Solution to task 627 from Chertov´s for extramural stud

Solution to task 627 from Chertov´s for extramural stud

627. For an approximate estimate of the minimum energy of an electron in a hydrogen atom, it can be assumed that the uncertainty Δr of the radius r of the electron orbit and the uncertainty Δp of the momentum p of the electron in such an orbit are respectively related as follows: Δr ≈ r and Δp ≈ p. Using these connections, as well as the uncertainty relation, find the value of the radius of the electron orbit corresponding to the minimum electron energy in the hydrogen atom.