Millikan Oil Drop 02-06-2009

012-06123D

MILLIKAN OIL DROPAPPARATUS

Instruction Manual andExperiment Guide for thePASCO scientificModel AP-8210

IncludesTeacher's Notes

andTypical

Experiment Results

The exclamation point within an equilateraltriangle is intended to alert the user of thepresence of important operating and mainte-nance (servicing) instructions in the literatureaccompanying the appliance.

i012-06123D Millikan Oil Drop Experiment

Table of Contents

Section PageCopyright, Warranty, and Equipment Return ........................................................... iiIntroduction .............................................................................................................. 12Equipment ............................................................................................................... 3 4Equipment Setup ........................................................................................................ 5Aligning the Optical System ...................................................................................... 6Functions of Controls ................................................................................................. 6Adjusting and Measuring the Voltage ....................................................................... 7Determining the Temperature of the Droplet Viewing Chamber ............................. 7Experimental Procedure ...........................................................................................7 9Computation of the Charge of an Electron ................................................................ 9Using a Projection Microscope with the Millikan Oil Drop Apparatus ................... 10Historical ................................................................................................................ 1115

Maintenance NotesCleaning .................................................................................................................... 16Replacing the Halogen Bulb ..................................................................................... 16Adjusting the Vertical Reticle and Viewing Scope Alignments .............................. 16Adjusting the Horizontal Reticle Alignment ............................................................ 17Touching Up the Black Painted Surface on the Plastic Spacer ................................ 17

AppendixA: Viscosity of Dry Air as a Function of Temperature ......................................... 19B: Thermistor Resistance at Various Temperatures .............................................. 20

Teachers Guide .................................................................................................... 2124

Technical Support ............................................................................................ Back Cover

ii

Millikan Oil Drop Experiment 012-06123D

Copyright NoticeThe PASCO scientific 012-06123C manual iscopyrighted and all rights reserved. However,permission is granted to non-profit educationalinstitutions for reproduction of any part of theMillikan Oil Drop Experiment manual providing thereproductions are used only for their laboratories andare not sold for profit. Reproduction under any othercircumstances, without the written consent of PASCOscientific, is prohibited.

Limited WarrantyPASCO scientific warrants the product to be free fromdefects in materials and workmanship for a period of oneyear from the date of shipment to the customer. PASCOwill repair or replace, at its option, any part of the productwhich is deemed to be defective in material orworkmanship. The warranty does not cover damage to theproduct caused by abuse or improper use. Determinationof whether a product failure is the result of amanufacturing defect or improper use by the customershall be made solely by PASCO scientific. Responsibilityfor the return of equipment for warranty repair belongs tothe customer. Equipment must be properly packed toprevent damage and shipped postage or freight prepaid.(Damage caused by improper packing of the equipmentfor return shipment will not be covered by the warranty.)Shipping costs for returning the equipment, after repair,will be paid by PASCO scientific.

Copyright, Warranty and Equipment Return

PleaseFeel free to duplicate this manualsubject to the copyright restrictions below.

CreditsEditor: Sunny Bishop

Equipment ReturnShould the product have to be returned to PASCOscientific for any reason, notify PASCO scientific byletter, phone, or fax BEFORE returning the product.Upon notification, the return authorization andshipping instructions will be promptly issued.

When returning equipment for repair, the units mustbe packed properly. Carriers will not accept responsi-bility for damage caused by improper packing. To becertain the unit will not be damaged in shipment,observe the following rules:

The packing carton must be strong enough for theitem shipped.

Make certain there are at least two inches ofpacking material between any point on theapparatus and the inside walls of the carton.

Make certain that the packing material cannot shiftin the box or become compressed, allowing theinstrument come in contact with the packingcarton.

Address: PASCO scientific10101 Foothills Blvd.Roseville, CA 95747-7100

Phone: (916) 786-3800FAX: (916) 786-3292email: [email protected]: www.pasco.com

NOTE: NO EQUIPMENT WILL BEACCEPTED FOR RETURN WITHOUT ANAUTHORIZATION FROM PASCO.

