A sealed discharge tube of unknown gas is examined with a calibrated grating…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure

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

Problem

A sealed discharge tube of unknown gas is examined with a calibrated grating spectrometer whose detector covers

480

750\,\mathrm{nm}

. Its resolving power gives

\Delta\lambda = 0.05\,\mathrm{nm}

at these wavelengths, and each measured line centre is uncertain by

\pm0.05\,\mathrm{nm}

, calibration and setting together; the table values below are good to

0.01\,\mathrm{nm}

. Five bright lines are measured, in air:

501.55\,\mathrm{nm}

587.58\,\mathrm{nm}

667.82\,\mathrm{nm}

706.55\,\mathrm{nm}

728.10\,\mathrm{nm}

. A laboratory reference table lists the strongest visible lines (air, nm; NIST ASD) of three common discharge gases. Helium:

447.15

501.57

587.56

667.82

706.52

728.14

. Neon:

540.06

576.44

585.25

614.31

640.22

659.90

667.83

. Argon:

696.54

706.72

727.29

738.40

763.51

. ((a)) For each measured line, list every table entry, from any gas, that agrees with it within the measurement uncertainty. ((b)) One measured line is explained equally well by two gases, and one lies close to an entry of a third gas. Decide which gas fills the tube, and say why neither of these lines changes the verdict. ((c)) Does the spectrum give any evidence that the tube also holds neon? Argue from the lines that are absent as well as from those present, and say what their absence cannot rule out.

Related theory

Interference and diffraction

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