User:Jacob R Jaramillo/Notebook/Balmer Series Lab

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Safety

 * Be careful when handeling the lamp as they can break and the glass can cause a serious injury.


 * Make sure to unplug the power supply for the light tubes when changing the tube.


 * Note which sides of the pellin broca prism are polished and try to avoid touching them as finger prints can cause poor optical transmission.

Equipment

 * Spectrometer with Pellin Broca Prism


 * Spectrum tube power supply (Model SP200, 5.0KV, 10mA)


 * Mercury, Hydrogen and Dueterium tube

Dueterium tube


 * We were unable to locate a ruler; therefore, we used the approximation that 1 sheet of paper equals 0.1mm and used 5 sheets of paper to adjust out slit width to approximatly 0.5mm.

Quick Explanation of a Pellin Broca Prism
A Pellin Broca Prism is a Prism which utilizes two important angles explained below (and noted 1,2 and 3 in below picture).

1 and 3. 56 degree angle: Is extremely important and well known as Brewsters Angle. At this angle, P-Polarized light is known to have very minimal Fresnel loss even without an anti reflective coating.

2. TIR (Total Internal Reflection): Which is calculated by the Critical angle

Critical Angle

Critical angle The critical angle is the angle of incidence above which total internal reflection occurs. The angle of incidence is measured with respect to the normal at the refractive boundary. The critical angle θc is given by:

Critical Angle = Arcsin (n2/n1)

n2 in this case is air (generally assumed as having an index of 1)

n1 in this case is glass (which can vary heavily based on the material, most common types are BK7 (n=~1.5) and Fused Silica (n=~1.4))

Due to TIR, the light that hits side 2 is transmitted to side three without any use of optical coatings.

Pellin broca prism

Calibrating
First thing we did is calibrated the spectrometer. We did this by locating a line of the mercury spectrum and compared where we found the lines as opposed to the data given, we then adjusted the line until it matched the data, after which we double checked our results by searching for other lines on the mercury spectrum and then compared it to our results. We recalibrated the spectrometer again on day 2, since it only take a few minutes and at the very least gave us a second set of values to confirm our day 1 results.

A very important precaution is the response lag of the dial, if you accidentally turn the dial the incorrect way, continue to make half a revolution and then go back, as any small amount of lag can easy cause a nano meter of inaccuracy.

Procedure Continued

 * Once calibrated, we replaced the mercury lamp with a hydrogen lamp.
 * Following the same procedures as when calibrating, we looked for the four lines of the hydrogen spectrum and then recorded the measured wavelengths. The wavelength's measurements are shown below
 * The first data chart is for day 1 only one trial was made since we were still getting familiar with the equipment. Day 2 data is seen below for both hydrogen and Dueterium.

Data Analysis
Next we found the Rydberg Constant by taking the measured wavelengths and applying it to the equation: $$\frac{1}{\lambda }=R(\frac{1}{2^{2}}-\frac{1}{n^{2}})$$, where, n=3,4,5.... and isolating R $$R=\frac{1}{\lambda }\frac{1}{(\frac{1}{2^{2}}-\frac{1}{n^{2}})}$$

Unfortunately the day 2 data only has one measurement for hydrogen, so our error will be considerable, when compared to our data for deuterium.

From the data in the above graph, you can see we were approximately 0.11%-0.39% from the accepted value of R (given by NIST). The main reason for our error in this lab is definitely calibration, from the start our red spectrum line never matched up no matter how many times we attempted to recalibrate the set up. I would then say the second cause for error would be backlash. I know there were a few times we turned the knob the incorrect way and even though we continues to turn the knob half of a revolution to reduce the backlash it appears that it wasn't sufficient. If I were to preform this lab again, I would make certain that I always turned the knob in the correct direction. Last but not least, I feel that another reason for error worth mentioning is visual sensitivity. Several times throughout this experiment, I had to take a minute or two to let my eyes rest as the violet lines are extremely difficult to see.

Summary
Balmer Series Summary