012-06123D Millikan Oil Drop Experiment

1

The electric charge carried by a particle may be calculatedby measuring the force experienced by the particle in anelectric field of known strength. Although it is relativelyeasy to produce a known electric field, the force exertedby such a field on a particle carrying only one or severalexcess electrons is very small. For example, a field of1000 volts per cm would exert a force of only 1.6 l0-9dyne on a particle bearing one excess electron. This is aforce comparable to the gravitational force on a particlewith a mass of l0-l2 (one million millionth) gram.The success of the Millikan Oil Drop experiment dependson the ability to measure forces this small. The behaviorof small charged droplets of oil, having masses of onlyl0-12 gram or less, is observed in a gravitational and anelectric field. Measuring the velocity of fall of the drop inair enables, with the use of Stokes Law, the calculation ofthe mass of the drop. The observation of the velocity ofthe drop rising in an electric field then permits acalculation of the force on, and hence, the charge carriedby the oil drop.Although this experiment will allow one to measure thetotal charge on a drop, it is only through an analysis of thedata obtained and a certain degree of experimental skillthat the charge of a single electron can be determined. Byselecting droplets which rise and fall slowly, one can becertain that the drop has a small number of excesselectrons. A number of such drops should be observedand their respective charges calculated. If the charges onthese drops are integral multiples of a certain smallestcharge, then this is a good indication of the atomic natureof electricity. However, since a different droplet has beenused for measuring each charge, there remains thequestion as to the effect of the drop itself on the charge.This uncertainty can be eliminated by changing the chargeon a single drop while the drop is under observation. Anionization source placed near the drop will accomplishthis. In fact, it is possible to change the charge on thesame drop several times. If the results of measurementson the same drop then yield charges which are integralmultiples of some smallest charge, then this is proof of theatomic nature of electricity.

The measurement of the charge of the electron alsopermits the calculation of Avogadros number. Theamount of current required to electrodeposit one gramequivalent of an element on an electrode (the faraday) is

Figure 1 Figure 2

Figure 2 shows the forces acting on the drop when it isrising under the influence of an electric field. In Figure 2,E is the electric intensity, q

is the charge carried by thedrop, and v

r is the velocity of rise. Adding the forces

vectorially yields:

EQUATION FOR CALCULATING THECHARGE ON A DROPAn analysis of the forces acting on an oil droplet willyield the equation for the determination of the chargecarried by the droplet.Figure 1 shows the forces acting on the drop when it isfalling in air and has reached its terminal velocity.(Terminal velocity is reached in a few milliseconds for thedroplets used in this experiment.) In Figure 1, vf is thevelocity of fall, k is the coefficient of friction between theair and the drop, m is the mass of the drop, and g is theacceleration of gravity. Since the forces are equal andopposite:

mg = kvf ( 1 )

INTRODUCTION

kvf

mg

Eq

kvr

mg

equal to the charge of the electron multiplied by thenumber of molecules in a mole. Through electrolysisexperiments, the faraday has been found to be 2.895 x l014electrostatic units per gram equivalent weight (morecommonly expressed in the mks system as 9.625 x l07coulombs per kilogram equivalent weight). Dividing thefaraday by the charge of the electron,

2.895 x l014 e.s.u./gm equivalent weight 4.803 x l0-l0 e.s.u.,

yields 6.025 x l023 molecules per gram equivalent weight,or Avogadros number.


2

The electric intensity is given by E = V/d, where V is thepotential difference across the parallel plates separated bya distance d. E, V, and d are all expressed in the samesystem of units. If E is in electrostatic units, V in volts,and d in centimeters, the relationship is:

(9 )Substituting equations ( 7 ) and ( 8 ) into equation ( 6 ) andrearranging the terms yields:

(10 )The terms in the first set of brackets need only bedetermined once for any particular apparatus. The secondterm is determined for each droplet, while the term in thethird set of brackets is calculated for each change ofcharge that the drop experiences.

The definitions of the symbols used, together with theirproper units for use in equation ( 9 ) are***:

q

charge, in e.s.u. , carried by the dropletd separation of the plates in the condenser in cm density of oil in gm/cm3g acceleration of gravity in cm/s2

viscosity of air in poise ( dyne s/cm2)b constant, equal to 6. 17 x l0-4 (cm of Hg) (cm)p barometric pressure in cm of mercury.a radius of the drop in cm as calculated by equation

( 5 )vf velocity of fall in cm/sv

r velocity of rise in cm/s

V potential difference across the plates in volts

Note: The accepted value for e is 4.803 x l0-l0 e.s.u.,or 1.60 x 10-19 coulombs.

( 2 )In both cases there is also a small buoyant force exertedby the air on the droplet. Since the density of air is onlyabout one-thousandth that of oil, this force may beneglected.Eliminating k from equations ( 1 ) and ( 2 ) and solvingfor q

yields:

( 3 )To eliminate m from equation ( 3 ), one uses theexpression for the volume of a sphere:

( 4 )where a is the radius of the droplet, and is the density ofthe oil.To calculate a, one employs Stokes Law, relating theradius of a spherical body to its velocity of fall in aviscous medium (with the coefficient of viscosity, ).

