Measuring the hydrogen Balmer series and Rydberg’s constant with a homemade spectrophotometer

In a recent paper (Amrani 2014 Eur. J. Phys. 35 045001), the author presented two different methods to measure the wavelength of visible lines of Balmer series from the hydrogen atomic spectrum and estimate the value of Rydberg’s constant with an error difference of a few tenths of a per cent. Here we discuss how low cost spectrometers, based on the use of either transmission or reflection diffraction gratings coupled with a commercial digital camera, can be employed with the same aim. The Rydberg’s constant values obtained with our pectrometers are R = 1.096 ± 0.007 × 107 m−1 for the transmission grating spectrometer and R = 1.094 ± 0.005 × 107 m−1 for the reflection spectrometer, with a difference of less than 0.30% from the accepted value of 1.097 373 × 107 m−1.