General Physics Lab Department of PHYSICS YONSEI University

Lab Manual (Lite)

Millikan Oil Drop Experiment Ver.20180903

Millikan Oil Drop Experiment

Setup1. Equipment setup (1) Adjust the height of the platform. Mount the apparatus on two support rods on the A-shaped base with the viewing scope at a height which permits the experimenter to sit erect while observing the drops.

(2) Measure the plate separation distance. Disassemble the chamber by lifting the Housing straight up and then removing the upper capacitor plate and spacer plate. Measure the thickness of the spacer (which is equal to the plate separation distance) with vernier calipers. Be sure that you are not including the raised rim of the spacer in your measurement. 𝑑𝑑 = _______________ (m)

(3) Reassemble the chamber.

The flat cut (with black painted hole) of the spacer ring must face the viewing scope.

NOTICE This LITE version of manual includes only experimental procedures for easier reading on your smartphone. For more information and full instructions of the experiment, see the FULL version of manual.

Setup

Caution To prevent electric shock, do not touch the plates inside

the chamber while the power supply is turned on. Prior to disassembling the chamber, you should be sure to turn off the power supply and rotate the plate charging knob to the Plate Grounded (middle) position.

Make sure fit the electric discharge terminal into the groove on the underside of the spacer, and leave no gap between the spacer and capacitor plates.

(4) Turn on the LED lamp. Connect the 12V DC adaptor to the lamp power jack.

(5) Focus the scope and adjust the position of the lamp. Remove the droplet hole cover. Unscrew the focusing wire from its storage place on the platform and carefully insert it into the hole in the center of the top capacitor plate.

Bring the reticle into focus by turning the reticle focus ring. View the focusing wire through the viewing scope and bring the wire into sharp focus by turning the droplet focusing ring.

Adjust the position of the lamp by using two lamp position knobs.

The light is best focused when the right edge of the wire is brightest (in highest contrast compared to the center of the wire).

Return the focusing wire to its storage location on the plat-form. Complete the reassembly of the chamber by placing the droplet hole cover on the upper plate and the lid on the hous-ing. (If you do not cover the droplet hole of the plate, the hole could be clogged with oil.)

Caution Be careful not to lose any parts of the chamber assem-bly, especially the droplet hole cover.

(6) Realign the optical system while observing the droplets. Move the air vent lever to the OPEN positon. Place the noz-zle of the atomizer into the hole on the lid of the chamber and squeeze the atomizer bulb with quick squeeze. While viewing a shower of drops through viewing scope, realign the optical system.

(7) Determine the temperature of the chamber and calculate the viscosity of the air.

Connect the multimeter to the thermistor connectors and measure the resistance of the thermistor. Refer to the Suther-land’s Formula and the Thermistor Resistance Table (see appendix) to find the viscosity of air. 𝜂𝜂 = _______________ (Pa ∙ s) (8) Connect the power supply to the plate voltage connectors.

(9) Set the output voltage of the power supply. Prior to turning on the power supply, set the plate charging

knob to Plate Grounded (middle) position and rotate voltage adjustment knob fully counterclockwise (𝑉𝑉 = 0 V). Turn on the power and increase SLOWLY the output voltage

to 300 V.

Caution To prevent electric shock, use ONLY safety patch cords

with shrouded banana plug. Do not apply voltage to the thermistor connectors.

Setup 2. Stopwatch Software (1) Run Watchy software.

(2) How to use the Watchy. [Start] or [F5] : Start the clock. [Stop] or [F6] : Stop the clock. [Reset] or [F7] : Reset the stopwatch to zero. Clear the log. [Lap] or [F10] : Add a lap time without stopping the clock. [Split] or [F11] : Add a split time without stopping the clock. [Split] records overall time at any given point, whereas [Lap] records elapsed time between splits.

Step 1. Setting the Plates Voltage (1) Set the potential difference across the parallel plates. Set the output voltage of the power supply to 300 V or any desired value. (Do not exceed 400 V.) 𝑉𝑉 = _______________ (V)

(2) Rotate the plate charging knob of the power supply to the Plate Grounded (middle) position. The plate charging knob changes the direction of the electric field between the plates. We will introduce the droplets into the chamber with no electric field by setting the knob to the Plate Grounded position.

Step 2.

Introducing Droplets into the Chamber (1) Move the air vent lever to OPEN position. Move the air vent lever to the OPEN position to allow air to escape from the chamber during the introduction of droplets into the chamber.

Procedure

Note It is recommended you do not use any air conditioner or

fan while performing your experiment. The airflow outside the chamber could affect the motion of oil droplets. The high velocity stream of air creates a region of lower pres-sure above the chamber lid, compared with standard atmospheric pressure inside the chamber. This pressure difference results in a net force pushing droplets up.

(2) Introduce the droplets into the chamber.

(3) When you see a shower of drops, move the air vent lever to the CLOSE position.

