Three effects act on the sodium lines: the fine-structure splitting between and , ;…

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure

Deriving the Spectrum, Ch Hyperfine structure and isotope shifts

Problem

Three effects act on the sodium

D

lines: the fine-structure splitting between

3P_{3/2}

and

3P_{1/2}

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

; the hyperfine spread of the

3P_{3/2}

level (from

F=0

F=3

), of order

60\,\mathrm{MHz}

; and an isotope shift between two sodium isotopes of order

500\,\mathrm{MHz}

. Use

1\,\mathrm{cm^{-1}} = 29.9792\,\mathrm{GHz}

to convert as needed. Three spectroscopic techniques are available, each with a resolution (minimum resolvable frequency difference) as follows: ((a)) A Doppler-limited absorption cell, resolution

1000\,\mathrm{MHz}

. ((b)) A saturated-absorption laser spectrometer, resolution

5\,\mathrm{MHz}

. ((c)) A grating spectrograph, resolution

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

. For each technique, state which of the three effects (fine structure, hyperfine structure, isotope shift) it can resolve.

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