User:Richard T. Meyers/Notebook/Phys307l/Millikan Oil Drop Lab 2

Lab Notes 10/25/10

Procedure
The procedure on line is

Equipment


multimeter

Millikan Oil Drop Apparatus - AP 8210

TEL- Atomic 50V & 500V Supply - UNM 195232

SMIEC Micrometer 0- 25mm

Roberts mineral oil - NDC 54092-417-06 (ρ=886 kg/m^3)

Data
plate separation=7.59-7.60mm

view through the scope a vertical yellow band of light


 * Side note for the data

We dropped particle one and two because there were not enough data points to get a good set.

Also in particle 3 we dropped the last fall time because it didn't have a corresponding rise time and we dropped point 1, 2, and 7 from particle 5 because they were obviously bad points.

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

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

I used this equation to calculate the pressure.

Then I wrote this matlab program to compute q:

%fundamental Charge 2

clc

d=7.6/1000; %m

g=9.81; %m/s

b=8.2*10^(-3); %Pa m

rho=886; %kg/m^3

p= 8.3327*10^4;%Pa

%Times

timer3=[5.34,5.93,5.67,5.94,5.51,5.90,6.13,6,5.34,5.88];%s

timef3=[13.23,13.27,12.23,12.88,12.48,12.57,11.73,13.7,13.06,13.13];%s

timer4=[4.26,3.73,3.98,4.08,3.5,6.9];%s

timef4=[15.27,15.42,16.1,17.72,17.03,17.26];%s

timer5=[4.87,4.94,4.79,4.96,5.7,4.34,4.53];%s

timef5=[16.88,14.07,14.07,15.24,15.24,15.83,15.52]%s

timert=[1.37,1.01,1.12];%s

timeft=[15.03,13.69,12.55];%s

timer7=[5.15,3.54,4.85,5.02,2.97,3.71,3.09,3.14];%s

timef7=[15.27,14.54,12.96,14.26,12.57,11.79,15.62];%s

timer8=[11.55,11.72,12.93,12.59,13.04,12.93,13.67,15.67,12.39,13.48];%s

timef8=[16.63,15.74,15.23,16.42,17.17,14.31,15.35,17.10,16.45,14.31];%s

STDTR3=std(timer3);

STDTF3=std(timef3);

STDTR4=std(timer4);

STDTF4=std(timef4);

STDTR5=std(timer5);

STDTF5=std(timef5);

STDTRT=std(timert);

STDTFT=std(timeft);

STDTR7=std(timer7);

STDTF7=std(timef7);

STDTR8=std(timer8);

STDTF8=std(timef8);

%Velocities

vr3=0.5/(mean(timer3)*1000);%m/s

vf3=0.5/(mean(timef3)*1000);%m/s

vr4=0.5/(mean(timer4)*1000);%m/s

vf4=0.5/(mean(timef4)*1000);%m/s

vr5=0.5/(mean(timer5)*1000);%m/s

vf5=0.5/(mean(timef5)*1000);%m/s

vrt=0.5/(mean(timert)*1000);%m/s

vft=0.5/(mean(timeft)*1000);%m/s

vr7=0.5/(mean(timer7)*1000);%m/s

vf7=0.5/(mean(timef7)*1000);%m/s

vr8=0.5/(mean(timer8)*1000);%m/s

vf8=0.5/(mean(timef8)*1000);%m/s

STDVR3=0.5/(STDTR3)*10^(-6);%m/s

STDVF3=0.5/(STDTF3)*10^(-6);%m/s

STDVR4=0.5/(STDTR4)*10^(-6);%m/s

STDVF4=0.5/(STDTF4)*10^(-6);%m/s

STDVR5=0.5/(STDTR5)*10^(-6);%m/s

STDVF5=0.5/(STDTF5)*10^(-6);%m/s

STDVRT=0.5/(STDTRT)*10^(-6);%m/s

STDVFT=0.5/(STDTFT)*10^(-6);%m/s

STDVR7=0.5/(STDTR7)*10^(-6);%m/s

STDVF7=0.5/(STDTF7)*10^(-6);%m/s

STDVR8=0.5/(STDTR8)*10^(-6);%m/s

STDVF8=0.5/(STDTF8)*10^(-6);%m/s

v_r=[vr3+STDVR3,vr4+STDVR4,vr5+STDVR5,vrt+STDVRT,vr7+STDVR7,vr8+STDVR8;vr3,vr4,vr5,vrt,vr7,vr8;vr3-STDVR3,vr4-STDVR4,vr5-STDVR5,vrt- STDVRT,vr7-STDVR7,vr8-STDVR8];%m/s

