Length Scale - Examples

Examples

• The atomic length scale is meters and is given by the size of hydrogen atom (i.e., the Bohr radius (approximately 53 pm)) which is set by the electron's Compton wavelength times the fine-structure constant: .

• The length scale for the strong interactions (or the one derived from QCD through dimensional transmutation) is around meters (or in natural units 100 MeV), and the "radii" of strongly interacting particles (such as the proton) are roughly comparable. This length scale is determined by the range of the Yukawa potential. The lifetimes of strongly interacting particles, such as the rho meson, are given by this length scale divided by the speed of light: seconds. The masses of strongly interacting particles are several times the associated energy scale (500 MeV to 3000 MeV).

• The electroweak length scale is shorter, roughly meters and is set by the rest mass of the weak vector bosons which is roughly 100 GeV. This length scale would be the distance where a Yukawa force is mediated by the weak vector bosons. The magnitude of weak length scale was initially inferred by the Fermi constant measured by neutron and muon decay.

• The Planck length (Planck scale) is much shorter yet - about meters ( GeV in natural units), and is derived from Newton's gravitational constant which has units of length squared.

• The Mesoscopic scale is the length at which quantum mechanical behaviours in liquids or solid can be described by macroscopic concepts.