# Homework Help: Millikan's Oil Drop (Finding modified charge)

1. Nov 10, 2007

### fbelzile

1. The problem statement, all variables and given/known data

Hi everyone,

I am working on Millikan's oil drop experiment. The first 2 columns were given to us, while we figured out the rest (chart/formulas below). I now have to complete another column beside "Mass" with the caption: "Excess Electrons" My teacher said that he modified the charge of electrons so we cant use the 1.602x10E-19 constant, instead, we have to find our own. He talked about getting a lowest common multiple of the numbers in the Mass column. How do I do that? He said there was an easy way that would take 5 minutes, yet he never told us how... Once I know the charge of the electrons, I can then find the excess number easily.

Here are the constants given to us:
Code (Text):

$$\rho$$oil = 930.000 kg/m3                d between plates = 2.000 x 10–2 m
$$\rho$$air = 1.230 kg/m3                  d between lens lines = 1.300 x 10-3 m
$$\eta$$air = 2.016 x 10-5 Ns/m2           g = 9.807 m/s2

Here is my table of values:
Code (Text):

Potential
Difference (V)    Time (s)  Velocity (m/s)      Radius (m)           Mass (kg)

222.656            21.29      6.10615E-05        7.79854E-07    1.84761E-15
-347.614       18.35     7.08447E-05         8.40007E-07    2.30898E-15
78.688              31.13     4.17604E-05         6.44928E-07    1.04498E-15
-804.663       6.61           0.000196672        1.39959E-06    1.068E-14
494.85              23.02     5.64726E-05         7.49978E-07    1.6433E-15
-231.743       18.35     7.08447E-05         8.40007E-07    2.30898E-15
-109.453       24.98     5.20416E-05         7.19954E-07    1.45374E-15
107.376            30.65     4.24144E-05         6.49959E-07    1.06962E-15
-275.638       16.35     7.95107E-05         8.89902E-07    2.74535E-15
-559.107       33.69     3.85871E-05         6.19941E-07    9.28161E-16
-357.002       21.84     5.95238E-05         7.69972E-07    1.77826E-15
103.731            49.79     2.61097E-05         5.09953E-07    5.16608E-16
-231.743       18.35     7.08447E-05         8.40007E-07    2.30898E-15
108.614            39.86     3.26141E-05         5.69944E-07    7.21222E-16
-153.001       21.84     5.95238E-05         7.69972E-07    1.77826E-15
-237.659       23.65     5.49683E-05         7.39921E-07    1.57808E-15
360.178            17.92     7.25446E-05         8.50026E-07     2.39259E-15
-204.993       31.62     4.11132E-05         6.39912E-07    1.02078E-15
183.994            17.67      7.3571E-05          8.56018E-07    2.44354E-15
-78.062            42.81      3.03667E-05         5.49957E-07    6.47973E-16
480.237            17.92      7.25446E-05         8.50026E-07    2.39259E-15
125.673            27.6           4.71014E-05         6.8493E-07      1.25173E-15
146.65             32.63      3.98406E-05         6.2993E-07      9.73753E-16
-220.688      17.11          7.5979E-05       8.69913E-07    2.56448E-15
-670.694      18.8            6.91489E-05         8.29893E-07    2.22658E-15
282.012            28.88      4.50139E-05         6.6958E-07     1.16944E-15
-168.613      29.73          4.37269E-05         6.59939E-07    1.11965E-15
96.35               29.73      4.37269E-05         6.59939E-07    1.11965E-15
-152.575      38.5            3.37662E-05         5.79923E-07    7.59772E-16
185.546            21.29      6.10615E-05        7.79854E-07     1.84761E-15
-323.371      19.26           6.74974E-05        8.19923E-07     2.14729E-15
256.295            14.17      9.17431E-05         9.55908E-07    3.40267E-15
335.137            12.95      0.000100386         9.99922E-07    3.89466E-15
-746.08            17.51      7.42433E-05         8.5992E-07      2.47711E-15
-231.743       18.35      7.08447E-05         8.40007E-07    2.30898E-15
256.889            27.2            4.77941E-05         6.89948E-07    1.27944E-15
307.489            31.62      4.11132E-05         6.39912E-07     1.02078E-15
-240.118       17.92      7.25446E-05         8.50026E-07    2.39259E-15
139.941            25.69      5.06033E-05         7.09936E-07    1.39389E-15
122.996            31.62      4.11132E-05         6.39912E-07    1.02078E-15

2. Relevant equations

Code (Text):

velocity = [U]d$$_{}lens$$[/U]        radius = [U] $$\sqrt{}(9/8)(n)(Vo)$$[/U]    (square root of the whole fraction)
t                      g(Pa-Po)

mass = (4/3)(pi)(r^3)(Po)              q = [u](m)(g)(Dp)[/u]
Volts

q = (N)(e)
^
|
-----(Where N is the excess electrons, and e is the charge)

3. The attempt at a solution

I tried taking the smallest number and dividing it by all the masses... This got me 40 other numbers. I need one number to be the charge of the electron.

Thanks for any help!!

2. Nov 11, 2007

### catkin

Try sorting the numbers by size, replacing any very similar ones with their average, removing duplicates, calculating differences ...

3. Nov 11, 2007

### fbelzile

Been there done that... Tried every possible combination of numbers and operations. I tried using the 1.602x10E-19 constant anyways, but it didn't work (numbers were not like: 32.00000234)

Any real pointers?

4. Nov 11, 2007

### catkin

Let's see the steps of your sorting, group averaging and difference calculations.

5. Nov 12, 2007

### fbelzile

Let's see you say: "I don't know... sorry" Like I said, the values are given to us and should work out without averaging (he told us).

I also handed in the lab (without that part answered) today. It's OK for now, but I'm still curious on how I'd go about solving this.

6. Nov 13, 2007

### catkin

Methinks you do exaggerate.

7. Nov 13, 2007

### fbelzile

I asked a friend how he did it. He said he subtracted the 2 smallest numbers and then divided that number by ten "a bunch of times" until it worked...

Any reasoning why that worked?

And catkin: "An exaggeration is a truth that has lost its temper." ~Kahlil Gibran

8. Nov 14, 2007

### catkin

Yes - my previous post.

Averaging is required iff [sic] ordering the data produces values that are the same except for experimental error as will be the case with typical Milikan experiemnts.

9. Nov 14, 2007

### catkin

Why didn't you calculate the column for q?

My algorithm was for using on the q fiqures and was designed to make charge e visible from "noisy" and unordered q values -- which is what an experiment would produce.

I guess you mean he subtracted the smallest number from the next smallest number. If he was working on q values and they happened to be one e different then he would get a rough value of e. Rough because he was not using averging to reduce the effect of experimental inaccuracies in the data.

It wouldn't make any sense to divide by 10 any number of times except to convert charge from Colulombs to microCoulombs or whatever.

Last edited: Nov 14, 2007