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 "hand" is a unit of measurement commonly used in the context of measuring the height of horses. In the United States and some other English-speaking countries, a hand is defined as exactly 4 inches or 10.16 centimeters.
Horses are typically measured in hands from the ground to the highest point of their withers (the ridge between the shoulder blades). This measurement is a convenient way to describe a horse's height without relying on feet and inches or meters.
For example, a horse that measures 15.2 hands is 15 hands and 2 inches tall. Horses can vary in height, and the hand system provides a standardized way to communicate a horse's size, which is particularly important in horse racing, equestrian sports, and the horse industry in general.