Physics307L:People/Gibson/Notebook/071008

Introduction
This lab was designed in the end measure the charge of an electron. The drops used in the experiment are very tiny so only a few electrons would be present on each of the drops. You are also required to introduce alpha particles to the oil drops, when introducing the drops to an electric field we are then able to control rise and fall times. These times are measured then we use equations found in the lab manual to determine the charge we find on each drop, and thus the charge of an electron.

Intro Measurements
We measured the spacer to be 7.511 mm (.0007511 meters)

Following the instructions given in the lab manual

Plate voltage: 500.6 V

Density of Oil 886 kg/m^3

Measure of Resistance between plates: 2.101 Ohms relates to 23.5 C

Data
Fall Time        |          Rise Time 7.18               2.97  6.22                3.01  6.43                2.72  5.98                2.44  6.63                2.97  6.27                2.57   6.51                2.55  7.09                2.73  7.18                2.78  6.93                2.98  7.2                 3.74  6.49                3.47  6.61                3.87

Fall Time                   Rise Time 5.54               3.73  5.47                4.32  5.26                4.16  5.75                4.67  5.34                4.07  5.83                4.6  5.73                4.33  5.63                3.83  6.07                4.38  5.58                4.12  5.79                4.16  5.69                4.44  6.32                4.51

We took additional measurements:

Fall Time        |          Rise Time 7.81               2.08  7.78                1.87  7.49                2.03  8.45                1.96
 * Drop 3

Fall Time        |          Rise Time 8.07               1.98  8.19                2.02  8.24                2.19  8.07                1.96
 * Drop 4

Equations

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

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


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


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


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


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

Results
Using the equations above we determined the charges.

Total charges from Drop 1: 8.8183e-019 9.9109e-019 1.0321e-018 1.1862e-018 9.4522e-019 1.0979e-018 1.0692e-018 9.4674e-019 9.2446e-019 9.0721e-019 7.5149e-019 8.6793e-019 7.9566e-019

Total charges for Drop 2: 9.6276e-019 8.9552e-019 9.5124e-019 8.1552e-019 9.4861e-019 8.1101e-019 8.5381e-019 9.3304e-019 8.0116e-019 9.0186e-019 8.6478e-019 8.4769e-019 7.5696e-019

Additional charge measurements:

Total charges from drop 3: 1.0749e-018 1.1736e-018 1.1323e-018 1.0576e-018

Total charges from drop 4: 1.0897e-018 1.0602e-018 9.8943e-019 1.0987e-018

Analysis
We calculated the mean values from the 4 drops:

Drop 1: 9.5361e-019 C  Drop 2: 8.7261e-019 C   Drop 3: 1.1096e-018 C   Drop 4: 1.0595e-018 C

From this we determined the approximate values of electrons on the drops:

Drop 1: 9.7981e-019 C +/- 1.01831e-019 Drop 2: 8.7261e-019 C +/- 6.563e-019 Drop 3: 1.1096e-018 C +/- 5.3289e-20 Drop 4: 1.0595e-018 C +/- 4.9527e-20