PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure · Radiative transitions, external fields and collisions
Reading the Spectrum, Ch Radial functions, orbital size and Rydberg states
Problem
Hydrogen's Balmer α line, at 656.3nm, is emitted by atoms making the transitions 3s→2p, 3p→2s and 3d→2p. Because hydrogen's energy depends on n alone, the 3s and 2s levels are separated by exactly the same energy as 3p and 2p. Someone argues: "since the 3s→2s energy gap gives the same real, observed wavelength, the 3s→2s transition must also be occurring and contributing to the Balmer α line." Take the hydrogen energies as En=−13.606eV/n2 and hc=1239.84eVnm.
((a)) Compute the photon energy and wavelength corresponding to the 3s→2s energy gap.
((b)) Apply the dipole selection rule to decide whether 3s→2s is allowed.
((c)) Explain the error in this reasoning.