Silicon's ground configuration is

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

, the same electron count as carbon's

2p^2

. Its lowest term

^3P

is split into levels

^3P_0

^3P_1

^3P_2

0

77.1

and

223.2\,\mathrm{cm^{-1}}

, and the next term,

^1D_2

, lies at

6298.9\,\mathrm{cm^{-1}}

(measured from

^3P_0

). ((a)) Compare the spread of the

^3P

term with its separation from

^1D_2

and say which of the residual electron repulsion and the spin-orbit interaction is the larger for silicon's

3p^2

electrons, and name the quantum numbers that are good as a result. ((b)) Within an LS-coupled term the Lande factor of a level is

g_J = 1 + (g_s - 1)\dfrac{J(J+1) + S(S+1) - L(L+1)}{2J(J+1)}

, with

g_s = 2

. Using

L = 1

S = 1

for silicon's

^3P

term, find

g_J

for the

^3P_1

and

^3P_2

levels. ((c)) Explain why this formula cannot be evaluated for the

^3P_0

level, and give, with a one-line physical argument (not the formula), the value of that level's magnetic moment.

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