Step 3. Charging the Droplets The apparatus uses the piezo igniter to charge droplets. An applied mechanical stress on piezoelectric ceramic in the igniter generates a high voltage. The voltage produces an electric field in the gap between the end of the connected wire and the lower plate in the chamber. Free electrons in the gap are accelerated by the electric field. As they collide with air molecules, they create additional ions and newly-freed electrons. The exponentially increasing elec-trons and ions cause regions of the air in the gap to become electrically conductive in a process called dielectric break-down and finally an electrical discharge or an electric spark occurs. The ions or electrons produced during this process could be captured on the falling oil droplets. (1) Charge the droplets by pressing the piezo igniter.

The droplets are charged with unknown charge. Some could have many electrons (or positive ions), some a few, and some could have no charge. If you find too few droplets have net charges, press the piezo igniter again. Step 4. Selection of the Drop (1) Select an appropriate droplet for your measurement. The following charts shows the graphs of Eq. (8) computed with conditions of 𝑉𝑉 = 300 V, 𝑑𝑑 = 0.0074 m, 𝜌𝜌 = 886 kg m3⁄ , 𝜂𝜂 = 1.862 × 10−5 Pa ∙ s (𝑇𝑇 = 25℃), and fall/rise dist.= 0.5 mm.. (Notice that graphs could be altered when your experimental conditions vary.)

Note The object is to get a small number of drops, not a

large, bright cloud from which a single drop can be cho-sen. ① To make oil droplets, squeeze the atomizer bulb with one quick squeeze. ② Then squeeze it slowly to force the droplets through the hole in the droplet hole cover, through the droplet hole in the top capacitor plate, and into the space be-tween the two capacitor plates. Excessive use of the atomizer can cause too many

drops to be forced into the viewing area and prevent ob-servation of drops. Besides, repeated squirts of the atom-izer can cause the plate hole to be clogged and fail to produce any drops in the viewing area. In such cases, turn off the power supply, disassemble the chamber, and then clean them with a soft tissue.

For example, if you select a droplet which requires 15 sec-onds to fall 0.5 mm when the plates are not charged, and if the droplet has 2, 3, 4, or 5 excess electrons, the droplet will rise the same distance in the 15.7, 7.7, 5.1, or 3.6 seconds when the plates are charged. If it has only 1 excess electron, it will never rise. The droplets which have more than 6 excess electrons are almost indistinguishable since there are small differences in rise time. A droplet which requires 5 seconds to fall 0.5 mm when the

plates are not charged, is good sample for measuring the charge of 6𝑒𝑒, 7𝑒𝑒, 8𝑒𝑒, 9𝑒𝑒, or 10𝑒𝑒. It will take about 38.4, 15.7, 9.9, 7.2, or 5.7 seconds for the droplet to rise 0.5 mm again. Thus, it is recommended to select the droplet for which it takes 5-20 seconds to freely fall 0.5mm (plates not charged), and for which it takes more than 5 seconds to rises 0.5mm (plates charged). If you have enough time for observations, you had better set the moving distance at 1.0mm because you can decrease measurement errors. However, you should also notice that a long-time observation is not always good, since your droplet could disappear from view during observation, or uncontrolla-ble factors could disturb your observation. If too many droplets are in view, charge the capacitor plates

and wait until many of them get out of sight. If you find that too few droplets have net charges to permit the selection of an appropriately sized and charged drop, press the piezo igniter again. When you find an appropriately sized and charged oil drop-let, fine tune the focus of the viewing scope. (The oil droplet is in best focus when it appears as a pinpoint of bright light.) Step 5. Collecting Data on the Rise and Fall of the Droplet Measure the rise (plates charged) and fall (plates not charged) velocities of the selected droplet about 5-10 times. The greatest accuracy of measurement is achieved if you time from the instant that the droplet passes the reticle line A to the instant that the droplet passes the reticle line B (or C). The distance between the reticle lines is 0.1 mm, so A and B are 0.5 mm apart, and A and C are 1.0mm apart.

(1) With the plates not charged, start the stopwatch at the moment the falling drop passes the line A. (2) At the moment that the droplet reaches the line B or C, record the lap time by clicking the [Lap] button of the stop-watch, and apply electric fields at the same time. (3) At the moment that the rising drop reaches the line A, rec-ord the lap time again and stop applying electric fields at the same time.

(4) Repeat step (2)~(3) 5~10 times.

distance(m) Fall time (s) Rise time (s)

1

2

3

4

5

…

average

(5) Calculate the average fall and rise velocities of the select-ed droplet. 𝑣𝑣𝑓𝑓 = _______________ (m/s) 𝑣𝑣𝑟𝑟 = _______________ (m/s)

(6) Calculate the charge on the droplet.