*

( 5 )Stokes Law, however, becomes incorrect when thevelocity of fall of the droplets is less than 0.1 cm/s.(Droplets having this and smaller velocities have radii, onthe order of 2 microns, comparable to the mean free pathof air molecules, a condition which violates one of theassumptions made in deriving Stokes Law.) Since thevelocities of the droplets used in this experiment will be inthe range of 0.01 to 0.001 cm/s, the viscosity must bemultiplied by a correction factor. The resulting effectiveviscosity is:

**

( 6 )where b is a constant, p is the atmospheric pressure, and ais the radius of the drop as calculated by the uncorrectedform of Stokes Law, equation ( 5 ).Substituting

eff in equation (6) into equation (5), andthen solving for the radius a gives:

( 7 )Substituting equations (4), (5), and (6) into equation (3)yields:

( 8 )

*For additional information about Stokes Law, thestudent is referred to Introduction to Theoretical Physics,by L. Page (New York, Van Nostrand), Chapter 6.** A derivation may be found in The Electron by R. A.Millikan (Chicago, The University of Chicago Press),Chapter 5.*** Modern calculations of q

are usually conducted in SIunits. (See Experimental Procedure, Computation of theCharge of an Electron, page 7.)

Eq = mg + kvr

q =mg (vf + vr)

Evf

a =9 vf2g

m = 43a3

eff = 11 + bpa

q = 6 93

2g 1 + bpa3 vf + vr vf

E (e.s.u.) = V (volts)300d (cm)

q = 400d 1g92

31 21 2

x 11 + bpa

3 23 2x

vf + vr vfV e.s.u.


3

PLATE V

OLTAGE

500VDC M

AX

+

CHAMBE

R TEMPE

RATURE

THERMI

STOR

IONIZAT

ION

SOURCE

IONIZAT

ION

SOURCE

SPRAY

DROPLET

RETICLE

FOCUS

DROPLE

T

FOCUS

DO NOT A

PPLY VOL

TAGE

POSITION

ON

IONIZATI

ON

SOURCE

:

THORIUM

232

0.008 C

i

THERMI

STOR RE

SISTANC

E TABLE

MILLIK

AN OIL

DROP

APPARA

TUS

AP-821

0

VERTICA

L

LAMP

ADJUST

MENT

HORIZO

NTAL

LAMP

ADJUST

MENT

LAMP

POWER

REMOVE

SCREW

S TO

REPLAC

E BULB

103.23

9

113.11

8

123.00

4

133.89

7

142.79

5

152.70

0

162.61

0

172.52

6

182.44

6

192.37

1

202.30

0

212.23

3

222.16

9

232.11

0

242.05

3

252.00

0

261.95

0

271.90

2

281.85

7

291.81

5

301.77

4

311.73

6

321.70

0

331.66

6

341.63

4

351.60

3

361.57

4

371.54

7

381.52

1

391.49

6

CX10

6 C

X106

CX10

6

UNSCRE

W TO

USE

REPLAC

EMENT

HALOGE

N BULB

PASCO

P/N

526-037

12V, 5W

FOCUSI

NG

WIRE

PLATE

VOLTAG

ETOPPLA

TE

PLATES

GROUND

ED

TOPPLA

TE

+

EQUIPMENTIncluded equipment:

apparatus platform and plate charging switch (seedetailed description below and on page 4)

12 volt DC transformer for the halogen lamp non-volatile oil (Squibb #5597 Mineral Oil, density =

886 kg/m3)* atomizer

* Note: We measured the density of the Squibb MineralOil and found it to be 886kg/m3. However, thedensities of different lots of mineral oil may varyslightly; therefore, for greatest precision, you shoulddetermine the density of the mineral oil you are using.

Figure 3. Included equipment

platform

atomizer

12 V DCpower

adaptor

oil

plate charging switch

support rod clamping screw

plate voltage connectors

droplet viewing chamber housing

viewing scopereticle focusing ring

droplet focusing ring

plate charging switch

support rod mount

focusing wire

thermistor resistance table

thermistor connectors

bubble level

support rod mount

support rod clamping screw

filament adjustment knob (horizontal)

filament adjustment knob(vertical)

convex lens

Figure 4. Apparatus platform

halogen lamp housing

lamp power jack

ionization source lever


4

Required equipment, not included: high voltage, well regulated power supply that

delivers up to 500 V DC, 10 mA minimum (forexample, the PASCO SF-9585 High Voltage PowerSupply)

digital multimeter (to measure voltage and resistance)(for example, the PASCO SB-9599A UniversalDigital Multimeter)

patch cords with banana plug connectors (4) (forexample, the PASCO SE-9415 Banana Plug PatchCord)

stopwatch (for example, the PASCO SE-8702ADigital Stopwatch)

