The ground state of ( , ) has

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · Radiative transitions, external fields and collisions

Deriving the Spectrum, Ch Atoms in magnetic fields

Problem

The ground state of

^{87}\mathrm{Rb}

(

J=\tfrac12

I=\tfrac32

) has

\Delta E_{\rm hfs}/h=6834.68\ \mathrm{MHz}

g_J-g_I'=2.0033

and

g_I'=-0.000995

, with

g_I'

the nuclear

g

-factor in Bohr magnetons. Take

\mu_{\rm B}/h=13.996\ \mathrm{GHz\,T^{-1}}

. In a uniform field

B

the

0

-to-

0

transition,

|F=1,m=0\rangle\to|F=2,m=0\rangle

, is measured at

7641.4\ \mathrm{MHz}

. ((a)) Use the Breit-Rabi formula to find

x

and

B

. ((b)) Find the field that the quadratic formula for

\delta\nu_{0\text{-}0}

would infer from the same measurement, and its percentage error. ((c)) At the true field, find the frequency of the line between

|F=2,m=2\rangle

and

|F=2,m=1\rangle

, and compare it with the weak-field prediction

g_F\mu_{\rm B}B/h

for

F=2

, nuclear term included.

Related theory

Quantum Mechanics

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