User:Dan C. Wilkinson/Notebook/Physics 307L/9/22/10

= Millikan Oildrop Experiment =

Goal
The goal of this lab is to determine the charge of the electron. We will do this by balancing the forces felt by a small oil drop in the presence of an electric field. It's motion will let us determine an overall charge of the oil drop. Collecting a large amount of data will allow us to determine the charge of the electron (the smallest divisor of the collected data).

Apparatus

 * Pasco Millikan Oil Drop Apparatus, model AP-8210
 * Roberts Travel Size Mineral Oil
 * Smeic Micrometer
 * Wavetek TrueRMS 85XT

Constants

 * Distance Between Plates = 0.76(cm)
 * Density of Oil = 0.866(g/cm^3)
 * Acceleration of Gravity = (cm/s^2)
 * Viscosity of Air in Poise = (dynes/cm^2)
 * Barometric Pressure = 29.80in Pressure Website (cm Mercury)
 * b–constant, equal to 6. 17 x l0-4 (cm of Hg) (cm)
 * Voltage Across Plates = 499.5 (V)


 * Resistance of Thermistor = 2.177Mohm (3:24pm), 1.987Mohm (4:38)

Procedure
StopWatch
 * Plug in Halogen light source to wall power supply
 * Remove plastic cover and black plastic piece and inserted focusing pin
 * Look through eyepiece and focus on the pin and the grid (the further adjustment knob brings the pin into focus and the closer knob brings the grid into focus.
 * Plugged in the DC power source and used the above mentioned multimeter to adjust the voltage to 499.5V.
 * Used the multimeter to measure the resistance of the thermistor getting 2.177Mohm, will check this resistance periodically (especially when making measurements) to ensure that the temperature is known.
 * We had to adjust the halogen lamp settings using the horizontal and vertical knobs on the light source. We noticed that moving these knobs changed the focus area of the oil drops. For example, at first the oil drops could only be seen on the left hand side. After some alignment we were able to move the plane of focus to the center of the grid.

Day 2 Nathan et. al. adjusted settings on the Millikan Oil Drop Apparatus. They reportedly cleaned and adjusted the optical settings on the machine. I turn the knob to vent position and spray in oil. As soon as Tyler sees drops I turn the knob back to the closed position. Tyler maneuvers the drop over the major gridlines and then lets it fall by using the voltage across the plates to force the droplet up or down. He tells me when to start the timer as the droplet passes behind a major line, and stop the timer when the droplet passes over the next major line. The grid is marked with the major lines every half millimeter and the minor lines every .1 millimeter. We measured the time for the droplet to fall a half millimeter under no voltage, and the rise time over the same distance under voltage. I used a timer provided by Timer. We found that if Tyler noted each .1 millimeter increment (the small grid lines) that the droplet passed, our measurements became more precise. We measure rise time, fall time, rise time, fall time, etc. instead of all fall times at once and all rise times at once as to guarantee we get at least some of both measurement types from each drop. After five rise times and fall times, we expose the droplets to ionizing alpha radiation from a thorium element in attempt to change the ionization of the droplets. We then take five more rise and fall time measurements.


 * The previous group didn't put the black stopper back, in week 2 and we didn't check if there it was in. This caused too much airflow in the chamber, forcing droplets in and out of the field of view too quickly to gather full data sets for drops 2 and 3.
 * For drop 4 we were not able to get any thorium data.
 * Drop 5 represents first good data set.

Data
%% Millikan Oil Drop Data Calculations close all, clear all, clc, format compact,format short tf1=[8.353,7.946,7.953,8.748,7.641,7.974,8.523]; tr1=[1.745,1.954,1.892,2.146,1.995,1.992,1.991]; q1=millikan(tf1,tr1,1); tf1thorium=[10.7,9.719]; tr1thorium=[1.169,1.296]; q2=millikan(tf1thorium,tr1thorium,1);

tf2=[6.73,6.469,6.205,6.671,6.66]; tr2=[10.227,9.664,10.172,10.142,9.888]; q3=millikan(tf2,tr2,2);

tf3=[15.281,13.838,14.296,13.249,14.26]; tr3=[3.195,2.867,2.941,3.75,3.35]; q4=millikan(tf3,tr3,3); tf3thorium=[16.879,14.743,14.286,13.666,15.272]; tr3thorium=[5.341,5.431,5.648,5.459,5.389]; q5=millikan(tf3thorium,tr3thorium,3);

tf4=[5.596,5.904,5.688,6.144,5.617]; tr4=[6.551,7.216,6.711,7.368,7.412]; q6=millikan(tf4,tr4,4); tf4thorium=[5.902,5.586,5.454,5.992,6.49]; tr4thorium=[16.581,15.387,15.883,16.66,18.36]; q7=millikan(tf4thorium,tr4thorium,4);

tf5=[10.195,11.693,11.14,11.606,11.84]; tr5=[2.36,2.793,2.48,3.463,2.551]; q8=millikan(tf5,tr5,5);

tf6=[10.653,10.731,12.33,11.867,11.125]; tr6=[6.878,6.423,6.13,6.687,6.476]; q9=millikan(tf5,tr6,6); tf6thorium=[11.695,11.08,12.689,11.564,12.437]; tr6thorium=[23.765,26.244,27.734,23.686,25.648]; q10=millikan(tf6thorium,tr6thorium,6);

tf7=[13.637,13.297,14.816,12.377,15.285]; tr7=[5.576,5.648,5.501,5.559,5.949]; q11=millikan(tf7,tr7,7);

Q=[mean(q1),mean(q2),mean(q3),mean(q4),mean(q5),mean(q6),mean(q7),mean(q8),mean(q9),mean(q10),mean(q11)].*10^19; Q1=[q1,q2,q3,q4,q5,q6,q7,q8,q9,q10,q11].*10^19; start=1; ending=15; steps=100000; e=linspace(start,ending,steps); for i=1:54 A(i,:)=Q1(i)./e; end for i=1:54 F(i,:)=(A(i,:)-round(A(i,:))).^2; end F=sum(F); [C,I]=min(F); qdet=(0.1+I*((ending-start)/steps))*10^-19 qdet/1.60217646E-19;

Q1=Q1*10^-19; frac=round(Q1./qdet); Qdivided=Q1./frac; plot(Qdivided) StandardDeviation=std(Qdivided) Stardarderrorofmean=StandardDeviation/sqrt(length(Q1))

Function
function q=millikan(tfall,trise,a) d= 0.00767;                                                            %plate seperation (m) DensityOil= 886;                                                       %Density of oil used (g/cm^3) g= 9.81;                                                               %Acceleration of gravity near earth surface (m/s^2) T= [23,23,24,25,26,26,26];                                          %Temperature slopen=1.88086/32;                                                     %Slope of viscosity function (its linear) n=(T*slopen+0.9299)*10^-5;                                             %Viscosity of Air (dyne s/m^2) b= 8.20E-3;                                                            %Constant p= [29.8,29.67,29.67,29.67,29.67,29.67,29.67]*3386;              %Barrometric Pressure in (Pascals) V= [499.5,501.4,501.4,501.4,501.4,501.4,501.4];                  %Voltage in volts qknown=1.60217646*10^-19;                                              %Accepted electron charge

vfall=0.0005./tfall; vrise=0.0005./trise; N=n(a)*ones(1,length(vfall)); qdrop=(4/3)*pi*DensityOil*g*((sqrt(((b./(2.*p(a))).^2)+(9.*N.*vfall)./(2*g*DensityOil))- b./(2*p(a))).^3).*((vfall+vrise)./((V(a)/d)*vfall));

q=qdrop;