Roberto Sebastian Rosales/Notebook/Physics 307L/2010/10/27

^{SJK 21:52, 21 December 2010 (EST)}

21:52, 21 December 2010 (EST)
Excellent primary notebook. Very helpful and honest description of the mistakes/ideas for future improvement. Also, it does look like you took some careful and good data!

Equipment

• Soar Corporation DC Power Supply Mod. 7403 ([math]\displaystyle{ V_f }[/math])
• Kepco Regulated DC Supply Mod. CK60-0.5 ([math]\displaystyle{ V_A }[/math])
• Tel 2501 Universal Stand
• Hertz Critical Potential Bulb #2533
• Tel 2021 Alarmed Meter and Stand
• Tel 2533.06 Battery Unit
• Wavetek Voltage Meter

Safety

• Standard electrical safety
• This lab required many cables for connecting the different devices, so it was important to make sure that we had everything connected correctly, and did not leave anything loose or unconnected.
• We were using two Power supplies, one of which needed to be handled carefully as to make sure that [math]\displaystyle{ V_f }[/math] did not exceed 2.5V.

Setup

As mentioned in the Lab Summary, we had some trouble setting up this lab. I actually think that we set it up correctly the first time, but because the picoamplifier is very sensitive, we thought that we had something connected wrong. We followed the circuit diagram from the lab manual which can be found below. The diagram is pretty straight forward to read, and I have also included pictures of our setup (and here is a link to Professor Gold's Lab Manual). We also used a digital voltmeter that was connected to the accelerating voltage power supply in order to get a more accurate reading of the voltage.

Diagram for Connections

Full Setup (without digital Voltmeter)

Power Supply Used for Filament Voltage and Picoamplifier

Power Supply Used for Accelerating Voltage and Picoamplifier

Bulb with Neon Gas and Ring

Procedure

For this Lab, we used Professor Gold's Lab Manual for the setup and procedure. As mentioned in the Lab Summary, we spent most of our time setting everything up. We began taking data by doing a rough scan between 0 and 30 Volts. We set the filament voltage to Vf = 2.1V, and took measurements in 1 volt increments. We then plotted the data right then and there to see if we had a graph similar to the one found in Professor Gold's Lab Manual. Our figure was similar, so we decided to do a more refined scan of the portion of the data where there were peaks. We scanned the 15-22 V range incrementing our data points by 0.25 V. We then tried to measure the ionization energy by flipping the battery. We then did the same rough scan from 0-30V in 1V increments. Finally we repeated the first process for collecting the excitation energy with the filament voltage set to Vf = 1.8V. The figures from Gold's Manual can be seen below. Our graphs for the corresponding data are very similar, but seem to be inverted. We are not sure why this is the case, but Prof. Koch agreed that our data matched what he has seen before.

In this lab we are recording the current that is flowing in the ring located in the bulb filled with Neon gas. The current in the ring changes because as electrons collide with Neon atoms, they are deflected toward and captured by the ring. The current is meaningful in that it allows us to determine where, or at what voltages, energy is lost by the free electrons (or absorbed by the bound electrons).

Excitation Energy Graph from Gold's Manual

Ionization Energy Graph from Gold's Manual

Data and Calculations

• Our Raw Data can be found in the chart below.

{{#widget:Google Spreadsheet |key=0At9fxsqtusShdC1icmZ3S2hCVmtwaGVoNmttMEdfclE= |width=1400 |height=650 }}

• The graphs for each of the trials are below.

Results

Note: We obtained the values for the excitation energies by finding the minimum peaks on our graphs.
From the Fine Run With [math]\displaystyle{ V_f = 2.1 V }[/math], we have the following Excitation Energies:

1st Excitation Energy: not apparent
2nd Excitation Energy: 18.0 eV with a 3.5% error from the accepted value
3rd Excitation Energy: not apparent
4th Excitation Energy: 21.0 eV with a 4.5% error from the accepted value

From the Fine Run With [math]\displaystyle{ V_f = 1.8 V }[/math], we have the following Excitation Energies:

1st Excitation Energy: 16.375 eV (we can assume that where there is a horizontal section of the graph, we failed to locate a minimum) with a 1.9% error from the accepted value
2nd Excitation Energy: 18.25 eV with a 2.1% error from the accepted value
3rd Excitation Energy: 18.875 eV (again, the horizontal portion means that we failed to locate the minimum)
4th Excitation Energy: 20.75 eV with a 3.2% error from the accepted value

Ionization Energy - This is where the slope changes from a lower slope, to a higher slope.

For [math]\displaystyle{ V_f = 2.1 V  }[/math]: 22 eV with a 2.0% error from the accepted value
For [math]\displaystyle{ V_f = 1.8 V  }[/math]: 22 eV with a 2.0% error from the accepted value

Because of our increments of 0.25V, all values are assumed to have a +/- 0.25 eV error.

Accepted Values

The accepted values for the excitation levels of Neon are:

• 16.7 eV
• 18.65 eV
• 19.75 eV
• 20.1 eV

The accepted Ionization energy for Neon is:

• 21.56 eV

Mistakes

^{SJK 21:51, 21 December 2010 (EST)}

21:51, 21 December 2010 (EST)
This is a really great discussion, and will help future students a bunch!

Matt and I made a really big mistake in this lab by not taking multiple trials for each filament voltage. Because of this, we were not able to do a proper analysis of our data, as well as an error analysis. I have no idea whether this data represents very closely the parent distribution of what we would have gotten with many trials, or if these measurements are terribly off. Also, after doing a coarse scan from 0-30V incremented by 1V, we did a refined scan incrementing by 0.25V. When trying to analyze the data, we found out that we should have done an even more refined scan. This probably would have allowed for a much more accurate report. If we had to go back and redo this lab, these are the two big things that we would do differently.

Error

We were not able to complete a proper error analysis for this lab. Because we took so long to set up this lab, we thought that taking one trial at [math]\displaystyle{ V_f = 2.1\lt ?math\gt and one trial at \lt math\gt V_f = 1.8 }[/math] would be sufficient data. Upon starting our data analysis, we quickly realized that with only one trial at each voltage, we would not be able to find an SEM for our data. We thought about averaging the two trials together, but this did not seem like the correct thing to do. Although they should lead to the same Excitation Energies, I do not believe that the two data sets are from the same parent distribution. So it seems that the values we report are very rough estimates of what many trials would have yielded. Despite the fact that we did not take many trials, it would seem as though our data is not too far off from the accepted values.

References

Professor Koch helped us set up the equipment in this lab, and I referenced Alex Benedict's Lab Notebook to compare our results.