Rydberg Constant from the Balmer Series

Hydrogen Balmer lines (n_f = 2). Measure λ at several n_i from a nanometre scale and recover R_H from a fit of 1/λ versus (1/4 − 1/n_i²).

School· 22 min·Related simulator: ChemistryHydrogen: Balmer / Lyman Lines

Goal

Determine the Rydberg constant from 1/λ = R_H (1/n_f² − 1/n_i²) with n_f = 2. The slope of 1/λ versus (1/4 − 1/n_i²) is R_H.

Equipment

Hydrogen discharge tube
Spectrometer (nm scale)
Balmer series

Experiment

Hydrogen spectrum, Balmer series. Scale in nm. No live λ on the bench.

Balmer series only (n_f = 2). The Rydberg constant is hidden. Select the upper level n_i. The spectrometer wavelength appears only after you record; there is no live λ or ΔE while you change n_i.

Upper level n_in_i = 3

Spectrometer: no reading

Record n_i = 3… at least 6 (through n_i = 8), then fit 1/λ versus (1/4 − 1/n_i²).

Measurements

№	n_i	λ nm	1/λ m⁻¹	1/4 − 1/n_i²
No measurements yet — take your first reading.

Data processing

Add at least 2 measurements to compute the fit.

Uncertainty

Lab report

Opens the system print dialog — choose “Save as PDF” or your printer. Header and footer are hidden when printing.

One click opens the print dialog — choose “Save as PDF”.

Rydberg Constant from the Balmer Series

Generated: 24 Aug 2026, 22:29

Goal

Determine the Rydberg constant from 1/λ = R_H (1/n_f² − 1/n_i²) with n_f = 2. The slope of 1/λ versus (1/4 − 1/n_i²) is R_H.

Measurement table

#	n_i	λ (nm)	1/λ (m⁻¹)	1/4 − 1/n_i²
No measurements yet — take your first reading.

Fit and derived value

Add at least 2 measurements to compute the fit.

Conclusion

The fitted Rydberg constant agrees with the hydrogen (reduced-mass) value. Main uncertainties: spectrometer noise and treating the lines as isolated Rydberg wavelengths.

PhysSandbox virtual lab — values come from your session; add your own discussion of error sources.

Theory

Balmer lines end on n = 2. In SI, 1/λ = R_H (1/4 − 1/n_i²). The bench hides λ and ΔE; you read a spectrometer after each measurement. The scale is in nanometres; the fit uses 1/λ in m⁻¹.

Procedure

Balmer series only (n_f = 2). Select the upper level n_i.
Record. The spectrometer logs λ with small readout noise. There is no live λ or ΔE while you change n_i.
The notebook computes 1/λ (m⁻¹) and x = 1/4 − 1/n_i².
Repeat for n_i = 3… at least 6 (through n_i = 8).
Fit 1/λ versus x; the slope is R_H. Compare with the reference.

Conclusion

The fitted Rydberg constant agrees with the hydrogen (reduced-mass) value. Main uncertainties: spectrometer noise and treating the lines as isolated Rydberg wavelengths.