# Physics307L F09:People/Dougherty/Balmer

fig. 1 prism

## Setup/Procedure

The apparatus we used was called a "constant deviation" spectrometer. As seen in fig. 2, we calibrated the spectrometer by moving the prism slightly to line up the right wavelength with its spectral line. To do this, we changed the adjustment dial, see fig. 3, to the wavelength noted to us in the lab manual and used the eye piece to view the right spectral color line. Then moving the prism slightly we aligned it exactly to the crosshairs in the eyepiece. The prism is set up and shaped to always have the light and incident light at 90 degrees as seen in fig. 1. The manual suggested we use mercury for the calibration, and gave us the exact wavelengths we needed for each colored line in the spectrum. This way we could calibrate the entire spectrometer. The lab manual gave us the wavelengths of each color to calibrate:

COLOR red yellow yellow green blue/green violet violet (faint)
WAVELENGTH (nm) 690.75 577 579 546.1 skip 435.8 404.7
• note: the manual told us to open the spectrometer slit,located on the spectrometer by the light box (see fig. 4), only about a milimeter to half a milimeter wide. letting in only a small amount of light. this sharpens the lines considerably.
SJK 03:16, 29 November 2007 (CST)
03:16, 29 November 2007 (CST)
Good that you had technique to get rid of backlash (dead spots), but it was not necessary to go "all the way clockwise"...just needed to go far enough so that coming back would be fully engaged.

After calibrating the spectrometer, we could start the experiment. We located the tubes of hydrogen and deuterium. Using these lights in the light box, wefound 4 spectral lines for each color and measured the wavelength in nm off the dial. In this experiment we started with the dial all the way counter-clockwise and moved it clockwise to find the spectral lines and wrote down the wavelengths off the dial. Then we turned the dial all the way clock wise and moved it counter-clockwise to find all the spectral lines. Doing this minimized the dead spots while turning the dial, giving us a more accurate reading and more wavelengths which we could average together.

## Final value of R

SJK 03:20, 29 November 2007 (CST)
03:20, 29 November 2007 (CST)
So it looks like you averaged together counter-clockwise and clockwise? See my comments on your other notebook page, but you should only use one or the other.
$\frac{1}{\lambda} = R_\mathrm{H}\left(\frac{1}{2^2} - \frac{1}{n^2}\right), n=3,4,5,...$
Hydrogen = 1.099*10^7 m^-1 +/- 0.00059*10^7 m^-1
Deuterium = 1.100*10^7 m^-1 +/- 0.00082*10^7 m^-1

## Possible Reasons for Error

SJK 03:21, 29 November 2007 (CST)
03:21, 29 November 2007 (CST)
And it is pretty cool that you can get so close to the accepted value, isn't it!

As we know its almost impossible for perfect results, and with this experiment it is also the case. This experiment is also a dark room experiment, and we had the door open, letting in the hall light. This might have skewed some of oure results in the spectra we looked at. Also the slit opening on the apparatus has a huge impact on where we lined it up with the cross hairs. As Linh pointed out, the smaller the slit, the more the line seemed to focus on the right side of the actual line. Meaning when the slit is big, the spectrum line is blurred and wide. But when the slit is smaller the line focused more to the right as we looked at it. This would probably help the wavelength calculation if we focused it that way. But it did come with disadvantages. For instance, the smaller the slit, the less light got in, therefore it was almost impossible to see the faint Violet spectrum line on the far right of the spectrum. We had to open up the slit more to actually see the line. (see raw calculations link above to view our spectrum lines for each element.) Another possible problems could be the apparatus itself. It is really old and could have small problems that could skew the results, including the dial. To me the dial seemed very easy to tamper with. If any student could possibly turn it to hard or knock it off its course, it could easily create wrong results for any one. Also the prism the light reflects and refracts through. It is also old and might be flawed by some one dropping it etc...

## Overall

Overall however, i think the experiment went very well. we came very close to the actual value of the Rydberg constant which is 1.0967758*10^7 m^-1. This experiment was fairly easy and was easy to compensate for some errors that might occur. For instance the dial dead points; which we compesated by two different directions of rotation.

We came up with a very small error of:

## error

$%error= \frac{|Actual-Experimental|}{|Actual|}x100$

actual value = 1.0967758*10^7 m^-1

Hydrogen e= 0.20%
Deuterium e= 0.29%

## What i would've done with more time

This experiment, though simple, was very fun though. it would be alot more fun to look at plenty of other elements we have and discover all the spectra lines it has to offer.

More time would also be including a perfect calibration of the prism, which i would spend at least a good half hour to calibrate to my liking. Another would be keeping the door closed and complete darkness while looking at the lines, which would detract any excess light not of the certain element i was looking at.