Operate a laboratory spectrometer

When do two nearby lines become distinguishable?

Relate instrument resolution to a synthetic spectrum without changing the underlying reference line centers.

A spectrometer records light through a finite wavelength response. Change the synthetic profile width to see how nearby features blend or separate. This activity uses approximate vacuum hydrogen positions calculated with the reduced-mass Rydberg model. Its equal-area profiles illustrate instrumental broadening, rather than reproducing a measured lamp spectrum.

Explore the model (optional)

EXPLORE THE MODEL

Change the resolving power

FOLLOW THE SIGNALConceptual instrument diagram

FWHM: 1.0 nm

The arrangement explains the signal path. The investigation below supplies the teaching output; this schematic is not a ray trace, micrograph, or instrument calibration.

View sampled plot values

Current values

Vacuum wavelength (nm)	Synthetic intensity (arbitrary units)
365.000	0.00000
375.125	0.93944
385.250	0.00078
395.375	0.00020
405.500	0.00000
415.625	0.00000
425.750	0.00000
435.875	0.00031
446.000	0.00000
456.125	0.00000
466.250	0.00000
476.375	0.00000
486.500	0.81517
496.625	0.00000
506.750	0.00000
516.875	0.00000
527.000	0.00000
537.125	0.00000
547.250	0.00000
557.375	0.00000
567.500	0.00000
577.625	0.00000
587.750	0.00000
597.875	0.00000
608.000	0.00000
618.125	0.00000
628.250	0.00000
638.375	0.00000
648.500	0.00000
658.625	0.00000
668.750	0.00000

Synthetic Gaussian emission profiles with equal teaching areas, using approximate vacuum line centers. Heights do not measure abundance.

Instrument FWHM1 nm

Wavelength window

TEACHING RELATIONSHIPI(λ) = Σ aᵢ G(λ; μᵢ, σ)

FWHM1.0 nm

Line-center modelApproximate vacuum Balmer

Amplitude meaningEqual integrated teaching areas

Increasing the width spreads each fixed-area line and can merge nearby features. Compare the crowded lines near the series limit.

Compare the separate NIST handbook reference records

These selected H I records use air wavelengths. The plot above uses approximate vacuum Rydberg calculations. They are deliberately not overlaid as interchangeable values.

Transition family	Air wavelength (nm)	Source reference
n=6 → 2	410.174	RCWM80
n=5 → 2	434.0462	MK00a
n=4 → 2	486.12786	MK00a
n=4 → 2	486.1287	MK00a
n=4 → 2	486.13615	MK00a
n=3 → 2	656.2711	MK00a
n=3 → 2	656.27248	MK00a
n=3 → 2	656.28518	MK00a

The table includes selected fine-structure components. MK00a is a calculation reference; the records are not uniformly measured laboratory lines. Unknown uncertainties remain unspecified.

Inspect the original NIST table ↗

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HOW DO WE KNOW?

Evidence & limits

Reference science + bounded teaching model

What this interaction establishes

Relate instrument resolution to a synthetic spectrum without changing the underlying reference line centers.

Synthetic Gaussian emission profiles with equal teaching areas, using approximate vacuum line centers. Heights do not measure abundance.

Source bindings for this explanation

Start here

Sources: S05, S06, SRC-CODATA.

Explore the science

The width control sets the full width at half maximum, or FWHM, of normalized Gaussian profiles. Each calculated line keeps the same integrated teaching area, so broadening lowers its peak height. Resolving power is commonly expressed as R = λ/Δλ with the width convention stated. The crowded window helps reveal blending among nearby features. Neither their equal areas nor their heights represent natural line intensities or hydrogen abundance.

Sources: S05, S06, SRC-CODATA.

Go deeper

Hold the source assumptions fixed when comparing widths so that a changed peak is not mistaken for changed composition. Both spectral windows use the same approximate vacuum line model. The separate NIST handbook table supplies air-wavelength reference entries, including resolved components where listed; these values are not directly substituted into the synthetic curve. Comparing them numerically requires compatible units, an air/vacuum conversion and attention to omitted structure. A realistic source would also require excitation, noise and instrument-response information.

Sources: S05, S06, SRC-CODATA.

Limitations

The plot uses normalized synthetic Gaussians at approximate vacuum Rydberg positions, not measured or directly imported NIST profiles. Each line has equal integrated teaching area; changing FWHM changes peak height without measuring abundance. Visible NIST handbook reference wavelengths are listed separately in air and require a convention-aware comparison.

Sources: S05, S06, SRC-CODATA.

Keep these boundaries in mind

The plot uses normalized synthetic Gaussians at approximate vacuum Rydberg positions, not measured or directly imported NIST profiles.
Each line has equal integrated teaching area; changing FWHM changes peak height without measuring abundance.
Visible NIST handbook reference wavelengths are listed separately in air and require a convention-aware comparison.

Inspect the references

Supplemental primary reference ↗Supplemental primary reference ↗

Scientific explanations with linked references. Model calculations retain their stated assumptions and limits.

Optional: check your understanding

MAKE THE CONNECTION YOUR OWN

Test your reasoning

Try freely. Saving progress is optional.

recognition

What does the resolution control change in this activity?

The number of protons in hydrogenThe reference element’s identityThe modeled width of the instrument response

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mechanism

Two close features merge under a broad response. What may a narrower response reveal?

That two modeled centers were already presentThat the instrument created a new elementThat all lines have become more abundant

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evidence

Which label is required for the trace generated here?

Measured in an unnamed laboratorySynthetic spectrum with the broadening and normalization assumptions statedUnmodified telescope observation

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transfer

A different instrument blurs the same sample’s nearby features together. Is absence of separate peaks proof that the sample has fewer elements?

Yes, fewer peaks always means fewer elementsYes, because blur changes atomic identitiesNo; resolution, sensitivity and source conditions can hide or blend features

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Atomic transitions and light Next: A spectrum from the sky