Quantum Mechanics in Three Dimensions — David J. Griffiths
Physics — Quantum Mechanics · hydrogenic_atoms
Problem
A hydrogenic atom consists of a single electron orbiting a nucleus with Z protons. (Z=1 would be hydrogen itself, Z=2 is ionized helium, Z=3 is doubly ionized lithium, and so on.) Determine the Bohr energies En(Z), the binding energy E1(Z), the Bohr radius a(Z), and the Rydberg constant R(Z) for a hydrogenic atom. (Express your answers as appropriate multiples of the hydrogen values.) Where in the electromagnetic spectrum would the Lyman series fall, for Z=2 and Z=3? Hint: There's nothing much to calculate here—in the potential (Equation 4.52) e2→Ze2, so all you have to do is make the same substitution in all the final results.