1-2: Millikan Oil Drop Experiment

In the Thomson Cathode Ray Tube Experiment, it was discovered that you can use the deflection of an electron beam in an electric and magnetic field to measure the charge-to-mass ratio (q/m_e) of an electron. If you then want to know either the charge or the mass of an electron, you need to have a way of measuring one or the other independently. In 1909, Robert Millikan and his graduate student Harvey Fletcher showed that they could make very small oil drops and deposit electrons on these drops (1 to 10 electrons per drop). They would then measure the total charge on the oil drops by deflecting the drops with an electric field. You will get a chance to repeat their experiments and, using the results from the Thomson assignment, be able to experimentally calculate the mass of an electron.

To start this activity, click this link for Millikan Oil Drop Experiment. The lab will load in a new tab. Click back to this tab to read further instructions and complete the questions below.
What is the purpose of the electron gun in this experiment?

How does this source affect the oil droplets in the oil mist chamber?

The detector in this experiment is a video camera with a microscopic eyepiece attached to view the oil droplets. Look in the Live Data tab and make sure the camera is on.

What do you observe on the video camera screen?

Do all the oil drops fall at the same speed?

What force causes the drops to fall?

The oil drops fall at their terminal velocity, which is the maximum velocity possible due to frictional forces such as air resistance. The terminal velocity is a function of the radius of the drop. By measuring the terminal velocity (v_t) of a droplet, the radius (r) can be calculated. Then the mass (m) of the drop can be calculated from its radius and the density of the oil. Knowing the mass of the oil droplet will allow you to calculate the charge (q) on the droplet.

IMPORTANT: Read instructions 4 and 5 before beginning the procedure for 5.

Measure the terminal velocity of a drop. Identify a small drop near the top of the window that is falling near the center scale and click the Slow Motion button in the video camera control area in Live Data. Wait until the drop is at a tick mark and start the timer (below the camera display). Let the drop fall for at least two or more tick marks and stop the timer. Do not let the drop fall off the end of the viewing scope. Each tick mark is 0.125 mm. Record the distance and the time in the data table below.
Measure the voltage required to stop the fall of the drop. Having measured the terminal velocity, you now need to stop the fall of the drop by applying an electric field between the two voltage plates. This is done by clicking on the buttons on the top or bottom of the Electric Field display below the camera display until the voltage is adjusted such that the drop stops falling. This should be done while in slow motion. When the drop appears to stop, turn the slow motion off and do some final adjustments until the drop has not moved for at least one minute. Record the voltage, V, indicated on the Electric Field display.

Complete the experiment for three drops and record your measurements in the data table.

Data Table

Drop	Distance (d, in meters)	Time (t, in seconds)	Voltage (V, in volts)
1
2
3

The Millikan Oil Drop Experiment is a classic due to the simplicity of the experimental apparatus and the completeness of the data analysis. The following calculations have reduced very complex equations into simpler ones with several parameters combined into a single constant. Millikan and Fletcher accounted for the force of gravity, the force of the electric field, the density of the oil, the viscosity of the air, the viscosity of the oil, and the air pressure.

Calculate the terminal velocity and record the value. Calculate the terminal velocity, v_t, in units of `m/s` using this equation:

`v_t=d/t`, where d is the distance the drop fell in meters and t is the elapsed time in seconds. Do not forget that the scale on the viewing scope is in mm (1000 mm = 1 m).

Drop #	Terminal Velocity (v_t, in m/s)
1
2
3

Each of the equations in instructions 7-10 is shown with and without units. You will find it easier to use the equation without units for your calculations.

Calculate the radius (r) of the drop and record the value. With the terminal velocity, you can calculate the radius, in m, of the drop using this equation:

`r=(9.0407*10^-5 m^(1/2)*s^(1/2))*sqrt(v_t) = (9.0407*10^-5*sqrt(v_t), "without units")`

Drop #	Radius (r, in meters)
1
2
3

Calculate the mass of the drop and record the value. You can use the answer from #7 for the radius (r) to calculate the mass of the drop given the density of the oil. The final equation to calculate the mass, in kg, is

`m=V_(oil)* rho _(oil)= 4pi/3*r^3*821(kg)/m^3` =`(3439.0 (kg)/m^3)*r^3` `~=` `(3439.0 *r^3, "without units")`

Drop #	Mass (m, in kg)
1
2
3

Since you applied a voltage across the Electric Field to stop the fall of the oil drop, the forces being exerted on the drop must be balanced; that is, the force due to gravity must be the same as the force due to the electric field acting on the electrons stuck to the drop: .

Calculate the total charge (Q_tot) on the oil drop due to the electrons using the equation:

`"Q"_("tot")="Q(n)"*e=(9.810*10^-2(C)/(kg*J))*m/V=(9.81*10^-2m/V,"without units")`

where Q(n) is the number of electrons on the drop, e is the fundamental electric charge of an electron, m is the mass calculated in #8, and V is the voltage.

This answer will provide the total charge on the drop (Q_tot). The fundamental electric charge of an electron (e) is 1.6 ´ 10^-19 C (coulombs). Divide your total charge (Q_tot) by e and round your answer to the nearest whole number. This is the number of electrons (Q(n)) that adhered to your drop. Now divide your total charge (Q_tot) by Q(n) and you will obtain your experimental value for the charge on one electron.

Drop #	Total charge on drop (Q_tot, in Coulombs)	Charge on one electron (C)
1
2
3

What is your average charge for an electron?

C

Average your results for the charge on one electron. Calculate the percent error by:

`%"Error"=abs("your answer"-1.6*10^-19)/(1.6*10^-19)*100`

What is your percent error?

%