# User:Tyler Wynkoop/Tyler's Page/Millikan

## Millikan Oil Drop Experiment

^{SJK 01:00, 14 October 2010 (EDT)}### The Lab

For a large portion of the history of the study of the inner workings of the atom, electrons were known to exist, but measuring the charge of a single electron was a daunting, if not impossible, task. In 1909 Robert Millikan and Harvey Fletcher devised and experiment designed to do just that. By measuring the rise and fall of a tiny oil drop floating between electrified plates, the minuscule charge of the electron could be discovered. It won Millikan the 1923 nobel prize in physics because of the experiment.

In this lab, we attempt to duplicate Millikan's success and measure the charge of the electron. The premise of Millikan's experiment is to measure the fall time of a droplet over a given distance (in our case, a half millimeter) due to gravity, and compare that to the rise time of the same droplet when voltage is applied across the chamber.

### Theory

The theory is here is in the balance of the forces between the charge of the drop and the pull of gravity. The charge of the electron may be calculated by the formula:
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle Eq=mg+kv_r}**
Where E is the electric field, q is the charge of the drop, m is the mass, g is the acceleration due to gravity, k is the coefficient of friction and **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle v_r}**
is the rising velocity. Mass can be found in terms of the volume of the droplet multiplied with its density, and k may be found by the relation between the rising velocity and the falling velocity.

### Results

^{SJK 00:54, 14 October 2010 (EDT)}The final calculation is obnoxiously large, but fairly straightforward. With the data gathered and applied to this formula, the resulting value over our best data is a multiple of q = 1.62E-19 ± 2.24E-21 C by means of the least squares approximation. This represents the fundamental charge on the electron. The accepted value of this charge is q = 1.60217646*10^-19C. This means that our estimate was off by approximately 1.10%

^{SJK 00:57, 14 October 2010 (EDT)}### Other Notes

^{SJK 00:56, 14 October 2010 (EDT)}The error and calculation was done all by matlab code courtesy of Dan Wilkinson, Cheers to you Dan. It, along with our step by step findings, data, and procedure can be found here [1].

The procedure, lab manual, and equipment manual can be found here [2]