# User:Thomas S. Mahony/Notebook/Physics 307L/2009/10/26

Millikan Oil Drop Revisited Main project page
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## Lab Summary

SJK 16:33, 14 November 2009 (EST)
16:33, 14 November 2009 (EST)
Excellent primary lab notebook, as usual!

# Equipment

### Equipment used in both the original experiment and the followup

• Pasco Scientific AP-8210 Millikan Oil Drop Apparatus
• Mineral Oil
• SMIEC Micrometer
• Wavetek 85XT Multimeter
• TEL-Atomic 500V DC Power Supply

### New equipment

• Light similar to the Magnoclip LED Work Light & Laser Pointer
• Creative USB webcam
• Logitech USB webcam
• CCD camera (typical for use in an optics lab)
• Plano convex lens with focal length ~10cm
• Ryan's Canon XH-A1 HDV Camera + tripod

Note: We forgot to write down the model numbers of the Logitech, Creative, and CCD cameras, but we will get this information the next time we are in the lab

# Week 1- No Camera

## Setup

First, we tried using the Creative and Logitech webcams to see the droplets and take data. Then we ended up just following the procedure we used in the original experiment.

## Data

First, we set up the Logitech camera. The focusing wire was easily seen, but the gridlines were hard to make out due to the camera's low resolution. We tried the same thing with the Creative camera, but again, the gridlines were hard to distinguish from one another. After putting the drops in for both cameras, the light was not bright enough to see anything, despite changing cameras' integration times, contrast, and brightness settings.

After our attempts with the cameras yielded no data, we took data in a similar fashion as the original experiment: we squirted some mineral oil into the chamber with the ionization source set to the spray droplet position. We then turned it off, played with the capacitor plates until we found a suitable drop, and proceeded to time it as it rose with the force of the electric field and fell due to gravity. We did not repeat our previous mistake of measuring the fall time of the droplet WITH the electric field on.

Raw data sheet:

Ryan decided to name our droplets

## Analysis

Charge on each droplet vs integer multiples of elementary charge

Though I couldn't put it into words at the time, I think the reason the gridlines were hard to make out using the cameras was that the gridlines were spaced so close together on the camera screen that sometimes multiple lines would be seen by the same pixel. This would explain the random spacing of what appeared to be "darker" lines rather than the thicker lines spaced every .5 mm apart.

Unlike the first experiment, the pressure was calculated using the barometric equation (from wikipedia):

$P = P_0 e^{-M g z/RT}\,$

and using the approximation that UNM is located at about 5335 feet above sea level according to UNM's soccer page.

The charges for 8 different droplets were calculated using the formula on page 9 in the Pasco Manual:

• Drop 1: $1.17(4)\cdot 10^{-19} C$
• Drop 2: $2.7(1)\cdot 10^{-19} C$
• Drop 3: $1.2(3)\cdot 10^{-19} C$
• Drop 4: $3.0(1)\cdot 10^{-19} C$
• Drop 5: $1.3(2)\cdot 10^{-19} C$
• Drop 6: $1(5)\cdot 10^{-19} C$
• Drop 7: $2.5(1)\cdot 10^{-19} C$
• Drop 8: $2.2(5)\cdot 10^{-19} C$
All the analysis was done using this spreadsheet.SJK 16:21, 14 November 2009 (EST)
16:21, 14 November 2009 (EST)
Impressive excel sheet, in that it appears you've shown all the calculations in much detail. However, I have to say I had a tough time following yours and Tom's spreadsheets, since it wasn't exactly the way I would have approached it. So, I can't confirm whether your analyses are correct. Given the amount of care you took in acquiring the data, I'd be surprised if the reason you're off is because of errors in timing. My guess would be either analysis error or perhaps with your new lighting technique, you were not looking in the correct plane, and maybe there was a magnification error.
Because there were uncertainties in both the up and down velocities, the process of getting an uncertainty in the charge involved using the method of partial derivatives (in my case approximated by a small change in the velocity) that can be seen on wikipedia.

Because droplets 3, 5, 6, and 8 had such wildly varying down times, their calculated charges are more likely to be erroneous despite their not always outrageously large SEMs (except in the case of drop 6. Poor Pubert).

These calculated charges can be compared to integer multiples of the accepted value of the charge of a single electron (from wikipedia):

e = $1.602176487(40) \cdot 10^{-19}$C

# Week 2- Camera

## Setup

For the second week we intended to use a camera to make the data taking process easier to see, and possibly more precise due to the use of recording and the ability to analyze the data frame by frame instead of using a stop watch. First, we set up Ryan's camera to look at the droplets. Before moving to the next camera, we removed the lamp housing with the incandescent bulb in it and replaced it with LED light. We tried Ryan's camera again. Finally we set up the 2" lens behind the eyepiece and put the camera at a distance about 10 cm away (we moved it until it looked to be most in focus).

