Balmer Series

Objectives
In this experiment we attempted to determine the Rydberg constant for two elements Hydrogen and Deuterium. To do this we used a constant-angle spectrometer to look at a gas-filled tube (for each element respectively) while working in low-light conditions. When this is done, a series of wavelengths available to each element appears in a unique fashion. We recorded each of the colors at the respective wavelengths and repeated this exercise to improve our precision. The Rydberg constant is key because it appears in each of these series (termed Balmer Series) and it used as an inverse of the wavelength which deals with each line spectra that is given off. Here is a link to my lab notebook:[Balmer Series]

Results
Using the formula :$$\frac{1}{\lambda} = \frac{4}{B}\left(\frac{1}{2^2} - \frac{1}{n^2}\right) = R_\mathrm{H}\left(\frac{1}{2^2} - \frac{1}{n^2}\right), n=3,4,5,...$$ We then proceeded to determine the Rydberg Constant for each element. For Hydrogen we found $$R_H=\left(1.0953 \pm .0039\right)\times 10^7 {m^-1}$$ to be the constant which was very close to the values we found online. For Deuterium we found $$R_D=\left(1.0953 \pm .0039\right)\times 10^7 {m^-1}$$ which was also very close to the accepted value.