Physics / Emission Spectra & Rydberg Constant
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EXPERIMENT 52 · PHYSICS LABORATORY

A Study of Spectra: Optical Emission Spectroscopy, the Balmer Series and the Rydberg Constant

To observe and map discrete atomic line emission spectra, measure the wavelengths of the visible Balmer series of hydrogen (H_α, H_β, H_γ, H_δ, H_ε, H_ζ) using a calibrated grating spectrometer, test the Bohr-Balmer wavelength relationship, and determine the Rydberg constant R_H. Explore a virtual apparatus, collect readings and analyse a graph.

CHANGE · OBSERVE · MEASURE

Your virtual workbench.

SPECTRAL EMISSION WAVELENGTH Λ—
MEASUREMENT STATUS

Ready for a virtual observation.

3.0
Replica Transmission Grating Constant: d = 1.6667 μm (600 lines / mm)

Adjust the apparatus, then take a reading.

Readings are generated by an ideal model. The diagram is schematic and is not to scale.

Simulation assumptions and limits

Calculations assume an ideal transmission grating obeying d sin θ = m λ with zero prism curvature, negligible Doppler thermal line broadening, and negligible ambient refractive index variations in laboratory air. Real spectrometers exhibit minor chromatic aberration in collimator lenses, mechanical backlash in the micrometer vernier drum, and a refractive index of air n_air ≈ 1.00028 that causes air wavelengths to be approximately 0.18 nm longer than vacuum wavelengths.

Know your apparatus.

High-Resolution Transmission Grating Spectrometer

Provides an optical bench with a precision bilateral entrance slit, collimating telescope with achromatic objective, central rotatable circular spectrometer table with replica diffraction grating (600 lines/mm), and viewing telescope with calibrated micrometer reticle graduated in tenths of a nanometer.

Capillary Hydrogen Geissler Gas Discharge Tube

Emits intense atomic hydrogen emission radiation produced by electron-impact dissociation and collisional excitation of molecular H₂ gas in a constricted capillary bore under low pressure (~1 mmHg).

High-Voltage Regulated Induction Power Supply

Delivers a stable 5,000 V AC/DC excitation potential to strike and sustain a steady glow discharge across the gas tube without filament thermal sputtering.

Sodium and Mercury Calibration Reference Lamps

Provide certified spectroscopic wavelength benchmark lines (sodium yellow doublet at 589.0 nm and 589.6 nm, mercury green line at 546.1 nm) for precise spectrometer reticle zero-offset and dispersion calibration.

Bunsen Flame Chemical Excitation Attachment

Permits comparative study of flame line emission spectra of alkali and alkaline-earth metal chlorides (NaCl, LiCl, SrCl₂, CaCl₂) introduced into a non-luminous gas flame on platinum/nichrome loops.

Digital Angle and Wavelength Micrometer Readout

Measures angular diffraction deviation θ and directly reads optical wavelength λ to 0.1 nm resolution using anti-parallax vernier drum optics.

FOLLOW THE METHOD

A reason behind every step.

To observe and map discrete atomic line emission spectra, measure the wavelengths of the visible Balmer series of hydrogen (H_α, H_β, H_γ, H_δ, H_ε, H_ζ) using a calibrated grating spectrometer, test the Bohr-Balmer wavelength relationship, and determine the Rydberg constant R_H. Suggested independent settings: 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 .

1

Spectrometer Optical Alignment and Reticle Focus

Illuminate the entrance slit with an incandescent lamp. Focus the viewing telescope crosshairs sharply on the slit image. Rotate the collimator tube until the slit image is strictly parallel to the vertical reticle hair, and adjust the collimator lens to produce a perfectly parallel incident beam (Schuster’s method). Set the diffraction grating perpendicular to the optical axis on the central turntable.

Why this step matters

Collimating the incident light into plane wavefronts ensures that the grating equation d sin θ = m λ holds rigorously without spherical aberration.

