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.
A "handbreadth" is a unit of length that is approximately equal to the width of an adult human hand, excluding the fingers. It is often used in various historical and cultural contexts as a convenient way to estimate small lengths or distances. The actual measurement of a handbreadth can vary somewhat depending on the size of an individual's hand, but it is typically around 3 to 4 inches (about 7.6 to 10.2 centimeters).
In some historical systems of measurement, particularly in the ancient Near East and the Bible, the handbreadth was used as a standardized unit for measuring length. It was one of the smaller units within a larger system of measurement, often used for small-scale applications like measuring cloth, the dimensions of objects, or architectural details.
While the handbreadth is not a commonly used unit of measurement in modern times, it remains a useful and intuitive way to approximate small lengths informally, especially when a quick estimate is needed.