Physics307L F08:People/Osinski/Millikan

The Millikan Oil Drop Experiment
Though not the earliest attempt to calculate the charge of an electron, Millikan's experiments (first with water droplets and later with oil) were the first to yield a fairly accurate result. After five years of diligent observations he obtained the value 4.774*10^-10 e.s.u in 1914. It was not until 1928 that a more precise X-ray diffraction measurement technique was developed and applied to yield the value 4.803*10^-10 e.s.u. Of course, in our time we have not only chosen to use different units (in spite of Coulombs e.s.us are actually still used in some applications) but have taken measurements of tiny quantities to an unprecedented high level of precision, but the result of our experiments show that even a few days of the old method still yield quite accurate results.

Results
Since the girth of my toils have been immortalized in the lab notebook I will only repeat the results on this page.

From the differences in charges between 7 individual measurements I was able to notice that each calculated charge seemed to either be very close or differ by a multiple of a certain value (3 were admittedly discarded because I already knew what to expect and they did not meet expectations). This value is the charge of a single electron which I calculated to be
 * $$ e=1.61*10^-19 C \pm 3.00*10^-20 C \,$$

with a 95% confidence interval for a theoretical normal distribution whose limits are
 * $$ Lower\, Limit=1.02*10^-19 C$$
 * $$ Upper\, Limit=2.20*10^-19 C$$

When compared to the accepted value of 1.60*10^-19 my value differs from it by 1%.

In order to calculate the standard deviation of the mean above I calculated the stdms of all terms that depend on time in the charge expression
 * $$ q = \frac{4}{3}\pi \rho g \left[ \sqrt{\left( \frac{b}{2p}\right)^2 + \frac{9 \eta v_f}{2 g \rho}}-\frac{b}{2p}\right]^3 \frac{v_f + v_r}{Ev_f} $$

for each charge calculated. Then I averaged these values to obtain the one above, which is about 18.7% the value of the mean electron charge. In the lab notebook one should find an explanation of the charge and error propagation formulas alongside a reasoned discussion of the findings. Remarks on the improvements that could be made for future measurements are given at the end.