Sunday, January 31, 2010

Measuring the Mass of a Penny (without measuring a single one)

In teaching chemistry this semester, the first topic I hit was the structure of the atom. One of my philosophies in teaching science is that we shouldn't simply state something as fact. We should present how we know it. So instead of simply stating "There's an atom with protons, neutrons, and electrons", I've been going through the history of their discovery.

Last week, I hit Millikan's oil drop experiment. In this experiment, Millikan sprayed tiny drops of oil into a chamber between parallel, charged plates. The oil drops had stray electrons on them (from him passing X-rays through the air), and since they became charged, he could use the electric field between the plates to control the fall rate of the oil drops. The strength of the electric field times the charge of the electrons times the number of electrons on the oil drop would create an upward force that would balance the downward force of gravity.

In other words, mg = nqE.

The problem with this was that Millikan couldn't be absolutely sure how many electrons were attaching to the oil drop. Thus, not only was q (the charge of an electron) unknown, but the number (n), was too. This left two unknowns for one equation.

What Millikan realized, however, is that n had to be an integer value. With that, Millikan was able to try out several divisors and find the common base unit that all trials showed.

As I explained this, I had a student that just wouldn't accept this was possible and refused to drop the point. So this weekend I came up with an analogy to demonstrate how this would work. I'm going to try it as a lab tomorrow and see how it goes.

Here's the way it works.:

1) I give students an opaque bag with a random number of pennies (1 - 50 roughly, all post 1981 when the composition of pennies changed).

2) Without counting, they weigh the bag, subtract out the weight of the bag, and then start dividing the total weight (minus the weight of the bag) by integer values (preferably in Excel to make things go faster although making them do all the math one at a time would be a joyous bit of Schadenfreude).

3) They repeat this numerous times and find what common factor they all share (making sure to get some prime number values in there so there's no accidents with additional common factors).

4)This common factor should be the mass of a single penny.

I'll let everyone know how this works out and if my student is satisfied.


Anonymous said...

Sounds great, I hope it works out!

Brian Roper said...

Sounds freaking awesome. Perhaps they might not find it so amazing, but its an ingenious thing for the electron

Wayne said...

Depending on the number of groups, you may also have them subtract the totals of two or more groups to create more "nq" values. If you pick similar masses to subtract, it also guarantees a smaller integer value (and thus fewer numbers to choose from).

Anonymous said...

Cool! Can't wait to hear how it goes. Did you do a few trials runs?

Wayne said...

I tried this with my Modern Physics class today. They picked the wrong value for the mass of a penny, but still thought that it was useful in getting the point across. I think more careful measurement of the masses will help, but otherwise I'm not sure how to improve it so that they actually get the correct answer.

Jon Voisey said...

One thing I concentrated pretty hard on was making sure all the pennies were all fresh. None with gum stuck to them, or corrosion eating away portions of them.

Perhaps another thing that could built on this would be to look at the standard deviations of different ones students think to be similar. When my students performed this, there were a few other masses that popped up a lot but the true one had the tightest distribution.