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
- [math]\displaystyle{ a=\sqrt{(b/2p)^2+9nv_f/2g\rho}{-b/2p}\,\! }[/math]
- Then I calculated the mass
- [math]\displaystyle{ m={4/3 \pi a^3 \rho}\,\! }[/math]
- Finally I calculated the total charge
- [math]\displaystyle{ q=\frac{mg(v_f+v_r)}{(V/d)v_f}\,\! }[/math]
Charges on Particles
- Particle 3:[math]\displaystyle{ q=3.345 \cdot 10^{-19}+/-3.99 \cdot 10^{-20}C\,\! }[/math]
- Particle 4:[math]\displaystyle{ q=3.269 \cdot 10^{-19}+/-7.64 \cdot 10^{-20}C\,\! }[/math]
- Particle 5:[math]\displaystyle{ q=3.272 \cdot 10^{-19}+/-3.97 \cdot 10^{-20}C\,\! }[/math]
- Particle 7:[math]\displaystyle{ q=4.141 \cdot 10^{-19}+/-1.16 \cdot 10^{-19}C\,\! }[/math]
- Particle 8:[math]\displaystyle{ q=1.635 \cdot 10^{-19}+/-2.02 \cdot 10^{-20}C\,\! }[/math]
Elementary Charge Found
Then I used the known elementary charge, [math]\displaystyle{ 1.9 \cdot 10^{-19}C\,\! }[/math], 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)
You have a typo in your known elementary charge.
- Particle 3:[math]\displaystyle{ e=1.672 \cdot 10^{-19}+/-1.99 \cdot 10^{-20}C\,\! }[/math]
- Particle 4:[math]\displaystyle{ e=1.635 \cdot 10^{-19}+/-3.82 \cdot 10^{-20}C\,\! }[/math]
- Particle 5:[math]\displaystyle{ e=1.636 \cdot 10^{-19}+/-1.94 \cdot 10^{-20}C\,\! }[/math]
- Particle 7:[math]\displaystyle{ e=2.067 \cdot 10^{-19}+/-5.78 \cdot 10^{-20}C\,\! }[/math] (2e)
- [math]\displaystyle{ e=1.765 \cdot 10^{-19}+/-3.85 \cdot 10^{-20}C\,\! }[/math] (3e)
- Particle 8:[math]\displaystyle{ e=1.635 \cdot 10^{-19}+/-2.02 \cdot 10^{-20}C\,\! }[/math]
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.
