User:Emran M. Qassem/Notebook/Physics 307L/2010/10/04

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 * style="background-color: #EEE"|[[Image:owwnotebook_icon.png|128px]] Millikan Oil Drop
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 * style="background-color: #F2F2F2" align="center"|  |Main project page


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Purpose
The main purpose of this lab is to calculate the charge of a single electron. The way to do this is to observe the fall and rise times of many charged drops of oil in an electric field so as to calculate the discrete charge of one electron by noticing that the charge on each oil drop is a multiple of a specific discrete value.

Equipment

 * PASCO scientific Model AP-8210 MILLIKAN OIL DROP APPARATUS
 * Power Supply	Tel-Atomic (50V and 500V power supply)
 * 2 multimeters, measuring Voltage and Resistance.
 * Roberts Travel Size (density 886 Kg/m^3) Mineral Oil

Safety
There are a few safety concerns in this lab:
 * 1. Personal safety first:
 * This device uses Thorium to charge the oil drops, which is a radiation source. Be careful around it and do not leave the source switch open unless charging oil drops.
 * The voltage is high, 500 volts, and can cause shock. Connect equipment when the power is off, and turn the power supply to the lowest settings before powering it on.  Turn on the power, then turn up the voltage to the required level as described in the procedure.
 * The apparatus has a lamp which uses a wall outlet. Be careful when plugging it in.
 * 2. Safety of the equipment:
 * Do not set the power to higher than the specified amount, this can cause damage to the device.
 * There are banana plug ports for measuring the resistance of a thermistor to measure the temperature. Do not put any current through these ports, as it can damage the thermistor.

Setup

 * Device Placement
 * Place the device on a steady surface.
 * Place it high enough so that when you look into the device, you will not be straining your neck or posture, as you will be looking through the eyepiece for extended periods of time.
 * Balance the device so that it is level. There is a leveling bubble (see image) that when the bubble is in the center, it is leveled.  Use the feet of the device to raise the different corners.
 * Device Preparation
 * Take apart the droplet viewing chamber (see image) and wash and dry the lid, the housing, the droplet hole cover, the upper capacitor, the spacer, and most importantly the spacer lens.
 * Make sure to blow the water out of the droplet hole cover.
 * Measure the plate separation (plastic spacer) with a micrometer.
 * Dry everything off and reassemble, making sure not to put any dust or finger prints on the lenses.
 * Device setup
 * Plug in the lamp.
 * Connect the power supply to the plate voltage connectors using the banana plugs and put a multimeter to monitor the voltage.
 * Connect another multimeter to the thermistor connectors to measure the resistance.
 * Move the ionization source lever to the off position.
 * Turn on the power supply
 * Adjust the eyepiece
 * To adjust the eyepiece, put the positioner pin into the center of the chamber.
 * With the light on, view the pin, and focus so that you can see the pin clearly, and have a gradient from light to dark from one side of the pin to the other. Do this using the lens focus and the lamp adjuster.
 * You also want to be able to see the grating that will be used to measure the distance the drop fell.
 * Take out the pin, and replace the droplet hole cover.

Procedure

 * Let the device warm up a bit.
 * take note of the temperature and the voltage
 * Take the atomizer and spray it onto a paper towel a few times till you feel the resistance of the oil traveling through the atomizer, this means it is primed.
 * Move the ionization source lever to the 'spray droplet' position.
 * Look through the eyepiece and spray into the top, and hold it till you see droplets coming down. releasing will make the droplets rise back up because of the vacuum pressure.
 * Move the ionization source lever to the off position.
 * Find a droplet that takes approximately 7 to 15 seconds between major gratings.
 * When one is found, turn on the ionization source lever to the on position for 5 seconds with the voltage off.
 * Now turn the voltage on and track the drop that you had identified and measure how fast it rises.
 * Keep track of temperatures and rise and fall times.
 * Do this as many times as you can with this drop.
 * Repeat with other drops.

