An electron of momentum p is at a distance r from a stationary proton. the system has a kinetic energy k p2/2me and potential energy u ke2/r. its total energy is e k u. if the electron is bound to the proton to form a hydrogen atom, its average position is at the proton but the uncertainty in its position is approximately equal to the radius, r, of its orbit. the electron’s average momentum will be zero, but the uncertainty in its momentum will be given by the uncertainty principle. treat the atom as a one-dimensional system in the following: (a) estimate the uncertainty in the electron’s momentum in terms of r. (b) estimate the electron’s kinetic, potential, and total energies in terms of r. (c) the actual value of r is the one that minimizes the total energy, resulting in a stable atom. find that value of r and the resulting total energy. compare your answer with the predictions of the bohr theory.