Physics307L:People/Knockel/Notebook/070912

Millikan's oil drop experiment (charge of the electron)

Experimenters: Nikolai Joseph and Bradley Knockel

Goal

I want to measure the charge of an electron by measuring the charge on a bunch of oil droplets and seeing if I can find that my calculated charges are integer multiples of some fundamental charge. I don't really see why the charge of the electron gets all the attention with this experiment since the charge of a proton is also measured. The actual value for fundamental charge is [math]\displaystyle{ e=1.60\times10^{-19} C }[/math]. The charge of the electron is -e.

Equipment

• power source (should go up to 500 V direct current)
• atomizer (to spray oil droplets)
• 2 multimeters
• banana cords
• banana plug patch cords
• DC transformer for light
• micrometer
• THE MILLIKAN DEVICE! (scope, viewing chamber, light, level, plate charging switch, focusing wire, thermistor, etc.) (Model AP-8210 by PASCO scientific)

Setup

1. plugged in power supply to wall and Millikan device (turned off)
2. hooked up multimeter using banana plug patch cords to check voltage from power supply
3. leveled the Millikan device
4. plugged in the light using DC transformer
5. focused viewing scope with focusing wire
6. aimed the lamp/light/filament
7. turned on power supply and checked it's voltage using first multimeter
8. attached another multimeter to the thermistor

Values

Known (given to as many significant figures as are reasonably certain):

• [math]\displaystyle{ d=7.59\times 10^{-3} m }[/math] (plastic spacer width using micrometer)
• [math]\displaystyle{ \rho=8.86\times 10^2 \frac{kg}{m^3} }[/math] (density of oil given on bottle)
• [math]\displaystyle{ g=9.8 \frac{m}{s^2} }[/math] (gravitational acceleration)
• [math]\displaystyle{ p=8.5\times10^4 Pa }[/math] (air pressure in Albuquerque)
• [math]\displaystyle{ b=8.20\times10^{-3} Pa\cdot m }[/math] (some stupid constant)
• [math]\displaystyle{ l=1\times10^{-3} m }[/math] (length droplet will be measured over)

To be found when taking data:

• [math]\displaystyle{ T }[/math] (temperature from thermistor in degrees celsius)
• [math]\displaystyle{ V }[/math] (Voltage between plates in viewing chamber in volts)
• [math]\displaystyle{ t_f }[/math] (time droplet takes to fall in no field in seconds)
• [math]\displaystyle{ t_r }[/math] (time droplet takes to rise in field in seconds)

To be calculated later:

• [math]\displaystyle{ \eta }[/math] (viscosity of air as a function of T found in a table)
• [math]\displaystyle{ v_f=\frac{l}{t_f} }[/math] (average velocity of oil droplet falling in no field in m/s)
• [math]\displaystyle{ v_r=\frac{l}{t_r} }[/math] (average velocity of oil droplet rising in a field in m/s)
• [math]\displaystyle{ a=\sqrt{\left(\frac{b}{2p}\right)^2+\frac{9\eta v_f}{2g\rho}}-\frac{b}{2p} }[/math] (radius of droplet in meters)
• [math]\displaystyle{ q=\frac{4}{3}\pi\rho g d\frac{a^3}{V}\frac{\left(v_r+v_f\right)}{v_f} }[/math] (charge of oil droplet in Coulombs)

Procedure

We will spray oil droplets into the viewing chamber using the atomizer by pumping droplet rich air into it. We then select drops that is barely falling through the viewing chamber in no electric field (we want drops that have little mass). From those drops, we select one that moves slowly in a field (we want drops that have little charge).

We will measure the speed at which it falls, [math]\displaystyle{ v_f }[/math]. We then create an electric field that causes the droplet to rise and measure the speed, [math]\displaystyle{ v_r }[/math]. We take many measurements of both of these speeds over and over on the same droplet. We will periodically introduce alpha particles which will change the charge of the oil droplet to be either more positive or negative depending on how the collision between the oil and alpha particles occur. We will record the new falling and rising velocities over and over.

This process takes practice, and one must be sure that the oil droplet being observed does not gain or lose charge unexpectedly.

The sign [math]\displaystyle{ V }[/math] can get a little tricky when calculating [math]\displaystyle{ q }[/math] (all other values used to find [math]\displaystyle{ q }[/math] are positive). When the plate charging switch is set to "-", this means that the top plate is negative and the value for [math]\displaystyle{ V }[/math] should be "+". To get the droplet to rise, [math]\displaystyle{ V }[/math] will sometimes need to be positive and sometimes negative, which means the charge [math]\displaystyle{ q }[/math] will sometimes be positive or negative.

Data

Droplet 1, Charge A:

• [math]\displaystyle{ V }[/math]=
• [math]\displaystyle{ T }[/math]=
• [math]\displaystyle{ t_f }[/math]= , , , ,
• [math]\displaystyle{ t_r }[/math]= , , , ,

Droplet 1, Charge B:

• [math]\displaystyle{ V }[/math]=
• [math]\displaystyle{ T }[/math]=
• [math]\displaystyle{ t_f }[/math]=
• [math]\displaystyle{ t_r }[/math]=

Calculating values

Droplet/Charge	[math]\displaystyle{ \eta }[/math]	[math]\displaystyle{ v_f }[/math] (m/s)	[math]\displaystyle{ v_r }[/math] (m/s)	a (m)	q (C)
1A
1B