Calculations
Particle 1 and 3 did not last, so they are not included in the calculations. Some of the droplets had big jumps in the rise times, so we disregarded those data points. Averages are calculated by taking the accepted data points, summing them up and dividing by the number of points. Standard deviation is calculated by taking the difference of the data point and the average value, squaring it, summing these results and dividing by the number of trials, then taking the square root of the result.

Calculating Charge This has 3 steps:
 * calculate the radius of the oil drop:
 * $$a=\sqrt{(b/2p)^2+9nv_f/2gp_r}{-b/2p}\!$$
 * calculate the mass of the oil drop:
 * $$m=4*pi*a^3*p_r\!$$
 * calculate the total charge of the oil drop:
 * $$q=\frac{mg(v_f+v_r)}{(V/d)v_f}\!$$

Using accepted value for charge of an electron is 1.6 * 10^(-19) C, we can estimate how much charge a particle will have and divide by the number of charges we guess to see our calculated value for the charge of an electron.

Particle 2

 * average fall time: 12.68s
 * std. dev. fall time: 0.963s
 * average fall velocity: 3.94(3) * 10^(-5) m/s
 * average rise time: 3.63s
 * std.dev. rise time: 0.128s
 * average rise velocity: 1.38(5) * 10^(-4) m/s

Calculating Charge
 * radius of oil drop: 5.65(2) * 10^(-7) m
 * mass of oil drop: 6.70(8) * 10^(-16) kg
 * total charge on drop: 4.25(4) * 10^(-19) C

Particle 2 has approximately: 3 * e charge. Calculate e to be: 1.4(1) * 10^(-19) C

Particle 4

 * average fall time: 7.80s
 * average fall velocity: 6.41 * 10^(-5) m/s
 * average rise time: 1.58s
 * average rise velocity: 3.16 * 10^(-4) m/s

Calculating Charge
 * radius of oil drop: 7.33 * 10^(-7) m
 * mass of oil drop: 1.46 * 10^(-15) kg
 * total charge on drop: 1.22 * 10^(-19) C

Particle 4 has approximately: 1 * e charge. Calculate e to be: 1.2 * 10^(-19) C

Particle 5

 * average fall time: 18.64s
 * std. dev. fall time: 3.31s
 * average fall velocity: 2.68(4) * 10^(-5) m/s
 * average rise time: 3.56s
 * std.dev. rise time: 0.90s
 * average rise velocity: 1.4(3) * 10^(-4) m/s

Calculating Charge
 * radius of oil drop: 4.6(4) * 10^(-7) m
 * mass of oil drop: 3.6(11) * 10^(-16) kg
 * total charge on drop: 2(2) * 10^(-19) C

Particle 5 has approximately: 1 * e charge. Calculate e to be: 2(2) * 10^(-19) C

Results
We got these 3 charges: The accepted value is:
 * $$ 1.4(1) * 10^{-19} C \!$$
 * $$ 1.2 * 10^{-19} C \!$$
 * $$ 2(2) * 10^{-19} C \!$$
 * $$ 1.6 * 10^{-19} C \!$$

The first calculation is off by two sigma from the accepted value, the second we did not calculate standard deviation but it's a little further off, and the third has a huge error.

Error
We had a lot of trouble with this lab in terms of particles disappearing, jumping in speed, moving from side to side, suddenly reducing in fall times, and so on. We also watched these particles for long periods of time which was physically straining as after a period of time our eyes would water and we would lose the particle. One of the biggest causes for error I believe would be a particle changing mass over time as it evaporates. Another would be human error as one person was watching and saying start and stop while the other person operated the stop watch. As you can see, in the end when we were tired, particle 5 had the worst data measurements and had the most inconsistent rise and fall times.

Acknowledgments/Citations
Randy for calculations and ideas during the lab. Dr. Gold's manual for suggesting the cleaning.


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