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General Physics Lab (International Campus) Department of PHYSICS YONSEI University

Lab Manual

Millikan Oil Drop Experiment Ver.20170911

Lab Office (Int’l Campus)

Room 301, Building 301 (Libertas Hall B), Yonsei University 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA (☏ +82 32 749 3430) / 19

[International Campus Lab]

Millikan Oil Drop Experiment

Determine the charge of an electron by observing the effect of an electric field on a cloud of charged oil droplets.

In 1909, Robert Millikan conducted the oil drop experiment

to determine the charge of an electron. He suspended tiny

charged droplets of oil between two metal electrodes by bal-

ancing downward gravitational force with upward electric

force. The density of the oil was known, so he could deter-

mine the droplets’ masses from their observed radii. Using

the known electric field and the value of gravity and mass, he

determined the charge on oil droplets in mechanical equilibri-

um. By repeating the experiment, he confirmed that the

charges were all multiples of some fundamental value. He

proposed that this value was the charge of a single electron.

The figure 1 shows a simplified scheme of Millikan’s oil drop

experiment. A fine mist of oil droplets is sprayed into the

chamber and some droplets enter the space between the

plates. The droplets become electrically charged by an ioniz-

ing radiation source such as an X-ray.

By applying a potential difference across a parallel pair of

horizontal metal plates, a uniform electric field is created in

the space between them. The electric field can be controlled

by changing the voltage across the plates.

The droplets can be observed through a viewing scope with

illumination by the bright light of a lamp. The scope has reticle

marks spaced to 0.1mm, so the velocity of the falling or rising

drop can be calculated.

Fig 1 (a) Simplified scheme of the Millikan oil drop experiment. (b) Forces on a falling drop. (plates not charged) (c) Forces on a rising drop. (plates charged)

Objective

Theory

----------------------------- Reference --------------------------

Young & Freedman, University Physics (14th ed.), Pearson, 2016

23. Electric Potential – Problem 23.81 (p.807)

-----------------------------------------------------------------------------


Lab Manual




Figure 1(b) shows the forces acting on a droplet when it is

falling in air. The velocity of drop has reached its terminal

velocity 𝑣𝑣𝑓𝑓 in a few milliseconds for the droplets used in this

experiment. The frictional force 𝐹𝐹fr = 𝑘𝑘𝑣𝑣 is proportional to the

velocity of the drop, where 𝑘𝑘 is the coefficient of friction be-

tween the air and the drop. Since the gravitational force

𝐹𝐹𝗀𝗀 = 𝑚𝑚𝘨𝘨 and the frictional force 𝐹𝐹fr are equal and opposite,

𝑚𝑚𝘨𝘨 = 𝑘𝑘𝑣𝑣𝑓𝑓 (1)

Figure 1(c) shows the forces acting on the drop when it is

rising under the influence of an electric field. The electric in-

tensity is given by 𝐸𝐸 = 𝑉𝑉 𝑑𝑑⁄ , where 𝑉𝑉 is the potential differ-

ence across the parallel plates separated by a distance 𝑑𝑑. If

the charge on the droplet is 𝑞𝑞 then there is an additional

electric force 𝐹𝐹e = 𝑞𝑞𝐸𝐸 on it. If the sign and magnitude of the

field are such to make the droplet rise, it will quickly acquire a

terminal velocity 𝑣𝑣𝑟𝑟 and the frictional force 𝐹𝐹fr = 𝑘𝑘𝑣𝑣𝑟𝑟 acts on

it. Adding the forces vectorially yields

𝑞𝑞𝐸𝐸 =𝑞𝑞𝑉𝑉𝑑𝑑 = 𝑚𝑚𝘨𝘨 + 𝑘𝑘𝑣𝑣𝑟𝑟 (2)

In both cases, there is also a small buoyant force exerted by

the air on the droplet. Since the density of air is only about

10−3 of that of oil, this force may be neglected.