## Results and Analysis

Ryan's camera was able to see the droplets with the incandescent bulb, though they were extremely out of focus. Also, we had to turn down the shutter speed to see them, which resulted in choppy video. He also turned up the gain setting, but it made the whole video much fuzzier, and since the droplets were already out of focus, they were just as difficult to see as with the gain turned down. After switching out the incandescent light with the LED, the droplets became even harder to see, due to the background becoming much brighter than before. Next we tried looking through the eyepiece to see if the droplets were easier to see. We ended up moving the light around in circles a little until the droplets were lit very brightly, but the background was dimmer. We repositioned Ryan's camera, hoping to see the droplets now that they were much brighter vs the more dimly lit background grid. We could not see them, however. I suspect that because the grid was now much dimmer, even though the droplets were brighter than before, the camera just wasn't receiving enough light.

We decided to switch to a much more sensitive CCD camera. We decided to focus the camera using the focusing wire before trying the droplets. After setting up the lens and focusing the CCD camera, we put in some droplets. They were not visible. We tried changing all the settings on the CCD camera: brightness, contrast, integration time, etc. We moved the light as close as possible to maximize the intensity, but it just wasn't enough. Despite how sensitive to light a bare CCD is, the fact that we had to place the camera so far from the eyepiece meant that there just wasn't enough light.

SJK 16:29, 14 November 2009 (EST)
16:29, 14 November 2009 (EST)
I am confident with enough time and the right optics, you could make it work very well with video. Hopefully even though it didn't work out, you got a good experience trying things out. Here is a paper from Dinesh Loomba (professor in our department) from work he did with Martin Perl's group at Stanford: http://link.aps.org/doi/10.1103/PhysRevLett.99.161804 They had a wicked video tracking setup and were able to track over 42 million drops!

# Conclusions

### Cameras

In our original experiment, we decided the idea of using a camera to collect data was a good idea to try. In this experiment we tried 4 different cameras, using 2 different light sources. I have decided that the use of cameras does not make this experiment any easier. First, most of the cameras need to have a resolution high enough the resolve the difference between 2 different gridlines. This rules out many commercial webcams. Next, the camera has to be able to be placed fairly close so that there is not a huge loss in intensity. This rules out most cameras used in the "scientific" setting, as they require longer distances to focus the image. If the system had been build with the use of a camera in mind, these cameras could have probably been accommodated, but as the Pasco setup is designed for the human eye, these cameras can also be ruled out. Finally, this leaves us with the only viable option of high definition cameras with high powered optical zoom capabilities, such as Ryan's. His camera was able to see the droplets using a dim light source, but was unable to focus on them. And this brings me to the definitive problem with using a camera for this set up. Camera's cannot easily focus back and forth between the grid and the droplets. Our eyes basically focus on whatever is in the center of our vision (a "focal point" if you will), and as this moves, our eyes refocus. Cameras cannot do this, since their "focal point" is fixed. Ryan's camera had an autofocus, but again, as it could not "track" the droplet's movement, and was sensitive to light changes as well, this feature really only made it harder to see the droplets. I have concluded that this experiment is better done with your eyes, at least to the extent of the options we tested.

### Light Source

The incandescent light source included in the Pasco setup is adequate to see the droplets. However, it caused eye strain after short periods of time, and caused us to switch out who took the role of watching the droplets. I would highly advise the use of the LED light we used, or something similar. With a few minor adjustments, both the droplets and the grid are much easier to see.

### Data Conclusions

We obviously had some huge systematic error here. If the calculated charge was proportionate to 1 variable in a simple way, I could estimate if our times were too long or too short, but since the relationship is fairly complicated I can only speculate that we must have made our errors somehow in the process of timing the droplets. To make an improvement, the only possibility I could imagine would be to take a lot more data.

It certainly would be possible to group the droplets into categories of having either 1 or 2 electrons. However, I feel like the extent of the error is disproportionately large when compared to the spacing of electron charge levels. For this reason, I could not specify with confidence how many electrons each droplet had. Despite the calculated charge of droplet 6 being the closest to any integer multiple of the elementary charge, it is simply a bad data point. It's error bars encompass anywhere from 4 e to -2. The droplets closer to having a charge of 1 e (with the exception of droplet 8) are all fairly close, but the droplets closer to 2 e are spaced pretty far apart, even to the extent that it looks as though some of them could have a 1 e charge.

## Acknowledgments

Thanks to Ryan, my lab partner, for his help. I'd also like to thank Dr. Koch and Pranav for their help in setting up the cameras.