v_f=[vf3+STDVF3,vf4+STDVF4,vf5+STDVF5,vft+STDVFT,vf7+STDVF7,vf8+STDVF8;vf3,vf4,vf5,vft,vf7,vf8;vf3-STDVF3,vf4-STDVF4,vf5-STDVF5,vft-STDVFT,vf7-STDVF7,vf8-STDVF8];%m/s

%Energies

E=[6.6737*10^4,6.6737*10^4,6.6737*10^4,6.6737*10^4,6.6737*10^4,6.7053*10^4;6.6737*10^4,6.6737*10^4,6.6737*10^4,6.6737*10^4,6.6737*10^4,6.7053*10^4;6.6737*10^4,6.6737*10^4,6.6737*10^4,6.6737*10^4,6.6737*10^4,6.7053*10^4];%V/m

%n

n=[1.842*10^(-5),1.848*10^(-5),1.852*10^(-5),1.852*10^(-5),1.852*10^(-5),1.854*10^(-5);1.842*10^(-5),1.848*10^(-5),1.852*10^(-5),1.852*10^(-5),1.852*10^(-5),1.854*10^(-5);1.842*10^(-5),1.848*10^(-5),1.852*10^(-5),1.852*10^(-5),1.852*10^(-5),1.854*10^(-5)];%Ns/m^2

%q

a=(sqrt((b/(2*p))^2+((9.*n.*v_f)./(2*g*rho)))-(b/(2*p)));

q=((4/3)*pi*rho*g).*a.^3.*((v_f+v_r)./(E.*v_f))

Q=[q(1)/2,q(4)/2,q(7)/2,q(10)/7,q(13)/2,q(16);q(2)/2,q(5)/2,q(8)/2,q(11)/7,q(14)/2,q(17);q(3)/2,q(6)/2,q(9)/2,q(12)/7,q(15)/2,q(18)]

AVEQ=(mean(Q(1:9))+mean(Q(13:18)))/2

STDQ=mean([Q(1)-Q(3),Q(4)-Q(6),Q(7)-Q(9),Q(13)-Q(15),Q(16)-Q(18)])

From both of these I've computed q

$$q=1.566*10^{-19}\pm 1.1*10^{-20}\,\!$$

$$q=1.539*10^{-19}\pm 5.1*10^{-21}\,\!$$

$$q=1.525*10^{-19}\pm 6.7*10^{-21}\,\!$$

$$q=1.954*10^{-19}\pm 4.5*10^{-21}\,\!$$

$$q=1.534*10^{-19}\pm 6.9*10^{-21}\,\!$$

Thorium
In the MATLAB program I calculated the particle that was radiated with Thorium for ten seconds:

$$q=1.5977*10^{-19}\pm 3.1*10^{-20}\,\!$$

From this I calculated that the particle went from two charges to 7 charges.

Setting Up Our Equipment
We set up the equipment the same way that the lab manual suggested, cited above. Instead of using the table we decided to elevate the system using the box that the apparatus came in and a thick text book.

Aligning The Optical System
As the lab manual states we used the focusing wire to initially focus the microscope; it suggested that we focus the lens until the right side of the wire reflected the most light and was sharp. The manual then told use to focus the grid lines to clarity using the reticle focus.

Adjusting and Measuring the Voltage
We then adjusted the voltage through the capacitor to about 500 volts, measuring with a multimeter.

Citation
1)Pressure versus altitude equation | here

2)Altitude of Albuquerque | 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.