PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure
Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch The hydrogen atom
Problem
Positronium is an electron bound to a positron, a particle of the same mass and of charge +e. The Coulomb potential energy is the same −e2/4πϵ0r as in hydrogen, but because the two masses are equal, the mass entering the radial equation is the reduced mass, whose value is quoted as mr=me/2. In this chapter's scaling, replacing me by a mass m multiplies the energy scale by m/me. Take 13.6 eV as the hydrogen energy scale and hc=1240 eV nm. Estimate, to two significant figures and ignoring annihilation and every splitting beyond this treatment:
((a)) the ground-state energy of positronium, in eV;
((b)) the wavelength of its n=2→n=1 line, in nm.