Atomic silicon 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

3p^2

, giving the same terms as carbon's

2p^2

^3P

^1D

^1S

. The measured levels are

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

^3P_1=77.115\,\mathrm{cm^{-1}}

^3P_2=223.157\,\mathrm{cm^{-1}}

^1D_2=6298.850\,\mathrm{cm^{-1}}

^1S_0=15394.370\,\mathrm{cm^{-1}}

. ((a)) Compute the

(2J+1)

-weighted centroid of the

^3P

term. ((b)) The single-configuration Slater-integral treatment of

p^2

predicts

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

. Test this using the centroid from (a) in place of a single

^3P

energy, and compare with carbon's measured value of

1.13

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

^3P

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

\zeta_{LS}

they give. State whether the term is normal or inverted. ((d)) Comment briefly on why silicon's Slater-integral ratio sits closer to

3/2

than carbon's does, given that both deviations are blamed on configuration interaction with same-parity configurations.

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