# Physics307L:People/Osinski/Balmer

This laboratory exercise was conducted by students Darrell Bonn and Boleszek Osinski.

^{SJK 03:22, 4 October 2008 (EDT)}In this lab we successfully measured the Balmer series of Krypton, Hydrogen, and Deuterium. Our measurements, graphs, and extensive commentaries are available in the official lab report. Here it will suffice to provide our final results.

^{SJK 03:17, 4 October 2008 (EDT)}- Rydberg constant of Hydrogen

We measured the Hydrogen spectrum in two runs:

- R_H=1.0934*10^7 (recalibrating each time)
- R_H=1.097014*10^7 (constant calibration)

The reason why we did this is provided near the end of the official lab report

- Rydberg constant of Deuterium

We gathered the raw data together for this one but calculated the constant on our own. I found the constant to be R_D=1.097088*10^7

- Resolution of apparatus

We are initially led that the resolution of the spectrometer lowers as wavelength increases due to the changing spacing on the vernier scale of the apparatus. This also makes sense when we realize the higher energy (lower wavelength) levels tend to be more closely spaced together than lower energies. Our observations accord with these expectations:

Within the purple region of the spectrum we found quite a few closely spaced lines. So we looked for 2 that were as close together as we could resolve. These lines were at 445.4nm and 445nm, indicating that we have a resolution well within 1nm. Repeating this procedure in the orange part of the spectrum we found two lines that were equally closely spaced together as the two purple lines, however they were at 605nm and 607nm, indicating to us that the resolution of our spectrometer at longer wavelengths was lower.

- Error analysis

Since the resolution of the spectrometer we used was found to vary over the visible light spectrum I decided it would be more accurate to calculate the standard deviations for each spectral line. Here are the results:

- H data (matlab)

Violet1--.9452nm

Violet2--1.0308nm

Green/Blue--1.6763nm

Red--sqrt(2)nm≈5.51nm

- H data (hand-calculated)

Violet1--0nm (this excellent result is rely due to the fact that we calibrated to this gas)

Violet2--0nm

Green/Blue--0nm

Red--sqrt(2)nm≈1.41421nm

- D data (hand-calculated)

Violet1--sqrt(.0736)≈.27129nm

Violet2--.402nm

Green/Blue--.08nm

Red--.94

In conclusion our error analysis indicates to us that our precision capabilities are not high enough to make ultimately certain statements on the closeness of the deuterium and hydrogen spectra, though we are under the impression that, under the lens, the two spectra did look slightly shifted from one another.