Potassium's principal doublet consists of the lines at and at ; the fine-structure…

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

Reading the Spectrum, Ch Atoms in a magnetic field: moments, the Zeeman effect and the Paschen-Back limit

Problem

Potassium's principal doublet consists of the lines

4{}^2\mathrm{P}_{3/2} \to 4{}^2\mathrm{S}_{1/2}

766.49\,\mathrm{nm}

and

4{}^2\mathrm{P}_{1/2} \to 4{}^2\mathrm{S}_{1/2}

769.90\,\mathrm{nm}

; the fine-structure interval of the

4p

level is

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

. A spectrum recorded in an unknown magnetic field shows one of the two lines, but the record does not say which. Its components sit at

-0.623

-0.374

-0.125

+0.125

+0.374

and

+0.623\,\mathrm{cm^{-1}}

from the zero-field position of the line. Take

\mu_{\rm B}B/hc = 0.467\,\mathrm{cm^{-1}}

per tesla. ((a)) Evaluate

g_J

for the three levels from the Lande formula, and work out the weak-field pattern of each line in units of

\mu_{\rm B}B

. Decide which line was recorded, using only features of the pattern that do not depend on the size of the field, and state the number of components in the recorded pattern. ((b)) Find

B

in tesla, and report the ratio

\mu_{\rm B}B/(hc\times57.7\,\mathrm{cm^{-1}})

as a check that the field is weak for the

4p

level. ((c)) State how many components the other line of the doublet would show in the same field, and predict the size of its component shifts, in

\mathrm{cm^{-1}}

, from the centre outward. Give the smallest wavelength separation between two neighbouring components of that line, in nm.

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