This quantity can be seen as the scale at which quantum field theoretic effects become important, and it is typically derived as a factor in the shift of a certain quantity when photons scatter off electrons.
The Proca Lagrangian for a massive spin-1 particle contains a term proportional to the product of the square of the field and the inverse square of this quantity. This quantity is used to define the effective region  within which vacuum polarization corrects the Coulomb potential. For the hydrogen atom, this quantity, modulo a factor of 2 pi, is equal to the fine structure constant times the Bohr radius. This quantity can be seen as the scale at which quantum field theoretic effects become important, and it is typically derived as a factor in the shift of a certain quantity when photons scatter off electrons. The lower bound on the space in which a particle can be localized, for 10 points, identify this length scale, given by Planck's constant over the quantity mass times speed of light, derived from its namesake scattering effect.
The Proca Lagrangian for a massive spin-1 particle contains a term proportional to the product of the square of the field and the inverse square of this quantity.
Compton wavelength [prompt on partial answers]