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 fathom is a unit of length used to measure the depth of water or the depth of objects underwater. In the international nautical mile system, one fathom is equal to exactly 1.8288 meters or approximately 6 feet. However, in the United States, the customary value for a fathom is often rounded to 6 feet.
Fathoms are commonly used in navigation, maritime activities, and underwater exploration to measure the depth of bodies of water, the draft of ships, and the depth of diving. Sailors, fishermen, and divers often use this unit to assess water depths.