The doubly-ionised lithium ion has a single electron bound to a 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 Radial functions, orbital size and Rydberg states

Problem

The doubly-ionised lithium ion Li2+\mathrm{Li^{2+}} has a single electron bound to a nucleus of charge Z=3Z=3. Its 1s1s radial wave function has the same form as hydrogen's with a0a_0 replaced by a0/Za_0/Z in the exponent, R10=2(Z/a0)3/2e−Zr/a0R_{10}=2(Z/a_0)^{3/2}e^{-Zr/a_0}. ((a)) Write down the radial probability density P(r)=r2∣R10∣2P(r)=r^2|R_{10}|^2 for this ion. ((b)) Find the radius rmaxr_{\rm max} at which P(r)P(r) is a maximum, in nm.

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