# User:Arianna Pregenzer-Wenzler/Notebook/Junior Lab/Millikan Oil Drop Summary

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## Contents |

## Millikan Oil Drop Summary

- link to the instruction guide/lab manual for Millikan Oil Drop (this experiment is not in professor Gold's manual

### purpose

The purpose of this experiment was to duplicate Millikan's famous experiment in which he was able to determine the charge of an electron to a very high level of accuracy. Millikan's result was later improved upon, yet his result was still a major accomplishment. In this lab Dan and I measured the rise and fall velocities of oil drops that were small enough in size to be suspended in air. We measured the fall velocities of the oil drops in a gravitational field and because I knew the density of the oil, the force acting on them (gravity), and the viscosity of the fluid in which they were suspended (air), and because it is assumed they are spherical in shape I was able to determine their radius. Once I knew the radius of the drops, their mass could be determined (this determination was built into the equations, I did not solve for it explicitly). The rise velocities are caused by an electric field, the speed at which a given drop will rise in this induced electric field is proportional to the charge carried by the drop. Using an expanded version of the equation given by Newton's 2nd law, qE = mg +kv_{r}where k in the coefficient of friction and E is the intensity of the electric field (voltage/separation distance between the plates producing the potential difference), it is possible to calculate the charge being carried by the oil drop. If we had done the entire experiment, we would have both measured the rise and fall velocities of our drop, then we would have changed the charge carried by the drop. By analyzing the change in the velocities caused by the change in charge we could have attempted to show the atomic nature of electrons by showing that the charges carried by the oil drops are integral multiples of some smallest charge. This would show that there is some smallest charged quantity, the electron.

^{SJK 02:34, 18 December 2008 (EST)}

^{SJK 02:36, 18 December 2008 (EST)}### analysis

Analysis for this experiment is tough because we did not change the charge on any of our drops, so while I was able to calculate a best guess for the charge on each of the four drops we took data on, I have no way of saying how this calculated charge compares to integral multiples of some smallest charge.

I calculated my best guess for the charges on our oil drops and the error by taking the average of the rise and fall velocities of the drops and the SEM. I then used these average velocities and the average velocities ± the SEM to calculate there values of the charge for each drop. I left my values for charge in e.s.u. (electrostatic units)

**q1 = (5.4±.05)E-9 e.s.u.**

**q2 = (2.7±.28)E-9 e.s.u.**

**q3 = (4.5±.28)E-9 e.s.u.**

**q4 = (4.3±.22)E-9 e.s.u.**

The accepted value for the charge of an electron is

**e = 4.803E-10 e.s.u**

Obviously my drops were all carrying more than one electron, but I am not going to compare my charges to the accepted value, because we did not take any data that would allow me to make any assumptions about the size of the smallest integral unit of charge being carried by these drops.

I chose to present my data by plotting my values for q along with their error bars. For the sake of comparison I also plotted integral multiples of e to see where my calculated charges fell in relation to the accepted value for the charge of one (or more electrons). You will see on my plot that one of my calculated values falls right on top of an integral multiple of e. While this might look good it says nothing, and that becomes apparent when you look at the error bars. In all cases they span at least one full multiple of e. Also, as I already stated, there is no way to look at the accepted value of e, and my data and draw conclusions between the two. I mainly did this graph as an exercise in computer skills and presentation.

### notes on data analysis

To things came up as I was analyzing my data that I want to comment on further:

- When I was calculating the components of the equation for charge I knew I was in trouble when my values for the radius of my oil drops were in the order of .03. All my data was in cm because my equation was in electrostatic units so these radii were around .03 cm or .3 mm, and the distance over which I had been watching the drops fall in the viewing chamber was .5mm. Big red flag, I went back over my units but couldn't find anything, so the only conclusion I was left with was that we had some extreme systematic error. I knew our technique had been poor, and this just pointed that out.
^{SJK 02:40, 18 December 2008 (EST)}

- I was a little unsure how to deal with my error, I had two sources the rise and the fall velocities and they each had different impacts on the final equation for charge. It occurred to me at the end that I had been using my upper(or lower) limit in both the rise and fall velocities in the same equation to calculate my upper (lower) limit range for q. I did this without thinking, I just automatically paired my max and min rise and fall velocities, but if a object falls faster it has greater mass while if it rises faster it has greater charge. Now thinking about it further it sounds like I paired the velocities correctly, because a greater charge would indicate more electrons and therefore a greater mass.

^{SJK 02:41, 18 December 2008 (EST)}My data analysis Excel sheet and my MatLab code published to a word document are attached at the end of the lab notebook entry

**Interesting**

I just uploaded a plot of my corrected data (with the actual measured value of the voltage and the viscosity on the day we took the data). I did not expect to see anything much different on the new plot compared to the original one, but seeing them side by side it looks the the values I calculated for the charge on my four drops correspond to integral multiples of the charge of an electron 3 out of 4 times when I put in the actual values for voltage and viscosity.

### what I learned

I gave the subject of data presentation a lot of thought in this lab, and I was very pleased that I was able to put together a plot that showed what I wanted it to show. I the process I thought a lot about my data, and what I actually had to show as far as results for this lab, not much, still it was a valuable experience.

I am also learning a great respect and admiration for the early pioneers of physics and math, like Millikan, and many others that I am learning about in this and other classes.