# Physics307L F08:People/Young/Young's millikan

## Millikan Oil Drop

### Summary

In this experiment attempted to spray a fine mist of charged oil droplets into a small container where they could be observed being effected by a positive potential difference, a negative potential difference and gravity. This experiment is a duplicate of Milikan's oil drop experiment explained in the lab manual Each drop measured in this experiment has a different value for mass and charge and by evaluating the drop velocity under gravity alone and the rise velocity in a potential difference I will find the value for mass and charge. Since the amount of charge on the oil drops are quantized we can assume that the value of charge in a integer times the value for a charge of an electron. With all of this we are going to find the charge of an electron. As given by

### Error Analysis

Due to the limited time provided in is experiment and the problems faced we were unable to acquire data for the the fall time of the droplets under a potential difference pushing the droplets downward. Also, we did not have time to change the charge on the droplets and then retake data. Therefore I have no way of comparing the same droplet with itself with a different charge. If I did have this information I could make a linear plot of various charges vs rise time and then I could find the value for charge by looking where the line crosses the one axis. I assume that data would gather around the true value and by averaging all of my various values for the quantized charges I could see what the elementary charge must be.

Also when taking data the manual suggested that we take up to 20 data points per trial per drop. When we were observing the drop we could only view the drop for a maximum of ten trials. I believe that the oil drops were loosing mass as it slid up and down. If this is the case it would explain why the drop slowly became less and less visible. Also, there if we were loosing mass this means that our fall time was changing since the droplet was loosing mass all the while. SJK 02:45, 18 December 2008 (EST)
02:45, 18 December 2008 (EST)
Hmmm...I would think it's more likely that the drop was drifting out of focus?

### Abstract

By knowing the fall time and the rise time we will use the equation.

$Eq = mg + kv_r \$

As explained in the lab manual, we come to the final equation.

$q = (400\pi d (\frac{1}{g\rho}[\frac{9\eta}{2}]^3)^\frac{1}{2})((\frac{1}{1+\frac{b}{pa}})^\frac{3}{2})(\frac{v_f+v_r\sqrt{v_f}}{V}) \$

$q \$ is the charge in Coulombs
$d \$ is the separation of plates in the condenser 7.64e-3
$\rho \$ is the density of our oil in kg/m^3
$g \$ is the acceleration due to gravity 9.8 m/s^2
$\eta \$ is the viscosity of air in 1.983e-5 kg/m*s
$b \$ is a constant equal to 6.17e-6 (m)
$p \$ is the barometric pressure of mercury
$r \$ is the radius of the drop
$v_f \$ is the fall velocity in cm/s
$v_r \$ is the rise time in cm/s
$V \$ is the potential difference of the plates

### Analysis and Discussion

Using the values described above I found the charges of each of my droplets to be

$q1=8.41*10^-6\$ C is the charge on the first oil drop
$q1=8.8841*10^-6\$ C is the charge on the first oil drop
$q1=10.01*10^-6\$ C is the charge on the first oil drop
$q1=5.49e*10^-6\$ C is the charge on the first oil drop
SJK 02:50, 18 December 2008 (EST)
02:50, 18 December 2008 (EST)
I can't find your analysis anywhere to look at, but clearly there is at least one major error in your calculation. These numbers are way way out of the ballpark. Like 13 orders of magnitude! You could deduce based on what you saw that the droplets only had slight charge. Furthermore, you can tell by looking at the data that drop 4 should have more charge than drop 3, since they have roughly the same fall time and 4 has much quicker rise time.

Much data is missing from this analysis as the results show. They are not even close to the accepted value for the charge of an electron. I believe that I misunderstood the meaning of a "good sized drop" and so a the data that we have does not show a good trend to begin with. During our 6 hours in this lab, 5 of them were me and my lab partner fiddling with the apparatus to get droplets that wouldn't disappear after 5-8 readings. I believed that if the droplets were getting less visible they were getting smaller. I hypothesized that the droplets were leaving trails of oil behind. Therefore the oil droplets were leaving mass behind and charge behind much like a drop of water on a windshield. In order to get droplets to appear we had to remove a plug that was used to reduce wind on our windshield. This effect might not have been so bad had it not been for this wind. Our droplets would zigzag from right to left. If the droplets only moved up and down then we would have known that the oil would have not been lost after one trial as a result of the oil droplet not loosing any more mass after retracing it's steps. With this wind in the apparatus the droplet was unresponsive to the Voltage after 5 trails.