Helium's first and second ionisation energies are and

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · Many-electron atoms and the periodic table · Many-electron atoms and the periodic table

Deriving the Spectrum, Ch Helium: exchange and the variational method

Problem

Helium's first and second ionisation energies are 24.587 eV24.587\,\mathrm{eV} and 54.418 eV54.418\,\mathrm{eV}, and the ion He+\mathrm{He}^+ is exactly hydrogenic with Z=2Z = 2. The measured ground-state energy is −79.005 eV-79.005\,\mathrm{eV}; take Eh=27.211 eVE_{\rm h} = 27.211\,\mathrm{eV}. ((a)) Find the energies, above the neutral ground state, of He+(n=2)\mathrm{He}^+(n=2) plus a free electron at rest and of He+(n=3)\mathrm{He}^+(n=3) plus a free electron at rest. ((b)) Estimate the energy of the doubly excited configuration 2s22s^2 by treating both electrons as independent hydrogenic n=2n=2 electrons with Z=2Z = 2. How far above the ground state does this put it, and does it lie between the first ionisation limit and He+(n=2)\mathrm{He}^+(n=2)? Would restoring the repulsion move it up or down? ((c)) The 2s2p 1P2s2p\,{}^1P resonance at 60.15 eV60.15\,\mathrm{eV} autoionises. Find the kinetic energy of the ejected electron when it leaves He+\mathrm{He}^+ in 1s1s, and say why it cannot leave He+\mathrm{He}^+ in n=2n=2.

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