Lithium's red resonance line at joins the ground level to the term

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · Many-electron atoms and the periodic table · Radiative transitions, external fields and collisions

Deriving the Spectrum, Ch Radiative transitions and lifetimes

Problem

Lithium's red resonance line at

670.8\,\mathrm{nm}

joins the ground level

2s\,{}^2S_{1/2}

to the

2p

term. Its two fine-structure components lie too close together to matter here, so treat them as one line from

2s

(

g_1=2

) to the whole

2p

term (

g_2=6

), with total absorption oscillator strength

f_{12}=0.747

. The next line of the series,

2s\to3p

, has

f=0.0047

. Treat the

2s

electron as the only active one, so that its oscillator strengths sum to one. The

2p

term can decay only to

2s

, and its measured lifetime is

27.1\,\mathrm{ns}

. ((a)) How much oscillator strength do all the transitions from

2s

other than the resonance line carry together, and how much is left for

4p,5p,\dots

and the continuum once

2s\to3p

is removed too? Contrast lithium with sodium, whose resonance pair carries

0.961

. ((b)) From

f_{12}

, find the spontaneous rate

A_{21}

2p\to2s

and the

2p

lifetime, and compare with the measured value. ((c)) Find the dipole matrix element

|\vec d_{21}|

(one upper sublevel, summed over the lower ones) as a multiple of

ea_0

. Hydrogen's

2p\to1s

value is

0.745\,ea_0

; explain why lithium's

2p

nevertheless lives longer than hydrogen's.

Browse the problem library