User:John Callow/Notebook/Junior Lab 307/2009/10/14

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Millikan oil drop
I worked with Johnny Gonzalez for this lab.

Link to lab manual used

Link to my summary

Materials
Included equipment

(1) Apparatus platform and plate charging switch (Millikan oil drop apparatus AP-8210)

(1) 12 volt DC transformer for halogen lamp

(1) Roberts mineral oil (formerly Squibbs mineral oil)

(1) Atomizer

Required equipment

(1) High voltage power supply capable of 500V DC, 10mA (Used tel-atomic 50 and 500V supply)

(1) digital multimeter

(4) patch cords with banana plug connectors

(1) stopwatch

(1) micrometer to measure the distance between the brass plates

Recommended equipment (1) PASCO ME-8735 Large Rod Stand

(2) PASCO ME-8736 Steel Rods, 45 cm

(1) bottle of soap

(1) cloth suitable for cleaning lenses

(1) video camera and a proper mount (we didn't manage to set this up for our experiment but if one is available to take recordings through the telescope with clear enough picture it could greatly reduce the difficulty of taking measurements)

We lacked the recommended equipment so in order to raise the apparatus platform up to a reasonable eye level we stacked a bunch of text books.

safety
experimenter safety

There is a high voltage power supply being used along with a capacitor which one should be careful around. Don't disassemble anything with any power on.

Equipment Safety

Make sure the setup is stable and not to drop the equipment.

Clean off any oil and such on the equipment before and after setting up.

Be absolutely sure not to plug the power supply into the thermistor.

Be sure to not scratch any the optical equipment, use proper cleaning materials. We used the cloth that came with my glasses to clean the lenses.

Don't scratch the brass plate and plastic spacer.

Setup
The standard setup procedure may be found in the lab manual.

It is probably best to begin by cleaning the lenses, plates, plastic spacer, and the rest of the housing with soap and a suitable cloth (we used the cloth used for my eyeglasses on lenses and paper towels for the rest). There is a photo of the housing on page 4 of the lab manual. Then With the housing off we used a micrometer to measure the spacing of the two plates with the plastic spacer between. It is mentioned in the manual to be sure not to include the raised rim on the plastic spacer. Now put the housing back together. If you have the proper rods and base, set the apparatus on a stable table and raise it up to a comfortable level for viewing in the telescope. If like us you don't have this equipment, a few textbooks seemed to work fine. Just make sure the apparatus is level by using the leveling bubble built in. Now that everything is cleaned up it is time to align the optical system. On the apparatus there is an unscrew-able cylinder that has a small wire hanging down as shown in the picture. Take off the top of the housing, and replace the black cylinder inside on top of the plates with this unscrewed cylinder, wire facing into the small hole on the brass plate. Be gentle as a bent wire would mess with alignment. Once the wire is inside, connect the 12V DC transformer to the lamp power jack in the halogen lamp housing. Now bring the reticle into focus by turning the reticle focus ring. This is the ring closest to the outside of the telescope or nearest your eye when looking in, as shown in the above picture. It is focused when a grid becomes clearly visible like in the picture on the left. Once that is done, focus on the wire by turning the droplet focusing ring or the ring closest to the plate housing.

Now to focus the halogen filament. Adjust the horizontal filament adjustment knob. This knob is on the side of the halogen lamp housing, right next to the bubble level. Try to have the right edge of the wire be as bright as possible when compared to the center of the wire. I'd recommend just starting the knob at one side and turning all the way through to get a feel for what areas are brightest first. After that turn the vertical knob on the halogen bulb housing found on top till the light is brightest on the wire in the area of the reticle. Again I'd recommend turning all the way through to get a feel for it. Once this is done return the cylinder with the focusing wire by screwing it back into its original spot and put the other cylinder back on top of the plates. Be sure that the hole on one of the bases of the cylinder is facing down into the hole on top of the brass plate. If the hole is not facing down, when it comes time to spray oil into the housing it will not be able to find its way into the area being viewed.

