1. The problem statement, all variables and given/known data An electron in a hydrogen atom does not fall to the proton because of quantum motion (which may be accounted for by the Heisenberg uncertainty relation for an electron localized in the volume with size r). This is true because the absolute value of the Coulomb potential energy goes to minus infinity with decreasing distance to the center r relatively slowly, like -1/r. Is such an ''atom'' stable for any potential behaving as -1/rs? If not, find the range of values of s at which the ''atom'' is stable, so that ''the electron'' does not fall to center. 2. Relevant equations 3. The attempt at a solution Based on Bertrand’s Theorem, the closed and stable motion will be that s equals to -2,1,2. However, I don't know how to solve this problem by uncertainty principle. Moreover, I can't figure out why electron not falling to the proton is related to quantum motion. Can someone give me some hints or correct my opinion??? Thanks!