Physics307L:People/Gibson/Millikan Oil Drop Summary

Purpose
The purpose of this experiment was to overall determine the charge of an electron based upon several rise and fall times of oil drops. To further explain this, we introduced oil drops into the Millikan device then subjected them to alpha particles. After allowing some small margin of time to pass for the oil drops to ball in between the viewable region (in between the two charged plates) we then proceeded to introduce a charge on the drop to either make it rise or fall. Grid lines in the viewing scope allowed us to measure a distance more accurately as we used the stop watch to calculate these times.

Equations

 * These are equations relating the constants and other important parameters, that allow us to calculate the charge of each drop.

Where:
 * $$\alpha$$ is the radius of the drop in m,
 * $$b$$ is a constant (8.20x10^-3 Pa*m),
 * $$p$$ is the pressure in pascals
 * $$\rho$$ is the density of oil in kg/m^3
 * $$\eta$$ is the viscosity of air in poise (Ns/m^2)
 * $$g$$ is the acceleration of gravity in m/s^2
 * $$V_f$$ is the velocity of fall in m/s


 * $$\alpha=\sqrt{\frac{b^{2}}{{4p}^{2}}+\frac{9nV_f}{2g\rho}}-\frac{b}{2p}$$


 * $$m=\frac{4}{3}\pi\left(\sqrt{\frac{b^{2}}{{4p}^{2}}+\frac{9nV_f}{2g\rho}}-\frac{b}{2p}\right)^{3}\rho$$


 * $$E=\frac{V}{300d}$$


 * $$Q=mg\frac{\left( V_f+V_r\right)}{EV_f}$$


 * $$Q=\frac{4}{3}\pi\rho g\left(\sqrt{\frac{b^{2}}{{4p}^{2}}+\frac{9nV_f}{2g\rho}}-\frac{b}{2p}\right)^{3}\frac{\left( V_f+V_r\right)}{EV_f}$$

Results

 * for this experiment we found that the elementary charge(i.e the charge of a single electron) to be

e=1.653x10^-19 C

and looking at the relative error with the accepted value of e, we have an error of Relative Error= 1.60x10^-19C - 1.60x10^-19C / 1.60x10^-19=0.032 = 3.2%

From these results we're more than happy with this amount of error.