Atomic germanium has ground configuration

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 Many-electron terms, levels and Hund's rules

Problem

4p^2

, in the same column as carbon and silicon, giving terms

^3P

^1D

^1S

. The measured levels are

^3P_0=0\,\mathrm{cm^{-1}}

^3P_1=557.13\,\mathrm{cm^{-1}}

^3P_2=1409.96\,\mathrm{cm^{-1}}

^1D_2=7125.35\,\mathrm{cm^{-1}}

^1S_0=16367.19\,\mathrm{cm^{-1}}

. ((a)) Compute the

(2J+1)

-weighted centroid of the

^3P

term. ((b)) Test the Slater-integral prediction

\dfrac{E(^1S)-E(^1D)}{E(^1D)-E(^3P)}=\dfrac32

using the centroid. ((c)) Test the Lande interval rule on the

^3P

term: compute the two intervals, their ratio, and the two

\zeta_{LS}

estimates. ((d)) Compare your results in (b) and (c) with carbon's measured

1.13

and

1.65

, and explain why a good Slater-integral ratio does not guarantee a good interval rule.

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