Millikan Oil drop experiment


by jenny777
Tags: experiment, millikan
DarthMatter
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#19
Feb13-14, 06:00 PM
P: 18
For drop 1 and 3 I get 10.8/6.4=1.6875=16875/10000=27/16.
jenny777
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#20
Feb13-14, 06:06 PM
P: 28
but that value doesn't make too much sense to me since, drop 2 has less charge than drop 3, but has 45 charges..... I have no idea why the author published such answers/methods on a textbook......
DarthMatter
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#21
Feb13-14, 06:17 PM
P: 18
Quote Quote by Vanadium 50 View Post
DarthMatter's advice is stunningly bad. If you were to follow it in a class that I was teaching, I would flunk you.

1) The point of a lab is not to see if you can find the "correct" value in a book somewhere and write it down.
2) Converting N measured values into N^2 pairs of values does not add information. It just adds complexity to the analysis.
Hi,

1) You can consider the literature to find out what the correct value should be, and discuss why you came to another conclusion. At least that is how I did it im many lab reports at my non-US university.
2) I was not converting N values into N^2 values (or just accidentally), just taking the differences of the smallest charge-multiples with the measured charges. This was similarly also considered by others. Most of these values can be thrown away since their absolute value is too big to be considered an elementary charge.
Vanadium 50
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#22
Feb13-14, 06:26 PM
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To add - most people are adopting the strategy "guess at the number of electrons on the sphere with the least charge, and see how well that agrees with the other measurements". This strategy fails if that sphere is mismeasured, even if all the others are perfect.

A better way, especially if you can use Excel, is to pick a candidate elementary charge, vary it, and find the charge that gives you the minimum total deviation from integer charges of the ensemble. If you do this, the charge you get will not be the book value, but it is a lot more honest.
DarthMatter
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#23
Feb13-14, 07:40 PM
P: 18
I was actually going to start another rant about how the number of usable values by my method was actually not squared and how it is pure rhetorics to claim it was, even if it seems mathematically right. But I consider your method with the total (standard?) deviation to be sophisticated and cool, so maybe you could elaborate a little more so I don't have to start to babble again.
jenny777
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#24
Feb13-14, 08:01 PM
P: 28
I tried to find a charge that when divided into each one of the measured charges gives a result within an error bar or two-three of an integer for each and every charge... but there was none in my 10 data sets

and by the way, after getting those 100 values, how should I plot it? what would my x-axis be?

Thank you :)!!
Vanadium 50
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#25
Feb14-14, 06:42 PM
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Jenny, please look at what other people are saying. The "100 values" technique will not help you. More importantly, you need more data. The data you have is not good enough for you to measure anything. You don't quote uncertainties, but you probably have at best about a 5% measurement of the charge of each sphere. That means that the only data points that will help you constrain e are those from spheres with fewer than 10 electrons on them: a 5% uncertainty means you cannot distinguish a 10 electron sphere that was measured high from an 11 electron sphere that was measured low.

DarthMatter, the way the method works is as follows. Assume the smallest charge is q. For each measurement q, find the smallest non-integral part of the number Q/q. If Q=11.5 and q = 2, Q/q = 5.75, so write down 0.25. (6-5.75 is 0.25). That's the minimum error on each measurement, assuming q = e. Now total all those up. For some value of q, this is at a minimum: that's the q for which the values of Q/q look most like integers, and is the best estimator of the fudamental charge.

This can be made more complicated in multiple ways, but the idea is to answer the question "What value of q makes my measured values of Q/q look most like integers?"
DarthMatter
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#26
Feb14-14, 11:43 PM
P: 18
@Vanadium 50:

So I was wondering why the differences of the original measured values should be worse data than the original values itself. The upside seems to be that you can cover more possibilities of sphere charges, by taking away all the charges of one sphere (which you measured) from another one (which you measured), even multiple times. But the answer seems to be: Because subtracting a 5% measurement from another may give a much bigger uncertainty? Would taking the differences be ok if you had made a very precise measurement of the charges?

I like the method with the minimum error best, I have to admit.

@Jenny777:

The graph shows each of your values minus i times your smallest measured charges for each measured data point, the idea was to just sort out the smallest values to get some candidates for the elementary charge. But only the values which have E-19 at the end can be considered as such candidates, since your smallest measured charge already is in this regime (which are actually around twenty). So the x-axis has no real meaning here, 0 on it would be your first data value minus 0 times the smallest charge, 1 on it would be your first data value minus 1 times your smallest charge, an so on, until you get to the next data point at "x=10". But I think that, considering the measurement uncertainity, the method Vanadium 50 described is more accurate.
Nugatory
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#27
Feb15-14, 02:14 AM
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Quote Quote by DarthMatter View Post
Would taking the differences be ok if you had made a very precise measurement of the charges?
The difference between two values is meaningful only if it is large compared to the error in the two values. This is true no matter how precise the measurements of the two values are.
Vanadium 50
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#28
Feb15-14, 07:03 AM
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Reason 1: There is no more information in 100 differences (or even 45) than there is in the original 10. There is, however, more calculational work required. So you cannot gain.

Reason 2: The uncertainty on the differences is, on average, 40% larger than the uncertainties on the original measurements. So you cannot even break even.

But the fundamental problem here is not the analysis technique. It's that there is not enough data, and in particular, there is not enough data with low charges. A sphere with q=27e does not help very much.
DarthMatter
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#29
Feb15-14, 08:08 AM
P: 18
I would (in this experiment, where the guy or girl in the lab assumes to have an elementary charge) not generally agree on reason 1. Lets say you (or me) knew nothing about integer numbers and you wanted to find the smallest positive integer number. Some guy gave you or me 10 integer numbers with the additional information that each sum of difference of these numbers is another integer number. If this data came out as ## \{3,7,45,34,9,14,18,22,26,15 \} ## all the differences could be taken and no smaller positive difference than 1 would be found, so therefore 1 would be the smallest positive integer number. If you had another data set where the '1' doesn't turn up as a difference you might even check the differences of the differences until you find 1 as the smallest positive difference.

If one has continuous data with non-negligible uncertainity, this may be another story. But I think reason 2 is reason enough to go with the smallest error method.

To add, I am not sure what the point is to ask a student (maybe even, as in my case, with questionable equipment) in the lab to take just 10 values in an experiment which would need many more and afterwards find out how little he or she will find out with this data.


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