A sodium lamp sits in a field of

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Atomic, Molecular & Optical Physics · Quantities, units and the practice of measurement

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

Problem

B = 2.0\,\mathrm{T}

. The vapour temperature gives the

589.0\,\mathrm{nm}

line a Doppler width of

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

. The light is examined with a grating used in third order (

m=3

) with

N = 25000

illuminated grooves. The weak-field pattern of the

589.0\,\mathrm{nm}

line (

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

) has six components at

\pm\tfrac13

\pm1

and

\pm\tfrac53

times

\mu_{\rm B}B

. ((a)) Find the wavenumber span between the two outermost (

\pm\tfrac53

) components, and the separation of neighbouring components. Convert the neighbouring separation to a wavelength separation using

\Delta\lambda = \lambda^2\Delta\tilde\nu

. ((b)) Estimate the grating's resolving power and compare it with the resolving power needed to separate neighbouring components. ((c)) Compare the neighbouring separation with the stated Doppler width and decide whether all six components are resolved thermally as well as instrumentally.

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