# Physics307L:People/Giannini/Millikan2

Steve Koch 20:14, 21 December 2010 (EST):Good work with the redo and getting some good drops.

My partner was Richard T. Meyers.

# Purpose

To discover the charge of an electron using the Millikan Oil Drop Apparatus, and then determining the charge on each one (which is some multiple of an electrons charge).

# Summary

We set up the Millikan Apparatus as specified here. We then proceeded to measure the fall and rise times of droplets I chose, after emptying the chamber of most other particles to reduce error. Afterward, I calculated the charge on the particles we looked at. A more in depth overview can be found here.

# Method

First I obtained our Average rise/fall times and our average rise/fall velocities. Then, I obtained the standard deviation, by using STDEV in google docs, in these. Finally I used a three step approach to calculate the charge on each of our particles.

• First I calculated the radius a of the oil drop
$a=\sqrt{(b/2p)^2+9nv_f/2g\rho}{-b/2p}\,\!$
• Then I calculated the mass
$m={4/3 \pi a^3 \rho}\,\!$
• Finally I calculated the total charge
$q=\frac{mg(v_f+v_r)}{(V/d)v_f}\,\!$

## Charges on Particles

• Particle 3:$q=3.345 \cdot 10^{-19}+/-3.99 \cdot 10^{-20}C\,\!$
• Particle 4:$q=3.269 \cdot 10^{-19}+/-7.64 \cdot 10^{-20}C\,\!$
• Particle 5:$q=3.272 \cdot 10^{-19}+/-3.97 \cdot 10^{-20}C\,\!$
• Particle 7:$q=4.141 \cdot 10^{-19}+/-1.16 \cdot 10^{-19}C\,\!$
• Particle 8:$q=1.635 \cdot 10^{-19}+/-2.02 \cdot 10^{-20}C\,\!$

## Elementary Charge Found

Then I used the known elementary charge, $1.9 \cdot 10^{-19}C\,\!$, to calculate the integer value multiple of this charge for my particles. I then used this to determine the charge of one electron. SJK 20:11, 21 December 2010 (EST)
20:11, 21 December 2010 (EST)
You have a typo in your known elementary charge.
• Particle 3:$e=1.672 \cdot 10^{-19}+/-1.99 \cdot 10^{-20}C\,\!$
• Particle 4:$e=1.635 \cdot 10^{-19}+/-3.82 \cdot 10^{-20}C\,\!$
• Particle 5:$e=1.636 \cdot 10^{-19}+/-1.94 \cdot 10^{-20}C\,\!$
• Particle 7:$e=2.067 \cdot 10^{-19}+/-5.78 \cdot 10^{-20}C\,\!$ (2e)
$e=1.765 \cdot 10^{-19}+/-3.85 \cdot 10^{-20}C\,\!$ (3e)
• Particle 8:$e=1.635 \cdot 10^{-19}+/-2.02 \cdot 10^{-20}C\,\!$

# Analysis of Results

Overall, most of my charges represent the elementary charge of an electron that has already been found, with Particle 7 being relatively accurate if we take it to have 3e.

# Error

Sources of possible error:

• systematic - the focus of our scope, the increasing voltage with time, the increasing temperature with time, multimeters not calibrated correctly.
• particles - loss of mass, interactions between particles, air drafts, spontaneous charge changes.
• human - delay in start and stop times by time taker, loss of concentration in person watching the particle, etc.