The Balmer-beta line of atomic hydrogen is the transition
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure
Reading the Spectrum, Ch The Coulomb spectrum from wave mechanics: quantum numbers and degeneracy
Problem
The Balmer-beta line of atomic hydrogen is the transition n=4→n=2. Use the Rydberg constant for hydrogen, RH=109677.58cm−1 (already built with the electron-proton reduced mass), and the level energies En=−hcRH/n2. Assume the atom is at rest and ignore any splitting within a level.
((a)) Calculate the wavenumber ν~ and the vacuum wavelength λ of the Balmer-beta line. Compare your λ with the measured vacuum wavelength, 486.27nm.
((b)) Hydrogen's 2s and 2p levels, of the same n, share their energy to within 4.5×10−5eV. Sodium's 3s and 3p levels, also of the same n, differ by 2.10eV. Calculate the ratio of these two energy gaps, and use its size to say what it shows about the potential felt by sodium's outer electron, compared with the pure Coulomb potential felt by hydrogen's single electron.