An unlabelled alkali-metal vapour lamp is examined with a teaching grating…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Atomic, Molecular & Optical Physics · Many-electron atoms and the periodic table

Reading the Spectrum, Ch Lines, series and the term diagram: what a spectrometer measures

Problem

An unlabelled alkali-metal vapour lamp is examined with a teaching grating spectrometer:

600

grooves per millimetre are illuminated over a width of

30\,\mathrm{mm}

, used in first order (

m=1

). Four lines are measured, in air, each uncertain by

\pm0.02\,\mathrm{nm}

404.41\,\mathrm{nm}

404.72\,\mathrm{nm}

766.49\,\mathrm{nm}

769.90\,\mathrm{nm}

. A reference table gives the strongest lines (air, nm; NIST ASD) of three alkali metals. Sodium (Na):

330.24

330.30

588.995

589.592

. Potassium (K):

404.41

404.72

766.49

769.90

. Lithium (Li):

610.36

670.78

. ((a)) Work out the spectrometer's resolving limit

\Delta\lambda

766\,\mathrm{nm}

. ((b)) State which metal is in the lamp. Use the measurement uncertainty to decide which table entries match, and use

\Delta\lambda

to check that each of the lamp's close pairs is resolved, so that four separate lines really were measured.

Related theory

Interference and diffraction

Browse the problem library