Deducing the Elementary Charge from Milikan's Oil Drop Experiments

[imatreyu]

Homework Statement

In an early set of experiments, Milikan observed that the following measure charges, among others, appeared at different times on a single oil drop. What value of elementary charge can be deduced from these data?

1) 6.563 x 10^-19 C
2) 8.204 x 10^-19 C
3) 11.50 x 10^-19 C
4) 13.13 x 10^-19 C
5) 16.48 x 10^-19 C
6) 18.08 x 10^-19 C
7) 19.71 x 10^-19 C
8) 22.89 x 10^-19 C
9) 26.13 x 10^-19 C

Homework Equations

I have no idea. :( Doing this graphically is NOT an option. My answer needs to be 5 significant figures.

The Attempt at a Solution

I subtract each of the answers in the manner... B-A, C-B and so on. From this, I get two distinct sets of numbers. I take the average of each set of data and get 1.62525 and 3.2665.Then I divide the 3.2665 by 1.62525 to get approximately 2. Then I divide 3.2665 by 2 and get 1.63325. . .

I have no idea why that works! What am I doing when I do that? It was explained to me by a friend, but I don't understand why that works or what that is doing. . .

 

[Borek]

Each charge is a multiply of elementary charge.

That means difference is also always a multiply of elementary charge.

Imagine you are given small bags with identical marbles inside. You can only weight the bags and you are asked to find mass of the single marble. Mass of each bag is a multiply of mass of a single marble, differences are also multiplies of a single marble mass. Lowest possible mass - and lowest possible difference - is that of a single marble.

 

[imatreyu]

Thank you so much for your explanation using the marbles-- it's very informative. Therefore-- yes, I understand that every charge is a multiple of the elementary charge.

However, I'm not sure how that applies to what I wrote above. . .still. . .

 

[Dadface]

Thank you so much for your explanation using the marbles-- it's very informative. Therefore-- yes, I understand that every charge is a multiple of the elementary charge.

However, I'm not sure how that is relevant, as I don't know any information regarding mass.

You do not need to know the mass of the particles in order to find the elementary charge.

 

[imatreyu]

My initial instinct was to use the GCF of all of the values; however none of them are integers and I imagine such an endeavour would be really challenging and hard. . . and maybe not even correct or useful. Ugh. . .

 

[Dadface]

Using your numbers what is the smallest charge you detect? Are the other measured charges integral amounts of this smallest charge?Could this smallest charge be the elementary charge?

 

[imatreyu]

Well the smallest charge is 6.563 x 10^-19 C. (Right?)
This is obviously not the elementary charge, though. . .

 

[imatreyu]

P.S. It would help if someone could read over my Attempt at a Solution and explain why that's correct/ what that does/ why I need to do that (if that's correct). I'm so sorry about this. I'm just horribly confused here. .

 

[Dadface]

Well the smallest charge is 6.563 x 10^-19 C. (Right?)
This is obviously not the elementary charge, though. . .

6.563? In your first post you identified a charge which was one quarter of this.

 

[imatreyu]

6.563? In your first post you identified a charge which was one quarter of this.

Really? I'm horrible at math; but isn't it that:

6.563 x 10^-19 C < 8.204 x 10^-19 C
6.563 x 10^-19 C < 11.50 x 10^-19 C
6.563 x 10^-19 C < 13.13 x 10^-19 C
6.563 x 10^-19 C <16.48 x 10^-19 C
6.563 x 10^-19 C < 18.08 x 10^-19 C
6.563 x 10^-19 C < 19.71 x 10^-19 C
6.563 x 10^-19 C < 22.89 x 10^-19 C
6.563 x 10^-19 C < 26.13 x 10^-19 C

?

 

[Dadface]

As I said above you have already identified a number which is smaller than 6.563.What is this number? Does it divide into all of your results an integral number of times? Remember that there are experimental errors and that the numbers are unlikely to be exact integers.

 

[imatreyu]

Ahh.. . I'm sorry. I just don't know what number you're referring to, and I still don't understand. Could you identify what number you're talking about? I don't see anything smaller than 6.563 x 10^-19 ... (Forgive me if this is just totally stupid, it's 2 AM where I am...and I'm a little dead.)

I really need an explanation of how the procedure I described in "Attempt at the Solution" works, if it's correct or if it's totally wrong. . . I would like to understand it. .

 

[Dadface]

You referred to the number in your first post with your attempt at a solution.The smallest number you found was 1.62 times ten to the minus nineteen approximately.Stick with it a little longer imatreyu and see what happens when you divide all of your results by this smallest number

 

[Borek]

You have calculated series of differences, right?

difference is also always a multiply of elementary charge.

The smallest number you found was 1.62 times ten to the minus nineteen

Do you see a link now?