Eliminating 𝑘𝑘 from equations (1) and (2) and solving for 𝑞𝑞

yields

𝑞𝑞 =𝑚𝑚𝘨𝘨𝑑𝑑𝑉𝑉 �1 +

𝑣𝑣𝑟𝑟𝑣𝑣𝑓𝑓� (3)

To eliminate 𝑚𝑚 from equation (3), we use the expression for

the volume of a sphere

𝑚𝑚 =43𝜋𝜋𝑟𝑟

3𝜌𝜌 (4)

where 𝑟𝑟 is the radius of the droplet, and 𝜌𝜌 is the density of

the oil. Substituting equation (4) into equation (3) yields

𝑞𝑞 =4𝜋𝜋3𝜌𝜌𝑟𝑟3𝘨𝘨𝑑𝑑𝑉𝑉 �1 +

𝑣𝑣𝑟𝑟𝑣𝑣𝑓𝑓� (5)

The velocities 𝑣𝑣𝑓𝑓 and 𝑣𝑣𝑟𝑟 of the equation (5) can be meas-

ured experimentally and only the radius 𝑟𝑟 of the oil droplet

remains unknown. The frictional force 𝐹𝐹fr = 𝑘𝑘𝑣𝑣 in figure 1

actually results from the viscosity between the oil and the air.

The viscous force on a small sphere moving through a vis-

cous fluid is given by

𝐹𝐹 = 6𝜋𝜋𝜋𝜋𝑟𝑟𝑣𝑣 (6)

Equation (6), known as Stokes’ law, is the frictional force

acting on the interface between a fluid and a particle, where

𝜋𝜋 is the viscosity, 𝑟𝑟 is the radius of the spherical object, and

𝑣𝑣 is the flow velocity relative to the object. (For accurate

analysis, Millikan suggested the corrected form of Stokes’ law

with effective viscosity 𝜋𝜋eff = 𝜋𝜋(1 + 𝑏𝑏 𝑝𝑝𝑟𝑟⁄ )−1 , where 𝑏𝑏 is a

constant and 𝑝𝑝 is the atmospheric pressure. We will neglect

this correction factor here.) Now Equation (6) can be substi-

tuted for 𝐹𝐹fr = 𝑘𝑘𝑣𝑣 in equation (1). Substituting equations (4),

(6) into equation (1) yields

43𝜋𝜋𝑟𝑟

3𝜌𝜌𝘨𝘨 = 6𝜋𝜋𝜋𝜋𝑟𝑟𝑣𝑣𝑓𝑓 or 𝑟𝑟 = �9𝜋𝜋𝑣𝑣𝑓𝑓2𝜌𝜌𝘨𝘨 (7)

Substituting equation (7) into equation (5) yields

𝑞𝑞 = 18𝜋𝜋𝑑𝑑𝑉𝑉�𝜋𝜋3𝑣𝑣𝑓𝑓3

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 (kg m3⁄ )

𝘨𝘨 : Acceleration of gravity (m s2⁄ )

𝜋𝜋 : 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⁄ )

The most precise value of the charge of an electron is

𝑒𝑒 = 1.602176487(40) × 10−19 C.


Lab Manual




1. List

Item(s) Qty. Description

Millikan Apparatus

1 Measures the elementary electric charge using a clas-sical method of Millikan.

Power Supply (Power cord included)

1 Supplies voltage for the capacitor plates. Produces regulated DC power up to 50mA in a voltage range 0 to 500 volts.

Power Adapter (for LED lamp)

1 Supplies voltage for the LED lamp.

Patch Cords (High Voltage) (with safety shrouded banana plugs)

2 Connect the power supply to the capacitor plates of the Millikan apparatus.

Patch Cords (with banana plugs)

2 Connect the multimeter to the thermistor of the Millikan apparatus.

Atomizer

1 Sprays oil droplets of density 𝜌𝜌 = 886 kg m3⁄

Multimeter

1 Measures voltage, current, and resistance.

A-shaped Base Support Rod (600mm)

1 2

Provide stable support for experiment set-ups.

Vernier Caliper

1 Measures external or internal diameter of an object with a precision to 0.05mm.

Equipment


Lab Manual




2. Details

(1) Millikan Apparatus

(2) Power Supply

The power supply provides regulated DC power up to

50mA in a voltage range 0 to 500 volts.

(3) Multimeter

The multimeter measures voltage, current, and resistance.

(4) Vernier Caliper

The Vernier caliper measures external, internal diameter or

depth of an object with a precision to 0.05mm.

① 22 mm is to the immediate left of the zero on the vernier

scale. Hence, the main scale reading is 22 mm.

② Look closely for and alignment of the scale lines of the

main scale and vernier scale. In the figure, the aligned (13th)

line corresponds to 0.65 mm (= 0.05 × 13).

③ The final measurement is given by the sum of the two

readings. This gives 22.65 mm (= 22 + 0.65).


