Hydrogen is the simplest atom, with only one proton and one electron interacting with a Coulomb potential of If the electron were a classical charged particle, its orbit around the nucleus would decay until it came to rest at the nucleus. Since the electron is a quantum object, this doesn't happen. One way to estimate the minimum radius allowed for a quantum electron is by saturating the Heisenberg bound, which puts a lower limit on the radius of the electron's orbit and its momentum : Treat the hydrogen atom as a two-body problem where the mass of the proton is much greater than that of the electron
Estimate the minimum radius of the electron orbit
Details: is the charge of an electron, is the permittivity of free space, and is the reduced Planck's constant.