Consider the hydrogen atom to be a proton embedded in a cavity of radius (Bohr's radius)
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Modern Physics · Modern Physics
Problem
Consider the hydrogen atom to be a proton embedded in a cavity of radius a0 (Bohr's radius), whose charge is neutralized by the addition of an electron to the cavity in vacuum, infinitely slowly.
(a) Estimate the average of total energy of an electron in its ground state in a hydrogen atom as the work done in the above neutralization process. Also, if the magnitude of the average kinetic energy is half the magnitude of the average potential energy, find the average potential energy. (IIT 1996)
(b) Also derive the wavelength of the electron when it is a0 from the proton. How does this compare with the wavelength of an electron in the ground state Bohr's orbit?