The valence electron of potassium in its ground state has an effective principal…

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

Reading the Spectrum, Ch Atoms in an electric field: the Stark effect and polarizability

Problem

The valence electron of potassium in its ground state has an effective principal quantum number n∗=1.77n^* = 1.77 (from its quantum defect) and orbital quantum number l=0l = 0, so its mean radius is ⟨r⟩=1.5(n∗)2a0\langle r\rangle = 1.5(n^*)^2a_0. ((a)) Model the potassium atom as a uniformly charged sphere of radius ⟨r⟩\langle r\rangle and use α/4πϵ0=R3\alpha/4\pi\epsilon_0 = R^3 to estimate its polarizability, giving the value in units of a03a_0^3 and, separately, its full magnitude in m3\mathrm{m^3}. ((b)) The measured value is α/4πϵ0=43.4×10−30 m3\alpha/4\pi\epsilon_0 = 43.4\times10^{-30}\,\mathrm{m^3} (293 a03293\,a_0^3). By what factor does the estimate differ from the measured value, and is it too high or too low?

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