Atomic sulfur 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^4

, which by the hole rule gives the same terms as

3p^2

^3P

^1D

^1S

, but with the fine structure of

^3P

inverted. The measured levels are

^3P_2=0\,\mathrm{cm^{-1}}

(ground),

^3P_1=396.055\,\mathrm{cm^{-1}}

^3P_0=573.640\,\mathrm{cm^{-1}}

^1D_2=9238.609\,\mathrm{cm^{-1}}

^1S_0=22179.954\,\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, and compare with oxygen's measured value of

1.14

for the analogous

2p^4

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

^3P

term: compute the two intervals

E_{J=1}-E_{J=0}

and

E_{J=2}-E_{J=1}

, their

\zeta_{LS}

estimates, and the ratio of interval magnitudes. Compare with oxygen's measured ratio of

2.30

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