User:Nathan Giannini/Notebook/Physics 307L/2010/12/10
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< User:Nathan Giannini  Notebook  Physics 307L  2010  12
Contents
Millikan Formal Report
NOTE
Please note that this is not my data, but had been one of my thought processes, looking at delay between when I said go/stop and when Richard started/stopped the stopwatch. As such, this page is just for a reference.
SetUp
 First we leveled the plateform for the Oil Drop Apparatus.
 We measure the width of the plastic spacer with a micrometer. This is the plate separation.
 Then we focused the viewing scope by using the focusing wire and adjusted the light.
 We connected the power supply to the plate voltage connectors using bannana plug patch plugs and applied 500V. We also connected a multimeter in parralel with the apparatus and power supply to better monitor the voltage.
 We connected another multimeter to the thermistor connectors to measure the resistance in the thermistor. This gave us the temperature within the viewing chamber.
 We used the atomizer to introduce oil drops into the chamber. This was done with the ionization source lever in the Spray Droplet Position, which allowed air to escape the chamber.
 Once there were droplets in the chamber we moved the ionization source lever to the Off Position. We tried to find a droplet with a fall velocity between 7 and 15 seconds. This was one of the hard parts of the experiment.
 When we chose a drop we measured as many fall and rise times as we could. The fall times are the times it takes the drops to fall from one major reticule line to the next. The major reticule lines are 0.5 mm apart. The rise times are the same, but with the voltage applied between the plates so that the drops rise against the force of gravity.
 For the last oil drop we measured several fall and rise times and then moved the ionization lever to the ON position and measured several more fall and rise times.
Equipment
 Millikan Oil Drop Apparatus
 TelAtomic (50V and 500V power supply)
 Oil of density 886 Kg/m^3
Data
Pressures are defined according to this article {{#widget:Google Spreadsheet key=0AlAK7TMhL37adHFYd2F0X1BiUS1hS3Jrem9FMVdsMHc width=800 height=600 }} {{#widget:Google Spreadsheet key=0AlAK7TMhL37adEVnZEU1Umk1UWltNWZEXzBtWG9CQ2c width=600 height=600 }}
Particle 3
 Velocity measurements are average values
 Standard Deviations obtained by STDEV in google docs
 Average Rise Time: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle t_r=5.367 +/ 0.281seconds\,\!}
 Average Rise Velocity: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle v_r=9.340 \cdot 10^{5}+/ 5.03 \cdot 10^{5}m/s\,\!}
 Average Fall Time: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle t_f=12.403 +/ 0.557seconds\,\!}
 Average Fall Velocity: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle v_f=4.039 \cdot 10^{5}+/ 1.85 \cdot 10^{6}m/s\,\!}
Calculating Charge of Particle 3
Errors here are such that they incur the greatest amount of error in the charge.
 I used a three step approach to the charge calculation.
 First I calculated the radius a of the oil drop
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle a=\sqrt{(b / 2 p)^2+9 n v_f/2 g \rho}{b/2p}\,\!}
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle a=5.76918 \cdot 10^{7} +/ 0.14187 \cdot 10^{8}m\,\!}
 Then I calculated the mass
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle m={4/3 \pi a^3 \rho}\,\!}

 Finally I calculated the total charge
Elementry charge
 Knowing that the accepted value for e is , it appears that particle 3 has e.
 Dividing q by 2 I get:
Particle 4
 Velocity measurements are average values
 Standard Deviations obtained by STDEV in google docs
 Average Rise Time:
 Average Rise Velocity:
 Average Fall Time:
 Average Fall Velocity:
Calculating Charge of Particle 4
 Errors here are such that they incur max error in charge.
 I used a three step approach to the charge calculation.
 First I calculated the radius a of the oil drop

 Then I calculated the mass

 Finally I calculated the total charge
Elementry charge
 Knowing that the accepted value for e is , it appears that particle 4 has 2e.
 Dividing q by 2 I get:
Particle 5
 I have eliminated bad data from this part of my calculations.
 Velocity measurements are average values
 Standard Deviations obtained by STDEV in google docs
 Average Rise Time:
 Average Rise Velocity:
 Average Fall Time:
 Average Fall Velocity:
Calculating Charge of Particle 5
 I used a three step approach to the charge calculation.
 First I calculated the radius a of the oil drop

 Then I calculated the mass

 Finally I calculated the total charge
Elementry charge
 Knowing that the accepted value for e is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle e=1.6 \cdot 10^{19}C\,\!} , it appears that particle 5 has 2e.
 Dividing q by 2 I get:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle e=1.636 \cdot 10^{19}+/1.94 \cdot 10^{20}C\,\!}
Particle 7
 Velocity measurements are average values
 Standard Deviations obtained by STDEV in google docs
 Standard Deviation in Rise Time: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 0.92seconds\,\!}
 Average Rise Time: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle t_r=3.93seconds\,\!}
 Average Rise Velocity: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle v_r=1.27 \cdot 10^{4}+/3.0 \cdot 10^{5} m/s\,\!}
 Standard Deviation in Fall Time: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 1.34seconds\,\!}
 Average Fall Time: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle t_f=13.91seconds\,\!}
 Average Fall Velocity: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle v_f=3.59 \cdot 10^{5}+/3.6 \cdot 10^{6} m/s\,\!}
Calculating Charge of Particle 7
 I used a three step approach to the charge calculation.
 First I calculated the radius a of the oil drop
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle a=\sqrt{(b/2p)^2+9nv_f/2g\rho}{b/2p}\,\!}
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle a=5.428 \cdot 10^{7}+/2.86 \cdot 10^{8}m\,\!}
 Then I calculated the mass
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle m={4/3 \pi a^3 \rho}\,\!}
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle m=5.935 \cdot 10^{16}+/9.89 \cdot 10^{17}Kg\,\!}
 Finally I calculated the total charge
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle q=\frac{mg(v_f+v_r)}{(V/d)v_f}\,\!}
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle q=4.141 \cdot 10^{19}+/1.16 \cdot 10^{19}C\,\!}
Elementry charge
 Knowing that the accepted value for e is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle e=1.6 \cdot 10^{19}C\,\!} , it appears that particle 7 has 2e.
 Dividing q by 2 I get:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle e=2.067 \cdot 10^{19}+/5.78 \cdot 10^{20}C\,\!}
 also we notice that this one has a possibility for a 3e charge on it, so for this we get:
Particle 8
 Velocity measurements are average values
 Standard Deviations obtained by STDEV in google docs
 Standard Deviation in Rise Time:
 Average Rise Time:
 Average Rise Velocity:
 Standard Deviation in Fall Time:
 Average Fall Time:
 Average Fall Velocity:
Calculating Charge of Particle 8
 I used a three step approach to the charge calculation.
 First I calculated the radius a of the oil drop

 Then I calculated the mass

 Finally I calculated the total charge
Elementry charge
 Knowing that the accepted value for e is , it appears that particle 8 has 1e.
 Therefore, I get:
Acknowledgements
 Randy Llafler  for helping me figure out how my calculations were off, for the setup and the equations seen on this page.