Now plug the high voltage DC power supply into the apparatus, making sure it is not plugged into the thermistor and adjust the supply so that it is at about 500 volts. Connect the multimeter to the thermistor and set it to record resistance. The readings here will be used to measure the temperature in the droplet viewing chamber. There is a chart on the apparatus that relates a specific resistance to a temperature. It is now time to test spray into the apparatus to see if all is working. At the bottom of the housing there is a lever, set it to the spray setting. Take the atomizer, align it perpendicular to the plastic hole at the top of the housing, do a quick spray, and then squeeze the atomizer slowly. If nothing happens the atomizer may need to be primed which may be done by just holding it over something such as a paper towel and squeezing over and over till oil starts spraying. If all went well you should see a bunch of tiny drops when looking through the telescope. If you do not, check that the black cylinder in the housing has the hole facing down and that the lever by the housing is set to spray and try again. If still nothing, then try redoing all the steps focusing the lenses. Once the drops are viewable the experiment is ready to start taking measurements.

Taking data
To take data begin by releasing a fresh squeeze of oil from the atomizer into the apparatus as done before. We found that with the lever in the spray position drops were still being rapidly ionized so after the spray we turned the lever to off. Now looking through the telescope you'll be picking out a single oil drop to keep track of. Because of the high number of drops at first, I recommend waiting a bit till a good majority of the drops fall out of view. Once a reasonable number of drops are viewable choose one, and make sure not to lose it. Now record how long it takes for your drop to fall one major grid line. We did this by having the person tracking the drop tell their partner when to start and stop timing. Without a partner it is likely possible to set up a program on a computer to start/stop/record data from a button push but we didn't have anything like that set up. After recording the fall time, turn on the electric field and measure how long it takes the drop to rise back up one major grid line. Repeat these two steps for as long as possible.

If you are able to after a few recordings, turn the switch by the housing to the ionization setting for a few seconds and then back off. Now using the same drop start doing recordings again. Chances are your drop has now been ionized and the rise time will be much different than before. After a few more measurements if your eyes aren't killing you repeat till you have to take a break. Make sure to mark in your data when you ionized your drop.

Some notes

Try to pick a drop that isn't really close to another or they may interact with each other.

If a drop suddenly changes its rise time by a significant amount, it likely became ionized.

If you are able to get a camera set up to record video, and the drops are viewable, it is possible to do the measurements while just watching the recording. We didn't manage to do this, but because you can measure much more precisely when the drop crosses major grid lines this method would likely result in much better measurements.

Formulas and constant values
The formula and derivation used for finding the charge q of a drop may be found on pages one and two in the lab manual.

$$ q = \left[400{\pi}d\left(\frac{1}{g{\rho}}{\left[\frac{9*{\eta}}{2}\right]^3}\right)^{\frac{1}{2}}\right]*\left[\left(\frac{1}{1+\frac{b}{pa}}\right)^{\frac{3}{2}}\right]*\left[\frac{V_f+V_r\sqrt {V_f}}{V}\right] e.s.u.$$

q-charge in e.s.u. carried by the droplet

d-separation of the plates in the condenser 0.808 cm

$${\rho}$$ - density of oil $$ \frac{.866g}{cm^3}$$

g-acceleration of gravity $$ \frac{981cm}{s^2}$$

$${\eta}$$-viscosity of air in poise. The thermistor read about 1.9*10^6 which from the chart on page 20 of the manual that gave a temperature of 27 degrees centigrade. Then using the graph on 19 this correlates to 1.856*10^-4 poise

b-constant equal to $$6.17*10^{-4} $$ cm of Hg

p-barometric pressure 76.0cm of mercury found at http://www.widespread.com/daily.aspx?id=2580&d=10%2f21%2f2009. Used value at time 15:56 as that is around when measurements took place. Unfortunately the pressure inside the lab is probably different, but we had no equipment to measure it.

a-radius of the drop in cm as calculated by

$$ a = \sqrt {\left(\frac{b}{2p}\right)^2 + \frac{9{\eta}*V_f}{2g{\rho}}}- \left(\frac{b}{2p}\right)$$

$$ V_f$$-velocity of fall in $$ \frac{cm}{s}$$

$$ V_r$$-velocity of rise in $$ \frac{cm}{s}$$

V-potential difference across the plates 500 volts

The maple worksheet used to calculate the propagated error for each drops charge may be found here

data and calculation of q for each drop
The major grid lines are .5 mm apart or .05 cm. To find the velocity I took this distance and divided by the time it took to travel the distance.

