# Physics307L:People/Meyers/Millikan Oil Drop Lab Summary

## Purpose

The purpose of this lab was to determine the value of the fundamental charge. A cursory goal was to understand more about the experiment and physics fundamental charge.

## Procedure

The procedure for this lab is posted here

Procedure Notes

Three important things that we forgot about on the second day of lab.

• Clean the equipment fully before each use.
• Make sure the focus on the microscope is sharp.
• If there are no droplets after the above two notes are completed, you can remove the cap off the top capacitor plate to aid in production of drops.

## Data

Mean Fall Velocity Drop 1=0.49278874986417mm/s Mean Fall Velocity Drop 2=0.63783406181584mm/s Mean Fall Velocity Thorium Drop=0.56471981900151mm/s Mean Rise Velocity Drop 1=0.033980195175056mm/s Mean Rise Velocity Drop 2=0.048294783234806mm/s Mean Rise Velocity Thorium Drop=0.03915374937937mm/s

## Calculation

Using the rise and fall velocities we can calculate the fundamental charge q

$\displaystyle q={4/3 \pi \rho g}{[\sqrt{({\frac{b}{2p}})^2+\frac{9ηv_f}{2g\rho}}-\frac{b}{2p}}]^3\frac{v_f+v_r}{Ev_f}\,\!$

With this equation we got values of q as

• Drop 1: $\displaystyle 3.613 \cdot 10^{-17}C$
• Drop 2: $\displaystyle 5.851 \cdot 10^{-17}C$
• Thorium Drop: $\displaystyle 4.528 \cdot 10^{-17}C$

Where as the accepted value is:

• $\displaystyle q=1.60 \cdot 10^{-19}C$

So if we take the accepted value and compare it with our experimental values we get

• $\displaystyle {\frac{3.613 \cdot 10^{-17}C-1.60 10^{-19}C}{1.60 10^{-19}C}}×100%=22481.25%$
• $\displaystyle {\frac{5.851 \cdot 10^{-17}C-1.60 10^{-19}C}{1.60 10^{-19}C}}×100%=36468.75%$
• $\displaystyle {\frac{4.528 \cdot 10^{-17}C-1.60 10^{-19}C}{1.60 10^{-19}C}}×100%=28200%$

These are extremely high error percentages. I believe these are from interactions in between the droplets and air currents from leaving the cap off of the top capacitor plate. These numbers for q also correspond to hundreds of charges per droplet.

## Conclusion

We had massive error in this lab partially because of air currents and equipment failure. We also failed to take good data on the first day of the lab which contributed to our failure. However, we can see that the charge of an electron is small and we did measure it down to 10^-17. This is close but still far off.

## Citation

1)Pressure versus altitude equation | here

2)Altitude of Albuquerque | here

3)Wiki math help | here

4)Accepted value of q here

## Thanks

1) Nathan for lab help along with data input and help with google docs.

2)Steve Koch for help in trouble shooting the lab.