### The Idea

Robert Millikan devised a brilliant technique to experimentally determine the charge of the electron, which resulted in him being awarded the Nobel Prize for Physics. This project lets you replicate Millikan's famous experiment. Basically, Millikan found a way to attach electrons to small droplets of oil, and then measure their response to an electric field. Because this is a more complex experiment than most of the other experiments in this book, it may be out of reach for many readers.

For this reason another option to explore this discovery is given. One of the problems Millikan had to deal with was he never knew how many electrons were on any given drop of oil. We can re-create some of the logical steps Millikan followed using pennies to represent electrons.

### What You Need

### Simulation

- film canisters or plastic prescription containers with covers
- spray paint
- about 150 pennies
- digital scale or spring balance

### Replicating the Millikan oil-drop experiment

- Millikan's oil-drop apparatus, as shown in Figure 122-1

### Method

### Setting up the simulated oil drops

- Spray paint or otherwise obscure the outside of about 8–12 plastic containers, so you can't see inside.
- Measure the mass of the empty containers.
- Distribute a different (random) number of pennies in each of the containers.
- The easy version of this includes at least one set of containers that differ by one penny (such as Container 7 with 12 pennies and Container 8 with 11 pennies).
- A slightly more challenging version is to have no container differing by one penny, but (because of the small statistical sample) to have at least one set of samples differ by two pennies and another set by two pennies.

### Finding the charge of a simulated "electron" (mass of a penny)

- Find the mass of each container with the pennies.
- Subtract the mass of the container to obtain the mass of just the pennies in each container.
- Arrange the mass measurements in order—smallest to largest.
- Subtract each mass measurement from the previous measurement in the list.
- Identify the smallest (non-zero) mass difference between any pair of containers.
- Divide each of the mass differences by the smallest mass difference in the list.
- If any fractional numbers are in the list, multiply all the number by a factor that leaves only integers in the list. (For instance, if one of the numbers is 1.5, multiply them all by 2.)
- Make a graph of the mass differences on the y-axis versus the integers in Step 7.
- Find the slope of this graph. This should give you the mass of the penny, following a similar form of logic Millikan used to measure the charge of the electron.

### The actual Millikan oil-drop measurement

- Determine the mass of the oil drop by measuring the velocity of the drop as it falls. Because air resistance affects larger drops to a greater extent, the velocity serves as a very accurate measure of the droplet mass.
- Using X-rays or another source of ionizing radiation, create a random number of charges on the electron.
- Determine the magnitude of the electric field that just balances the gravitational pull on that droplet. The gravitational force can be found from the mass of the droplet determined in Step 1 and the density of oil. The greater the charge, the greater the force needed to balance it.
- At this point, we know the charge, but we don't know how many electrons are on any given droplet. This is very similar to the situation we just addressed with the pennies. Although we did not know how many pennies were in any particular container, we were able to find the mass of a single penny. Using a similar logic, Millikan was able to find the mass of an electron.

### Expected Results

Following the previous simulated procedure using pennies, the slope of the line in Figure 122-2 is 2.7 grams, which is the mass of a single penny. This is a reasonable average for pennies minted before and after 1982. A more precise value can be established by sorting pennies into groups before and after 1982.

The charge of an electron determined by Millikan is –1.6 × 10^{–19} Coulombs.

### Other Things to Try

Marbles can be used to simulate the logical process pursued by Millkan in a similar manner that was done with pennies. The marbles have a greater mass, which may make it easier to detect difference. However, finding a relationship graphically may be more difficult because of the variation in mass for a random set of marbles.

### Why It Works

The size of an oil drop is found by observing its free-fall velocity in air. The oil drop is then given a charge by exposing it to ionizing radiation. The electric field that establishes equilibrium with gravity is related to the force. Although the exact number of electrons on any give oil drop cannot be determined directly, the common multiple leads us to identify the charge of a single electron.

### The Point

The Millikan oil-drop experiment determines the charge of an electron by measuring the response of an oil drop charged by electrons in an electric field.

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