The level of an alkali atom with nuclear spin (so as well) has four hyperfine levels

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

Deriving the Spectrum, Ch Hyperfine structure and isotope shifts

Problem

The

4\,{}^2P_{3/2}

level of an alkali atom with nuclear spin

I = \tfrac32

(so

J = \tfrac32

as well) has four hyperfine levels

F = 0, 1, 2, 3

. The measured intervals are

\begin{aligned} E(F{=}1) - E(F{=}0) &= 48\,\mathrm{MHz},\\ E(F{=}2) - E(F{=}1) &= 90\,\mathrm{MHz},\\ E(F{=}3) - E(F{=}2) &= 120\,\mathrm{MHz}. \end{aligned}

Someone argues as follows:"The interval rule says

E_F - E_{F-1} = A_{\rm hfs}F

, so I can read off

A_{\rm hfs}

from each interval:

48/1 = 48\,\mathrm{MHz}

90/2 = 45\,\mathrm{MHz}

120/3 = 40\,\mathrm{MHz}

. These agree well enough, so I average them:

A_{\rm hfs} \approx 44\,\mathrm{MHz}

, and since the three estimates are close there is no significant quadrupole coupling,

B_{\rm hfs} \approx 0

." ((a)) Find the error in this reasoning. ((b)) Use the measured intervals correctly to find

A_{\rm hfs}

and

B_{\rm hfs}

for this level, in MHz.

Browse the problem library