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 However, the use of the chain as a standard unit of measurement has largely been replaced by the more modern and standardized metric and imperial systems, which use units like meters, feet, and yards.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.
The Bohr radius, often denoted as "a₀," is a fundamental physical constant in quantum mechanics and atomic physics. It is named after the Danish physicist Niels Bohr, who made significant contributions to our understanding of atomic structure.
The Bohr radius represents the average distance between the nucleus and the electron in the lowest energy state (ground state) of a hydrogen atom, or a hydrogen-like ion with a single electron (e.g., helium ion with only one electron remaining). It is a key parameter in the Bohr model of the hydrogen atom.
The Bohr radius is defined as:
a₀ = (4πε₀ħ²) / (me²),
where:
When you calculate the Bohr radius using these constants, you get a value of approximately 5.29177210903 x 10⁻¹¹ meters, or about 0.5292 angstroms (Å).
The Bohr radius is a critical parameter in understanding the structure of atoms, particularly hydrogen-like atoms. It provides a basic scale for the size of atomic orbitals and helps in describing the energy levels of electrons in these atoms.