# Homemade Millikan-experiment to Determine the Elementary Charge of an Electron

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## Introduction: Homemade Millikan-experiment to Determine the Elementary Charge of an Electron

Hello!

In physics there are several natural constants such as the speed of light c in a vacuum, the Planck constant h or the elementary charge e. An electron has exactly the charge -e, a proton + e. The size of this elementary charge is 1.6 * 10 ^ -19 C. It was first determined by the two physicists Robert Millikan (1868-1953) and Harvey Fletcher (1884-1981). Only Millikan received the Nobel Prize in Physics in 1923.

The measuring principle is simple: using an atomizer, the smallest drops of oil are brought between the two plates of the capacitor and ionized there using X-rays. The resulting charge is a multiple of the elementary charge e. In the earth's gravity field, the oil drops slowly drift downwards without voltage on the capacitor. The radius r can be calculated from the drift velocity v using Stokes' law. If you then apply a certain voltage to the capacitor, you can make the oil drop float with the appropriate setting. Then the force of gravity and the force in the electric field balance each other exactly. The electrical charge q of the oil drop can then be determined from this.

Millikan and Fletcher recognized that electrical charges of any size did not occur, but only integer multiples of a basic charge. With this the elementary charge e was found.

I don't use oil drops for my Millikan experiment. Instead, microparticles with a precisely known size are used. This greatly simplifies the measurements. Instead of determining the drift speed without an electric field, it is now sufficient to make the particles float. The electrical charge of the microparticle can be calculated directly from the voltage U required for this. X-rays or a radioactive source are also not necessary when using these microparticles. When atomizing, some particles are charged automatically.

## Step 1: Parts

The following parts are necessary for the experiment:

• Wooden plate
• Digital microscope with screen (amazon)
• Plexiglass tubes with 50mm / 44mm diameter in different lengths (ebay)
• a small round 4mm thick plexiglass plate as a lid
• 2 round 50mm brass disks (ebay)
• M4 threaded rod and wing nuts
• a pipe clamp for mounting the microscope rail
• foam rubber as a seal
• a CCFL inverter to generate the high voltage (Neuhold electronics)
• some electrical parts such as an LM317 for the high voltage circuit
• a digital 1000V panel meter (ebay)
• a white 3W LED (ebay)
• Chair bracket for mounting the LED
• a step-down converter with a series resistor to supply the LED (ebay)
• a 12V DC power supply to supply the high-voltage circuit and the LED
• 1.5 µm microparticles of polystyrene (ebay) dissolved in water (0.25g in 14 ml water)

or ready to use 1 µm latex microspheres (science first)

• a medical atomizer (I got mine from ebay for 25 USD including shipping)

The whole experiment costs about 170 USD. This is a lot cheaper than the commercial products you can buy. and it is a lot more fun and satisfying to tinker it by yourself.

## Step 2: The HV-power Supply

For the high voltage power supply you need the ccfl-inverter and some other components (LM317, potentiometer, UF4007 diodes, 10nF/3kV capacitors)

## Step 3: The Building and Setup

To find the right focus you can take the 1mm thrill used for the entrance-hole and try to get him sharp.

## Step 4: The Measurements

First you focus the image of the microscope. For this it is advisable to also see the 1mm opening in the upper capacitor plate in the picture. This is used to orient yourself when focusing. Later, when microparticles can be seen, the focus may have to be adjusted once again. This is not that easy because the area of sharp images is very small.

The optical magnification of the microscope should be around 20 times.Then set a fairly low voltage of approx. 100V using the potentiometer. The atomizer is then taken and the latex balls or microparticles dissolved in water (0.25g in 12 ml water) are sprayed into the chamber above the capacitor. Now you have to watch the microscope screen closely. If you discover a particle that reacts to the change in the electrical voltage, adjust it with the potentiometer so that the particle floats and does not move up or down. This voltage U is noted and then the experiment is repeated a few times.

The plexiglass tubes must of course be cleaned again after a few passes. Also, the inlet opening in the upper capacitor plate must not be covered by a drop.

## Step 5: The Calculations

If the particle hovers, the weight force F_g = m * g and the electrical force F_e = Q * E = Q * U / d cancel each other out exactly. E corresponds to the electrical field strength in the interior of the capacitor, Q the electrical charge of the microparticles, U the voltage across the capacitor and d the plate spacing of the capacitor. In my case d = 5 mm.

The following applies to the mass m of the microparticle: m = density * volume = density * 4 * Pi * r³ / 3 with the particle radius r. The values for the density of the microparticles and their radius must be known. For example, my microparticles have a radius of 0.75 µm and a density of 1050 kg / m³. If you put all of this into the equation above, you get the following expression for the charge Q:

Q = (d / U) * 4 * Pi * r³ * density * g / 3

Concrete example: d = 0.005 m, r = 0.75 * 10 ^ -6 m, density = 1050 kg / m³, g = 9.81 m / s², U = 273V

This results in an electrical charge Q = 3.33 * 10 ^ -19 C. As you can see, the charge corresponds approximately to the double elementary charge e = 1.6 * 10 ^ -19 C.

If you repeat the experiment and calculate the charge Q, you can see that only certain charges occur. If everything went correctly you should see that only multiples of the charge e = 1.6 * 10 ^ -19 C occur. If you succeed, you can be justifiably proud of yourself and feel like Robert Millikan and Harvey Fletcher.

## Step 6: Thanks for Your Interest

Perhaps you will also set up the experiment and follow the path of a physics nobel prize winner. You can find more experiments here on my Youtube channel: my channel 