The Planck length, denoted as "ℓ," is a fundamental unit of length in the realm of quantum mechanics and theoretical physics. It is named after the physicist Max Planck, who made significant contributions to the field of quantum theory.
The Planck length is defined as:
ℓ = √(ħG / c³),
where:
When you calculate the Planck length using these constants, you get a value of approximately 1.616255 x 10⁻35 meters. This extremely tiny length scale is believed to be the smallest meaningful length that can exist in the universe, according to current physical theories.
The Planck length plays a crucial role in theories of quantum gravity, including string theory and loop quantum gravity, where it is considered a fundamental limit for the precision of measurements and the size of structures in the fabric of spacetime. At scales smaller than the Planck length, the classical notions of space and time break down, and a more complete theory of quantum gravity is expected to be necessary to describe the physics of such extreme conditions.
An "angstrom" (symbol: Å) is a unit of length that is commonly used in the field of nanotechnology, molecular biology, and atomic-scale physics and chemistry. It is named after the Swedish physicist Anders Jonas Ångström, who made significant contributions to the study of spectroscopy and the understanding of atomic and molecular structure.
One angstrom is equal to 0.1 nanometers (nm) or 1 × 10^-10 meters (m). In other words, it is a very small unit of length, often used to describe the size of atoms, molecules, and the wavelengths of electromagnetic radiation such as X-rays and gamma rays.
The angstrom is particularly useful when dealing with structures at the atomic and molecular scale, where measurements are often in the range of a few angstroms. For example, the diameter of a hydrogen atom is about 0.1 angstroms, and the bond length between two carbon atoms in a molecule like benzene is approximately 1.4 angstroms.