Bohr's model (Chapter 2) assigned its third orbit a single radius
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
Bohr's model (Chapter 2) assigned its third orbit a single radius 9a0, a single angular momentum of magnitude 3ℏ, and the energy −13.6eV/32. In the wave treatment of this chapter the same label n=3 arises from n=nr+l+1 with nr≥0, and a state labelled by l has orbital angular momentum of magnitude L=l(l+1)ℏ (the l(l+1)ℏ2/2mer2 term of the effective radial potential built in Chapter 11). The proton is treated as a fixed point charge.
((a)) Give the energy of the n=3 level in eV from the levels derived in this chapter.
((b)) Count the independent states at this energy, ignoring spin and then counting spin.
((c)) Give the magnitude of L, in units of ℏ, for each allowed l at this energy, smallest first, to three significant figures where it is not exact.