In the field of atomic and molecular physics, an "atomic unit of length" is a unit of measurement that is used to express distances at the atomic and molecular scale in a dimensionless way. It is part of a system of atomic units (a.u.) that simplifies calculations involving fundamental physical constants and properties of atoms and molecules.
The atomic unit of length (a.u. of length) is defined in terms of the Bohr radius (a₀), which is a fundamental constant in atomic physics. The Bohr radius is approximately 0.52917721067 angstroms (Å) or 5.2917721067 x 10^-11 meters (m).
In atomic units, the Bohr radius is set to exactly 1 a.u. of length. Therefore, when using atomic units, distances are expressed relative to the Bohr radius, and the value of 1 a.u. of length corresponds to the typical size scale of atomic and molecular structures.
The use of atomic units simplifies many quantum mechanical calculations and allows physicists and chemists to work with dimensionless quantities, making it easier to compare and analyze atomic and molecular properties.
A chain is a unit of length used in some older systems of measurement, particularly in surveying and land measurement. In the United States, one chain is equal to 66 feet or 22 yards. Internationally, it's defined as exactly 20.1168 meters.
Chains were historically used for measuring large plots of land and for surveying purposes, often in agriculture and real estate. However, the use of the chain as a standard unit of measurement has largely been replaced by the more modern and standardized metric and imperial systems, which use units like meters, feet, and yards.
The term "chain" comes from the practice of physically measuring land using a chain made of linked metal bars or wire. Each chain was typically 66 feet long, and surveyors would lay out chains end to end to measure distances across large areas. Today, modern surveying equipment such as electronic distance measuring devices (EDMs) and GPS technology have largely replaced the use of physical chains in land surveying.