Millikan Oil Drop Apparatus Simulation
This simulation allows you to reproduce Millikan’s results, without the mess and
expense of a real Millikan apparatus. You can practice your technique on fixed-mass
beads and move to droplets, and then, using a fictional value for e, reproduce Millikan’s
data collection and analysis to identify the value. Since the droplets and beads fall very
slowly, there is a built in time-lapse mechanism to “speed up” the passage of time. The
built in stopwatch – used to time the falling droplets to calculate terminal velocity – is
tied in with the time speed.
Choose oil droplets
or fixed-mass beads
Full
instructions
Real or unknown
value of e
Speed up time for
faster analysis
Built-in
stopwatch
Adjust plate
spacing
Reversible polarity
Adjust power
supply voltage
Using the Millikan Oil Drop Simulation
The experiment:
The apparatus for this experiment was developed by Millikan and Fletcher in 1909 to
determine the charge of an individual electron. The experiment is both simple and
elegant. If a droplet of oil can be suspended between charged plates, then the upward
electric force on the droplet exactly matches the downward force of gravity on the
droplet. If the mass of the droplet can be found, then the charge on the droplet can be
found. This experiment is often performed with microscopic spheres of known mass, but
originally the mass of oil droplets was determined by timing the fall of the droplet, and
using the density and terminal velocity to find the mass. Either method may used in this
simulation.
Why use a simulation?
Performing this experiment in the classroom or lab using real equipment is daunting for
many instructors. It is time consuming to perform the experiment and the high voltage
can be dangerous. In addition, the equipment must be cleaned and maintained. Using
the simulation, set up and clean up times are non-existent, and there is no danger of
electrocution. In this simulation, students still need to make all measurements and
calculations in order to determine the values.
An extra feature of this simulation is that time may be accelerated in order to speed up
observations of motion, as the terminal velocity of the miniscule droplets is very slow.
Modes
There are two modes for running the experiment. Using the correct, real world value of
e (the fundamental charge), students may use either beads (microspheres of fixed
mass) or oil droplets (mass must be determined by finding the terminal velocity) to
determine the number of excess electrons on the particle. When the mode is switched
to ‘Unknown value of e’, the program uses an alternate value for the fundamental
charge. Students use beads or oil drops to determine that charge, just as Millikan and
Fletcher did. All unknown values of e are close to the real value. These values are
known to the author, but not made public – so nobody can cheat. Students using this for
a lab must collect enough evidence to make a valid argument, and the instructor will
have to gauge the result by the quality of the data and presentation, not by accuracy.
Further instructions are provided in the HELP file in the program itself and copied below
for review.
Using the Simulator
Begin by launching an oil droplet using the New Droplet button. Unlike the original
experiment, this simulation launches only one droplet at a time. If Oil Droplets is
selected, the mass of the droplet is random. If Bead is selected, the droplet has a fixed
mass of 1x10-15 kg.
The plates are initially set at a separation distance of 2.5 cm. The spacing can be
adjusted using the buttons below the lower plate. The scale (marked in 1 mm
gradations) can also be turned on or off as necessary.
Turn the power on by clicking the On button. Use the coarse and fine voltage
adjustments to adjust the potential so that the droplet remains motionless. The polarity
switch reverses the polarity of the plates. When tuning the voltage, the Time Speed
slider may be used to speed up the apparent rate of motion so that the voltage can be
set more precisely.
Once the potential required to support the droplet is determined, cut the power and use
the built-in stopwatch to time the rate of descent (each mark on the scale is 1 mm).
Since the droplets are very small, they reach terminal velocity almost instantly. Using
the values for potential and terminal velocity, the charge can be determined.
Determining the charge on an electron
Given the density of the oil droplet (in this case, 900 kg/m3), the mass of the droplet can
be found using the equation
4
𝑚 = 𝜋𝑟 3 𝜌
3
The radius, in turn, can be found if the density and viscosity of air are known, using the
equation:
9
𝑛𝑣0
𝑟= √
2 𝑔(𝜌 − 𝑝0 )
Combining these two, we get the equation:
3
𝑚=
4
9
𝑛𝑣0
𝜋𝜌 ( √
)
3
2 𝑔(𝜌 − 𝑝0 )
Inserting the density of the oil, the density of the air and the viscosity of the air, this
equation simplifies to the following:
𝑚 = 3.32477 × 10
−9
3
(𝑣02 )
Given the terminal velocity v0, the mass can easily be calculated.
When the droplet is suspended motionless, the electric and gravitational forces are
balanced:
𝐹𝑒 = 𝐹𝑔
𝐸𝑞 = 𝑚𝑔
The charge on the electron can be determined using:
𝑞=
𝑚𝑔
𝐸
or 𝑞 =
𝑚𝑔𝑑
𝑉