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 league is a unit of length that has been used historically in various cultures to measure distance, especially over land or at sea. The length of a league can vary from one region to another, and its value has changed over time.
In most cases, a league is roughly equivalent to 3 miles or approximately 4.828 kilometers. However, the exact value of a league has varied in different historical contexts and regions. For example:
Marine League: In nautical terms, a league is often considered to be equivalent to 3 nautical miles, which is approximately 5.556 kilometers. This is commonly used for measuring distances at sea.
Spanish League: In Spain and some Spanish-speaking countries, the league historically referred to the "legua," which was usually defined as 5,000 varas. The vara is an old Spanish unit of length, and the actual length of a Spanish league could vary by region. It was typically around 4.18 miles or 6.73 kilometers.
French League: In France, the league (or "lieue" in French) was historically used, and its length could vary from region to region. One French league is roughly equivalent to 4 kilometers (about 2.49 miles).
Historical Leagues: In various historical contexts and regions, leagues were used as a convenient way to measure distances over land. These leagues often had different values depending on local custom and geography.
It's important to note that the use of leagues as a unit of measurement has largely been replaced by the more standardized metric system in modern times. Therefore, leagues are not commonly used for precise measurements today but may still appear in historical documents, literature, or discussions of older measurements.