A beam of a one-electron ion (a single electron bound to a bare nucleus of charge , )…

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure · One-electron atoms and the origins of atomic structure

Reading the Spectrum, Ch The Coulomb spectrum from wave mechanics: quantum numbers and degeneracy

Problem

A beam of a one-electron ion (a single electron bound to a bare nucleus of charge ZeZe, Z≤10Z\le 10) emits a line identified as its 2p→1s2p\to1s transition at a vacuum wavelength of λ=7.594 nm\lambda = 7.594\,\mathrm{nm}. Treat the nucleus as effectively infinitely heavy, so that RM≈R∞=109737.32 cm−1R_M \approx R_\infty = 109737.32\,\mathrm{cm^{-1}}. ((a)) Use the hydrogenic scaling En=−Z2hcR∞/n2E_n = -Z^2hcR_\infty/n^2 to find ZZ, and hence identify the ion. ((b)) State the Bohr radius of this ion's ground state and its ionisation energy in eV.

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