A megaparsec (Mpc) is a unit of measurement used in astrophysics and cosmology to express vast distances on cosmic scales. It is equal to one million parsecs. A parsec (pc) is a unit of length used in astronomy to describe astronomical distances, and it is approximately equal to 3.09 × 10^16 meters or 3.09 × 10^13 kilometers.
So, a megaparsec is equivalent to:
1 megaparsec (Mpc) = 1,000,000 parsecs (pc)
Megaparsecs are typically used to describe distances between galaxies and galaxy clusters in the universe. Since astronomical distances are extremely large, the parsec and its multiples, such as the megaparsec, provide a convenient way to express these distances without dealing with unwieldy numbers of kilometers or light-years. Cosmologists often use megaparsecs when discussing the large-scale structure of the universe, the size of galaxy clusters, and the expansion of the cosmos.
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.