Lab Manual




Setup 1. 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.

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.

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.

Caution

Be careful not to lose any parts of the chamber assem-

bly, especially the droplet hole cover.


Lab Manual




(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.)


Lab Manual




(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 Suth-

erland’s Formula and the Thermistor Resistance Table (see

appendix) to find the viscosity of air.

𝜋𝜋 = _______________ (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 volt-

age 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.


Lab Manual




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.

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.


Lab Manual




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.

(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.

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.


Lab Manual




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⁄ ,

𝜋𝜋 = 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.)

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.)


Lab Manual




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�𝜋𝜋3𝑣𝑣𝑓𝑓3

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⁄ )

𝜋𝜋 : 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.


Lab Manual




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 appendix for more instructions.


Lab Manual




1. Viscosity

Sutherland’s formula can be used to derive the viscosity 𝜋𝜋

of an ideal gas as a function of a temperature

𝜋𝜋 = 𝜋𝜋0𝑇𝑇0 + 𝐶𝐶𝑇𝑇 + 𝐶𝐶 �

𝑇𝑇𝑇𝑇0�32

𝐶𝐶 : Surtherland’s constant

𝑇𝑇 : input temperature (K)

𝑇𝑇0 : reference temperature (K)

𝜋𝜋0 : reference viscosity (Pa ∙ s) at reference temperature 𝑇𝑇0

Surtherland’s constant and reference values for dry air are

𝐶𝐶 = 120

𝑇𝑇0 = 291.15 K

𝜋𝜋0 = 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

The following table is an example of 200 observations of the

droplet charge. We now consider a statistical approach to find

the elementary charge using the data.

No. 𝑞𝑞 (× 10−19)

No. 𝑞𝑞 (× 10−19)

No. 𝑞𝑞 (× 10−19)

No. 𝑞𝑞 (× 10−19)

No. 𝑞𝑞 (× 10−19)