𝑞𝑞 = 18𝜋𝜋𝑑𝑑𝑉𝑉�𝜂𝜂3𝑣𝑣𝑓𝑓3

2𝜌𝜌𝘨𝘨 �1 +𝑣𝑣𝑟𝑟𝑣𝑣𝑓𝑓� (8)

𝑞𝑞 : Charge carried by the droplet (C) 𝑉𝑉 : Potential difference across the plates (V) 𝑑𝑑 : Separation of the plates of the capacitor (m) 𝜌𝜌 : Density of oil (886 kg m3⁄ ) 𝘨𝘨 : Acceleration of gravity (m s2⁄ ) 𝜂𝜂 : Viscosity of air (Pa ∙ s = N ∙ s m2⁄ ) (See appendix.) 𝑣𝑣𝑓𝑓 : Velocity of fall without E-field (m s⁄ ) 𝑣𝑣𝑟𝑟 : Velocity of rise without E-field (m s⁄ ) If the result of this first determination for the charge on the drop is too great, you should use slower moving droplets in subsequent determinations. Step 6. Changing the Charge of the Droplet It is desirable to observe as many different charges on a single drop as possible. If the droplet is still in view, attempt to change the charge on the droplet and measure the new rising velocity many times, if possible. (1) Bring the droplet to the bottom of the field of view using the plate voltage switch. (2) Rotate the plate charging switch to the charging position to the droplet to rise. (3) Change the charge on the droplet by pressing the piezo igniter as described previously. If the rising velocity of the droplet changes, make as many measurements of the new rising velocity as you can. (4) Repeat Step 5. (5) If the droplet is still in view, repeat Step 6 as many times as you can. Step 7. Additional Measurement Repeat step 1 to 6 with other droplets. Repeat the experiment with at least 20 different charge through the steps 5~7. It is desirable to get as many data as you can. Step 8. Analysis Consider appropriate analysis methods to find the elemen-tary charge with your experimental data. For example, the following statistical approach can be considered when lots of data collected. The following chart shows an example of the measured charges of 200 oil drops. Red dots are measured values and blue lines represent theoretical values of 𝑛𝑛𝑒𝑒. Because of ran-dom errors, your measurements may be deviated from an expected value in every trial. Usually random errors follow a normal distribution, so the assumption of normality can be a good first approximation.

A histogram is a good tool giving a rough sense of the densi-ty of the underlying distribution of the data. In the process of dividing the entire range of charge values into series of inter-vals, and then counting how many values fall into each inter-val, we can get the following histogram. As the histogram shows, the example data have a distribution that is nearly normal at several peaks. Curve fitting can be used to find the best fit curve, and finally the elementary charge is obtained.

See the appendix of the FULL version of manual for more

instructions.

1. Viscosity Sutherland’s formula can be used to derive the viscosity 𝜂𝜂 of an ideal gas as a function of a temperature

𝜂𝜂 = 𝜂𝜂0𝑇𝑇0 + 𝐶𝐶𝑇𝑇 + 𝐶𝐶 �

𝑇𝑇𝑇𝑇0�32

𝐶𝐶 : Surtherland’s constant 𝑇𝑇 : input temperature (K) 𝑇𝑇0 : reference temperature (K) 𝜂𝜂0 : reference viscosity (Pa ∙ s) at reference temperature 𝑇𝑇0 Surtherland’s constant and reference values for dry air are 𝐶𝐶 = 120 𝑇𝑇0 = 291.15 K 𝜂𝜂0 = 1.827 × 10−5 Pa ∙ s

2. Thermistor A thermistor is a specialized resistor, intentionally designed to be thermally sensitive and its primary characteristic is its ability to alter its electrical resistance in response to changes in case temperature. The resistance of a 10 kΩ thermistor at 𝑇𝑇(℃) follows the table below.

𝑇𝑇 (℃)

𝑅𝑅 (kΩ)

𝑇𝑇 (℃)

𝑅𝑅 (kΩ)

𝑇𝑇 (℃)

𝑅𝑅 (kΩ)

0 27.616 26 9.6306 36 6.6859

5 22.266 27 9.2768 37 6.4535

10 18.066 28 8.9879 38 6.2304

15 14.748 29 8.6132 39 6.0162

20 12.110 30 8.3020 40 5.8104

21 11.650 31 8.0037 45 4.8965

22 11.210 32 7.7177 50 4.1454

23 10.789 33 7.4435 60 3.0106

24 10.386 34 7.1805 80 1.6669

25 10.000 35 6.9281 100 0.97771

3. Analysis See the appendix of the FULL version of manual.

Please put your equipment in order as shown below.

□ Delete your data files from your lab computer. □ Turn off the lab computer. □ With the voltage adjustment knob set at zero, turn off the power supply and unplug the power cable.

□ Unplug the dc adapter of the LED lamp. □ Assemble the chamber.

(Be careful not to lose any parts of it.) □ Screw the focusing wire to its storage location on the platform. □ Place the atomizer into the holder on the platform. (Handle the atomizer with care. It is very fragile.)

□ Do not unplug the high voltage patch cords.

Appendix

End of LAB Checklist