy ''E<sub>h</sub>'' may be taken as base quantities, and other quantities are derived. In particular, ''time'' is a derived quantity, ℏ''/E<sub>h</sub>''. Because ''length'' is a basic unit, the [[speed of light]] is a measured quantity in a.u., ''c=1/α'' where the [[fine structure constant]] ''α'' = 1/137.035 999 11(46). | ||
== | ==Units== | ||
{| class="wikitable" style="margin:1em auto 1em auto" | {| class="wikitable" style="margin:1em auto 1em auto" | ||
! colspan="4" | | ! colspan="4" |Basic atomic units <ref name=Taylor/> | ||
|- | |- | ||
| Line 38: | Line 38: | ||
|[[mass]] | |[[mass]] | ||
|9.109 3826(16) × 10<sup>−31</sup> kg | |9.109 3826(16) × 10<sup>−31</sup> kg | ||
|- | |- | ||
|Reduced [[Planck constant]] | |Reduced [[Planck constant]] | ||
| Line 54: | Line 49: | ||
|4.359 744 17(75) × 10<sup>−18</sup> J | |4.359 744 17(75) × 10<sup>−18</sup> J | ||
|- | |- | ||
|} | |||
{| class="wikitable" style="margin:1em auto 1em auto" | |||
! colspan="4" |Derived atomic units <ref name=Taylor/> | |||
|- | |||
|'''Name''' | |||
|'''Symbol''' | |||
|'''Quantity''' | |||
|'''Value in [[International System of Units|SI units]]''' | |||
|- | |- | ||
|[[a.u. velocity]] | |[[a.u. velocity]] | ||
| Line 59: | Line 62: | ||
|[[velocity]] | |[[velocity]] | ||
|2.187 691 2633(73) × 10<sup>6</sup> m/s | |2.187 691 2633(73) × 10<sup>6</sup> m/s | ||
|- | |||
|[[Reduced period of first Bohr orbit]] | |||
|'''ℏ/E<sub>h</sub>''' | |||
|[[time]] | |||
|2.418 884 326 505(16) × 10<sup>−17</sup> s | |||
|- | |- | ||
|} | |} | ||
Revision as of 14:11, 10 March 2011
The atomic units, abbreviated a.u. is a set of units used in atomic calculations.[1][2] In the a.u. system any four of the five quantities charge e, mass me, action ℏ, length a0, and energy Eh may be taken as base quantities, and other quantities are derived. In particular, time is a derived quantity, ℏ/Eh. Because length is a basic unit, the speed of light is a measured quantity in a.u., c=1/α where the fine structure constant α = 1/137.035 999 11(46).
Units
| Basic atomic units [2] | |||
|---|---|---|---|
| Name | Symbol | Quantity | Value in SI units |
| elementary charge | e | charge | 1.602 176 53(14) × 10−19 C |
| Bohr radius (bohr) | a0 | length | 0.529 177 2108(18) × 10−10 m |
| electron mass | me | mass | 9.109 3826(16) × 10−31 kg |
| Reduced Planck constant | ℏ | action | 1.054 571 68(18) × 10−34 Js |
| Hartree energy (hartree) | Eh | energy | 4.359 744 17(75) × 10−18 J |
| Derived atomic units [2] | |||
|---|---|---|---|
| Name | Symbol | Quantity | Value in SI units |
| a.u. velocity | vB≡αc | velocity | 2.187 691 2633(73) × 106 m/s |
| Reduced period of first Bohr orbit | ℏ/Eh | time | 2.418 884 326 505(16) × 10−17 s |
Here, c = speed of light and α = fine structure constant.
Notes
- ↑ For an introduction, see Gordon W. F. Drake (2006). “§1.2 Atomic units”, Springer handbook of atomic, molecular, and optical physics, Volume 1, 2nd ed. Springer, p. 6. ISBN 038720802X.
- ↑ 2.0 2.1 2.2 Tabulated values from Barry N. Taylor (2008). International System of Units (SI), Revised 2008 ed. DIANE Publishing, Table 7, p.34. ISBN 1437915582.