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.


 * 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.