Substituting the above values along with the values from the section on formulas and constants into

$$ a = \sqrt {\left(\frac{b}{2p}\right)^2 + \frac{9{\eta}*V_f}{2g{\rho}}}- \left(\frac{b}{2p}\right)$$

I find that $$a = 4.95*10^{-5} cm$$

and then plugging everything into

$$ q = \left[400{\pi}d\left(\frac{1}{g{\rho}}{\left[\frac{9*{\eta}}{2}\right]^3}\right)^{\frac{1}{2}}\right]*\left[\left(\frac{1}{1+\frac{b}{pa}}\right)^{\frac{3}{2}}\right]*\left[\frac{V_f+V_r\sqrt {V_f}}{V}\right] e.s.u.$$

I found $$ q = 4.74(15)*10^{-9} e.s.u.$$ assuming my error propagation program worked.

Doing the same for drop 2 I find that

$$ q = 9.17(16)*10^{-9} e.s.u.$$

$$ q = 9.74(28)*10^{-9} e.s.u.$$

and after ionization

$$ q = 6.74(13)*10^{-9} e.s.u.$$

$$ q = 5.35(18)*10^{-9} e.s.u.$$

after ionization

$$ q = 5.83(13)*10^{-9} e.s.u.$$



Finding the charge of a single electron e
What I want to do is try and find a linear function that is a line of best fit for these values. Problem is I only know the y coordinates and could find no formula to do this. I'm sure there is one, and this being the second time I've wanted to do this (the first time was in the Balmar series experiment where instead of trying to solve for n, m I just looked them up). I would like to have an analytical formula for this (if it is even possible) but for now I'll settle for making an algorithm in maple.

Assumptions made - To do this I am making a few assumptions. First that every electron is the same, and second that there is no fractional charges. From my experience with the e/m lab (lab notebook for e/m)this seems reasonable (also because books tell me this is true). If electrons could have different charges then it wouldn't be reasonable to expect there to be any sort of focused beam at all. I also observed nothing that looked like a half electron shooting off in that experiment and so have no reason to believe there is anything like that.

With these assumptions it would be true that

e*n=q for some n = 1,2,3...

My goal is to fit e such that n is as close to a natural number as possible for each different charge q found above. After a few hours of maple failing me I wrote the same script in matlab with instant success. The script is as follows

start = .1

ending = 5

steps = 100000

e = linspace(start,ending,steps);

n1 = (4.74./e);

n2= (9.17./e);

n3 = (9.74./e);

n4 = (6.74./e);

n5 = (5.83./e);

n6 = (5.35./e);

K = ((n1-round(n1)).^2+(n2-round(n2)).^2+(n3-round(n3)).^2+(n4-round(n4)).^2+(n5-round(n5)).^2+(n6-round(n6)).^2);

[C,I]=min(K)

e = .1 + I*((ending-start)/steps)

I based it off of least square minimization, but I don't have the error for q yet so that will have to be added later when google comes back up. With this Matlab finds e to be 0.4834 or correcting the fact that I canceled 10^-9 out in my script to keep my computer happy

$$e = 4.834*10^{-10} e.s.u.$$

Which is really close to the expected value (originally I had 2.785 here due to an error when entering data into my script.)

Complications
Maple may be great for symbolic manipulation, but for computations stick with matlab. Maple didn't like trying to find the value for e.

We forgot to turn the lever to spray many times.

We had the black cylinder upside-down a few times resulting in no oil making it into the viewing area.

The grid was way off and so had to be aligned, and even after that was a little bit off.

I stored all my data on googledocs, and just as my error propagation program in maple started to work properly it appears to have died on me. Luckily it came back up before I decided to go to sleep.

Originally entered the data into the matlab script wrong, after correcting this our best guess is really close to the accepted value.

questions
I'm wondering how Millikan originally found e using the charges. From the lab manual his data looks far more complete than ours so perhaps he just guessed at the values for n. Is there a better or more efficient way of finding e, perhaps finding an analytical formula if possible? This same problem came up when doing the Balmar series lab but I wasn't thinking too hard about it at that point.

LabVIEW files
Steve Koch 14:29, 30 October 2009 (EDT): Here are the LabVIEW files, in case you want to build off them.
 * [[Image:John Callow Millikan Analysis.vi]]
 * [[Image:Simulate Millikan Charge.vi]]
 * [[Image:Play Callow Function as WAV.vi]]


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