2

Wavelength Calibration with Sodium and Mercury Reference Standards

Place the sodium vapor lamp in front of the entrance slit. Locate the intense first-order yellow emission lines. Align the reticle crosshair on the resolved sodium doublet (D₁ = 589.6 nm, D₂ = 589.0 nm) and calibrate the spectrometer drum index. Verify the calibration against the mercury 546.1 nm green line to confirm linear dispersion across the focal plane.

Why this step matters

Establishing a certified reference benchmark eliminates spectrometer zero-point index error and guarantees absolute wavelength accuracy.

3

Hydrogen Discharge Tube Alignment and Continuous vs Line Comparison

Mount the hydrogen Geissler tube directly in front of the entrance slit within a protective shielded housing. Energize the high-voltage supply to initiate the pink-purple glow discharge. Observe the spectrum through the telescope and identify the four brilliant visible Balmer lines against the faint molecular background band.

Why this step matters

Constricting the discharge inside the capillary bore maximizes the current density and enhances atomic emission relative to molecular continuous bands.

4

Precision Wavelength Measurement of the Visible Balmer Lines

Rotate the telescope slowly toward the red region and bisect the vivid ruby-red H_α line (n = 3 → 2) with the crosshairs. Read and record its wavelength λ = 656.3 nm. Progressively measure the cyan H_β line (n = 4 → 2 at 486.1 nm), the blue-violet H_γ line (n = 5 → 2 at 434.0 nm), the deep violet H_δ line (n = 6 → 2 at 410.2 nm), and the near-ultraviolet limits H_ε (n = 7 → 2 at 397.0 nm) and H_ζ (n = 8 → 2 at 388.9 nm).

Why this step matters

Sampling six consecutive Balmer transitions spanning n = 3 through n = 8 provides extensive leverage for linear regression testing of the Rydberg formula.

5

Comparative Study of Alkali Metal Flame Spectra and Solar Fraunhofer Lines

Introduce platinum wires wetted with sodium chloride (yellow 589 nm), lithium chloride (crimson 671 nm), and strontium chloride (red 680 nm, blue 461 nm) into a non-luminous Bunsen flame. Record the characteristic flame line positions. Direct solar light through the slit using an exterior heliostat mirror to observe the dark Fraunhofer absorption lines (C, D, F, G) matching the hydrogen and sodium emission wavelengths.

Why this step matters

Comparing atomic flame emission with solar absorption directly demonstrates Kirchhoff’s law of radiation and proves the presence of terrestrial elements in stellar atmospheres.

6

Linear Regression Analysis and Rydberg Constant Determination

For each spectral line n, compute the Bohr quantum geometric factor x = 1/4 − 1/n² and the optical wavenumber y = ν̃ = 1 / λ (in m⁻¹). Plot ν̃ on the vertical axis against (1/4 − 1/n²) on the horizontal axis. Compute ordinary least-squares linear regression to determine the slope S = R_H (in m⁻¹) and the vertical intercept b. Compare the measured Rydberg constant against the standard CODATA value (1.0967758 × 10⁷ m⁻¹).

Why this step matters

Linear regression over all six Balmer transitions averages out spectrometer drum reading quantization and tests the inverse-square quantum energy level structure of the Bohr atom.

YOUR NOTEBOOK · 0 OBSERVATIONS

Turn measurements into a result.

See a complete example report ↗

Points are your observations. The fit uses SI x and y values before display scaling.

LINEAR FIT · y = mx + b
ν̃ = 1 / λ = R_H · (1/2² − 1/n²) + b; R_H = m_slope
#Upper energy level quantum number n ()Spectral emission wavelength λ (nm)Bohr level factor (1/4 − 1/n²)Wavenumber ν̃ = 1/λ (m⁻¹)Remove

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CHECK YOUR UNDERSTANDING

Explain what the measurements mean.

In the Bohr model of the hydrogen atom, what physical transition produces the prominent ruby-red H_α spectral line at 656.3 nm?

Why do the spectral lines of the Balmer series crowd closer together as the upper quantum number n increases toward higher values (n = 6, 7, 8...)?

If a linear plot of wavenumber ν̃ = 1/λ versus (1/4 − 1/n²) is constructed for the Balmer series, what does the slope of the best-fit line represent?

What causes the dark Fraunhofer lines observed in the solar spectrum?