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 "fermi" (symbol: fm) is a unit of length used in physics to describe extremely small distances at the atomic and subatomic scale. One fermi is equal to 10^-15 meters or 0.000000000000001 meters. It is named after the Italian physicist Enrico Fermi, who made significant contributions to nuclear physics and particle physics.
The fermi is particularly useful for describing the sizes of atomic nuclei and the distances between particles within atomic nuclei. For example, the typical diameter of an atomic nucleus is on the order of a few femtometers (1 femtometer = 1 fm). It is also used in high-energy particle physics to describe the cross-sectional area of particle interactions.
In summary, the fermi is an essential unit of length for understanding the microscopic world of atoms, nuclei, and subatomic particles, where distances are incredibly small.