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.
"Aln" is a unit of length that is used in some parts of Scandinavia, particularly in Sweden and Norway. The term "aln" is derived from the Old Norse word "alinn," which means "forearm." Historically, it was a common unit of measurement for cloth, textiles, and land.
The exact length of an aln could vary by region, but it was generally around 2 Swedish feet or approximately 59.4 centimeters (or about 23.4 inches) in Sweden. In Norway, an aln was somewhat longer, typically around 62.7 centimeters (about 24.7 inches).
The use of the aln as a standard unit of measurement has largely been replaced by the metric system in Scandinavia and most parts of the world, but it may still be referenced in historical or traditional contexts.