Physics307L:People/Gonzalez/Balmer Series Summary

History
In 1885 Johann Balmer discovered (or created) an formula for the computing the wavelengths from visible spectral lines of hydrogen:
 * $$\lambda =\frac{hm^{2}}{m^{2}-n^{2}}$$

In later years it was discovered that Balmer's formula was a special case in the Rydberg formula:
 * $$\frac{1}{\lambda }=R_{h}\left(\frac{1}{n^{2}_{1}}-\frac{1}{n^{2}_{2}} \right)$$

However, it would not be until 1913 that the Rydberg constant R could be explained, when the Bohr model was created.
 * $$R=\frac{\mu e^{4}}{8\epsilon ^{2}_{0}h^{3}c}$$, where $$\mu$$

is the reduced mass of the atom.

Summary of procedures
Measuring the spectral lines of mercury was the first step in order to properly calibrate the spectrometer to the prism inside. Once the prism was at a proper angle and good measurements were taken and compared to the given mercury lamp numbers then we were able to measure the hydrogen spectral lines followed by the spectral lines of deuterium. The data collecting simply involved looking into the spectrometer until a line of a particular color could be seen, the color was recorded and the line was aligned with the cross-hairs on the spectrometer, once the line was properly aligned the number on the knurled ring was recorded as well, this number would be the wavelength of the given line in nanometers. Data was collected, but unfortunately, only two complete measurements were taken from the hydrogen lamp. Below are the computed Rydberg constants for both hydrogen and deuterium.

Purpose of the experiment
The Balmer series shows us that the frequency of the line spectrum is related to an integer (n), which is the quantum number, this hints that light emits energy in fixed amounts, which eventually shows that light is quantized. The photon's energy is directly related to its frequency and therefore can be measured through its wave number. The higher the quantum number the more energy that the photon has and the shorter the wavelength will become.

Data Analysis


The following is the R value measured for hydrogen, its average, standard error, and the standard error of the mean.

Since the Violet 1 numbers were so far off due to measuring the wrong line i made two sets of calculations, one including Violet 1, the other excluding it. The numbers given show us that the average value for R is R=$$1.0807300X10^{7}m^{-1}$$, while the R value without Violet 1 measurements are $$1.0975266X10^{7}m^{-1}$$, the R value without the Violet 1 values are far closer to the accepted value of $$R=1.0967758X10^{7}m^{-1}$$

The R value with Standard error of the mean is R=$$1.08073X10^{7}(17)m^{-1}$$ Without the Violet 1 numbers R=$$1.09752X10^{7}(56)m^{-1}$$

Therefore my best guess and ranges are: Best guess: $$1.0975266X10^{7}m^{-1}$$ range 1 (R+SEM)=10980900$$m^{-1}$$ range 2 (R-SEM)=10969700$$m^{-1}$$ This still falls out of range for the accepted value. more measurements should be taken.

The deuterium R values are as follows:

As before the R value with the range is computed the same way. Giving us the following: R=$$1.0998X10^{7}(6)m^{-1}$$

Best Guess: $$R=10992433$$ Range 1: (R+SEM)=10998544 Range 2: (R_SEM)=10986322

Reasons For Error
Several things could've gone wrong and did go wrong in this experiment. More measurements could've reduced error, as well as being more careful in measuring the line spectrum. The large measuring knob has a lot of gear back lash, which was noticed a few times by myself and my lab partner Jacob. Also we found that reading the dial proved difficult for us, and at one time we realized that we may have been reading it wrong.

What I've learned
This lab helped me to better understand the importance of the Balmer series and how it was one among the many steps taken into the creation of quantum mechanics. I now recognize the similarities and importance between the line spectrum and their relation to the emitted photons and the gas necessary to emit them. Other than the lab I am better understanding how to use google docs and more important, beginning to have a greater appreciation and understanding for error and data analysis involving error.

Acknowledgments
The picture above was not taken by me, but by Anatastasia and Alex.(Steve Koch 11:58, 21 October 2009 (EDT): Good job crediting ... would be much better to credit in the figure caption so that a reader would be sure to notice the credit.) The history on the Balmer series was found in both |The lab manual and on | Wikipedia's webpage about Johann Balmer And a link to a website that had a hydrogen line spectrum as was seen through the spectrometer.

Other Links
A link to my notebook for this lab. Balmer Series notebook Jacob's page. User:Jacob_R_Jaramillo