1 3.531 41 9.307 81 9.944 121 6.392 161 3.440

2 5.073 42 1.531 82 9.147 122 3.063 162 9.108

3 10.682 43 4.265 83 6.113 123 11.549 163 9.667

4 3.196 44 1.894 84 11.253 124 3.262 164 9.392

5 9.814 45 6.676 85 6.434 125 3.304 165 9.706

6 7.564 46 6.576 86 9.316 126 4.485 166 1.310

7 1.524 47 9.486 87 11.345 127 11.141 167 5.176

8 9.415 48 1.804 88 5.300 128 11.163 168 4.914

9 6.698 49 3.650 89 7.686 129 5.983 169 6.085

10 8.377 50 11.126 90 6.215 130 5.154 170 9.567

11 3.335 51 1.342 91 3.139 131 2.863 171 10.952

12 4.818 52 6.491 92 9.944 132 4.978 172 4.399

13 7.682 53 6.288 93 3.752 133 5.289 173 3.050

14 9.362 54 3.491 94 9.834 134 11.228 174 4.452

15 1.399 55 6.319 95 1.552 135 8.476 175 1.499

16 6.674 56 10.890 96 9.198 136 6.276 176 10.055

17 1.590 57 7.607 97 9.546 137 3.297 177 7.870

18 3.430 58 1.081 98 4.727 138 1.283 178 8.071

19 8.024 59 11.260 99 9.722 139 3.536 179 4.521

20 10.045 60 3.313 100 8.142 140 3.181 180 2.777

21 6.356 61 5.106 101 7.990 141 9.900 181 10.925

22 1.010 62 9.749 102 8.502 142 9.149 182 3.292

23 1.670 63 6.577 103 9.369 143 3.569 183 4.326

24 1.254 64 3.636 104 6.730 144 4.993 184 10.047

25 10.089 65 8.569 105 6.215 145 10.891 185 1.994

26 11.158 66 11.731 106 9.928 146 7.661 186 11.221

27 11.096 67 8.134 107 9.782 147 6.123 187 6.480

28 9.145 68 4.332 108 4.996 148 11.630 188 8.093

29 10.808 69 7.595 109 2.122 149 2.663 189 4.788

30 9.805 70 3.072 110 1.805 150 9.834 190 9.311

31 6.001 71 1.894 111 3.100 151 4.772 191 6.287

32 7.967 72 6.204 112 1.704 152 9.502 192 2.482

33 7.777 73 8.201 113 7.964 153 5.007 193 9.542

34 6.508 74 11.333 114 2.666 154 8.070 194 8.394

35 11.220 75 6.911 115 3.175 155 5.922 195 9.636

36 9.850 76 5.846 116 1.523 156 10.345 196 1.837

37 4.726 77 9.901 117 4.894 157 1.676 197 10.184

38 6.859 78 7.836 118 4.955 158 11.065 198 5.772

39 5.254 79 9.453 119 8.189 159 10.612 199 9.505

40 6.237 80 11.339 120 1.002 160 11.125 200 9.567

Appendix


Lab Manual




The following chart shows the distribution of the measured

charges of 200 oil drops as in the previous table. X-axis is

sequential number of droplets and y-axis is charge. Red dots

are measured charges of each oil droplet. Theoretical values

of 𝑛𝑛𝑒𝑒 are plotted in blue lines.

To create a histogram, we need a frequency distribution

table which contains the counts of the occurrences of values

within particular intervals or bins. The theory of statistics in-

troduces several rules for how to choose the optimal bin size.

However, in this example, we simply set it to 0.1602(× 10−19)

which is 1/10 of the elementary charge. Divide the range into

as follows and count how many values fall into each bin. Now

we have the following distribution table and histogram.

Bin Frequency

0 0

0.1602 0

0.3204 0

…

1.4418 4

1.602 6

1.7622 3

…

You can easily carry out the previous process using any

spreadsheet application such as ‘Excel’, which providing au-

tomated function to generate frequency table and histograms.

To create a histogram in Excel (the following guide applies

to Excel 2013 or prior versions), you need to load [Analysis

ToolPak] (분석 도구). Click [File] (파일) tab, click [Options]

(옵션), and then click [Add-Ins] (추가 기능) category. In the

[Manage] (관리) box, select [Excel Add-ins] (Excel 추가 기능)

and then click [Go] (이동).

In the [Add-Ins] (추가 기능) box, check the [Analysis Tool-

Pak] (분석 도구) checkbox, and then click [OK] (확인). Now

you can use [Data Analysis] (데이터 분석) in the [Analysis]

(분석) group on the [Data] (데이터) tab.


Lab Manual




In one column, type bin numbers (evenly distributed inter-

vals) in ascending order. These represent the intervals by

which you want to measure the frequency.

Click [Data] (데이터) tab, click [Data Analysis] (데이터 분석)

and then select [Histogram] (히스토그램).

In the [Input Range] (입력 범위) box, enter the cell refer-

ence for the data range that has the droplet charges. In the

[Bin Range] (계급 구간) box, enter the cell reference for the

range that has the bin numbers. Under [Output Options] (출력

옵션), choose an output location. Check [Chart Output] (차트

출력) to shows an embedded histogram chart.

A frequency table and a histogram will be automatically

generated as follows.

The next step requires data analysis applications such as

‘Origin’ or ‘MATLAB’, since Excel does not provide complex

curve fit models such as Gaussian curve or multi-peak fitting.

When any data analysis app is not available, we recommend

the lightweight application, ‘MagicPlot’. (You can download

the free version of it at magicplot.com.)

(Continued)


Lab Manual




Run MagicPlot application and click [Create new Table] icon.

Type bin numbers in A column and frequency data in B col-

umn. (Or, use keyboard shortcuts such as Ctrl+C and Ctrl-V

to copy and paste data from Excel to MagicPlot.)

To create a Fit Plot, select your B column in Table, then click

[Create Fit Plot] button in the toolbar. Select [Line & Marker].

Now the following plot is generated.

To customize your plot, click [Line & markers] tap of [Curve

properties] window. Select [Vert Bars] for line type and check

[Fill] the lines.

To add a Fit Curve, click [Add] button in the [Fit Curves] tab

and select [Gaussian].


Lab Manual




Fitting process assumes that certain initial values of pa-

rameters are set before fitting. So you have to approximately

locate peaks before fitting. Using two circles on the fit curve,

drag the fit curve on corresponding position in data plot.

Add additional Gaussian curves and rearrange them. In the

example, the data plot has 7 peaks, so we added 7 fit curves.

Click [Fit by Sum] button. Then MagicPlot will fit the data

with the sum of each fit curves.

You can find the parameters of each Gaussian curves in the

[Fit Curves] tab.


Lab Manual




Your TA will inform you of the guidelines for writing the laboratory report during the lecture.

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.

Result & Discussion

End of Lab Checklist

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