CHEMISTRY · Multi-part · CBSE · Chemistry · Structure of Atom · Structure of Atom
Problem
Consider an electron bound to a proton. Treat the electron as being confined within a spherical region of radius r around the proton and assume that its minimum possible momentum uncertainty is governed by the confinement size.
(a) Express the electron’s kinetic energy in terms of r.
(b) Write the electrostatic potential energy of the electron–proton system for the same separation r.
(c) Obtain an expression for the total energy E(r) and determine the value of r for which E(r) is minimum.
(d) Show that the radius obtained in part (c) is of the same order as the Bohr radius (≈0.53A˚) for the ground state of the hydrogen atom and comment on the physical significance of this result.