Sodium's , and levels lie , and below its ionisation limit. Take and…

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 The central field and the periodic table

Problem

Sodium's

3s

3p

and

3d

levels lie

5.139\,\mathrm{eV}

3.035\,\mathrm{eV}

and

1.522\,\mathrm{eV}

below its ionisation limit. Take

hcR = 13.606\,\mathrm{eV}

and

1\,\mathrm{eV} = 8065.5\,\mathrm{cm^{-1}}

. ((a)) Find the effective quantum number

n^*

and the quantum defect

\delta_l

of each level. ((b)) Assuming

\delta_p

is the same at

n=4

as at

n=3

, predict how far the

4p

level lies below the limit, and the wavenumber of the

3s\to4p

absorption line. ((c)) The line is measured at

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

. Find the

\delta_p

this measurement implies for

4p

, and say what the difference from (a) shows.

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