Question

Consider the hydrogen atom to be a proton embedded in a cavity of radius a₀ (Bohr's radius) whose charge is neutralised by the addition of an electron to the cavity in vacuum, infinitely slowly. Estimate the average total energy of an electron in its ground state in a hydrogen atom as the work done in the above neutralisation process. Also, if the magnitude of the average kinetic energy is half the magnitude of the average potential energy, find the average potential energy. 

Answer 1

Work done in bringing an electron infinitely slowly from infinitely to the proton of radius a₀

Total energy (TE)  = Potential energy (PE) + Kinetic energy (KE) The magnitude of KE is half the magnitude of PE

PE is -ve and KE is +ve.

Let PE is equal to -x. Therefore KE is equal to x/2