Sodium's principal-series levels lie

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

Sodium's principal-series levels lie, above the ground state, at

30\,270.7\,\mathrm{cm^{-1}}

(

4p

35\,042.0\,\mathrm{cm^{-1}}

(

5p

) and

37\,297.2\,\mathrm{cm^{-1}}

(

6p

). Fitting the

5p

and

6p

levels with a constant defect puts the limit

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

above the measured ionisation energy,

41\,449.45\,\mathrm{cm^{-1}}

. Take

R_{\rm Na} = 109\,734.7\,\mathrm{cm^{-1}}

, and let the defect drift as Ritz proposed,

\delta_p(n) = \delta_0 + \delta_2/(n-\delta_0)^2

. (a) Write the three equations that fix the limit

L

\delta_0

and

\delta_2

from the three levels. (b) Solve them, and compare

L

with the measured ionisation energy. (c) Use the fit to predict

\delta_p

for

3p

, a level not used in the fit, and compare it with the value

0.883

that sodium's

3p

energy gives.

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