Along the isoelectronic sequence with electrons

PHYSICS · Subjective · 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 The central field and the periodic table

Problem

Along the isoelectronic sequence with

19

electrons, the

3d

4s

gap (with

3d

above

4s

) is measured to shrink as the ionic charge rises:

\mathrm{K}

(neutral,

Z=19

4s

is the ground state,

3d

lies

2.67\,\mathrm{eV}

above it.

\mathrm{Ca}^+

(

Z=20

4s

is still the ground state, but

3d

lies only

1.70\,\mathrm{eV}

above it.

\mathrm{Sc}^{2+}

(

Z=21

3d

has become the ground state. Predict, with a reason based on core penetration, which orbital (

4s

3d

) is the ground state of

\mathrm{Ti}^{3+}

(

Z=22

), the next member of this

19

-electron sequence, and give its predicted ground configuration in the form

[\mathrm{Ar}]\ldots

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