Additional recommended equipment: PASCO ME-8735 Large Rod Stand PASCO ME-8736 Steel Rods, 45 cm (2)

Components of droplet viewing chamber (Figure 5) lid housing droplet hole cover upper capacitor plate (brass) plastic spacer (approximately 7.6 mm thick) lower capacitor plate (brass)

- thorium-232 alpha source (0.008 mcurie)- electrical connection to upper capacitor plate

convex lens

Components of platform: droplet viewing chamber (see details below) viewing scope (30X, bright-field, erect image) with

reticle (line separation: 0.5 mm major divisions, 0.1mm minor divisions), reticle focusing ring, anddroplet focusing ring

halogen lamp (12 V, 5 W halogen bulb and dichroic,infrared heat-absorbing window, horizontal andvertical filament adjustment knobs)

focusing wire (for adjusting viewing scope) plate voltage connectors thermistor connectors (thermistor is mounted in the

bottom plate)

Note: Thorium-232 is a naturally occurring, lowlevel alpha-particle emitter with a half-life of 1.41 x1010 years. It is not regulated in its use and posesno hazard to the user of the PASCO Millikan OilDrop Apparatus.

thermistor table (resistance versus temperature) ionization source lever (with three positions:

Ionization ON, Ionization OFF, and Spray DropletPosition)

bubble level support rod mounts and screws (to permit mounting of

platform on a PASCO ME-8735 Large Rod Stand, soviewing scope can be raised to a comfortable eyelevel)

3 leveling feet plate charging switch (on a 1 meter cord to prevent

vibration of platform during switching activity)

Figure 5. Droplet viewing chamber

thorium-232

upper capacitor

housing pins

droplet hole cover

lower capacitor

lid

housing

spacerelectrical connector

base ofapparatus

It is recommended that you store theequipment in the original packing material.After unpacking, remove the foam insertfrom the droplet viewing chamber. Storethe plate charging switch on the velcro tabslocated on the platform.

WARNING: Do not apply voltage to thethermistor connectors.


5

Equipment Setup

Figure 6. Equipment setup

Measuring plate separation

1. Disassemble the droplet viewing chamber by liftingthe housing straight up and then removing the uppercapacitor plate and spacer plate. (See Figure 5.)Measure the thickness of the plastic spacer (which isequal to the plate separation distance) with amicrometer. Be sure that you are not including theraised rim of the spacer in your measurement. Theaccuracy of this measurement is important to thedegree of accuracy of your experimental results.Record the measurement.

Adjusting the height of the platform and leveling it1. Place the apparatus on a level, solid table with the

viewing scope at a height which permits theexperimenter to sit erect while observing the drops. Ifnecessary to achieve the proper height, mount theapparatus on two support rods (ME-8736) on the largerod stand (ME-8735) (Figure 6).

2. Using attached bubble level as a reference, level theapparatus with the leveling screws on the rod stand orthe leveling feet of the platform, as is appropriate foryour setup.

Adjusting the environment of the experiment room1. Make the room as dark as possible, while allowing for

adequate light to read the multimeter and stopwatch,and to record data.

2. Insure that the background behind the apparatus isdark.

3. Select a location that is free of drafts and vibrations.

Adjust to comfortable eye level.

high voltage DC power supply

sturdy, non-vibrating table

support rods

rod stand

Use care when handling the brass platesand plastic spacer to avoid scratching them.

All surfaces involved in the measurementshould be clean to prevent inaccuratereadings.


6

Functions of ControlsIonization source lever

1. When the lever is at the ionization OFF position, theionization source is shielded on all sides by plastic, sothat virtually no alpha particles enter the area of thedrops.

2. At the ON position, the plastic shielding is removedand the drop area is exposed to the ionizing alphaparticles emitted from the thorium-232.

3. At the Spray Droplet Position, the chamber is ventedby a small air hole that allows air to escape when oildrops are being introduced to the chamber.

Plate charging switchThe plate charging switch has three positions:

1. TOP PLATE : negative binding post is connectedto the top plate.

2. TOP PLATE +: negative binding post is connectedto the bottom plate.

3. PLATES GROUNDED: plates are disconnectedfrom the high voltage supply and are electricallyconnected.

3. Connect the 12 V DC transformer to the lamp powerjack in the the halogen lamp housing and plug it into awall socket.

Focusing the halogen filament

1. Adjust the horizontal filament adjustment knob. Thelight is best focused when the right edge of the wire is

Focusing the viewing scope

1. Reassemble the plastic spacer and the top capacitorplate onto the lower capacitor plate. Replace thehousing, aligning the holes in its base with the housingpins. (See Figure 5.)

Figure 7. Insertion of the focusing wire into the topcapacitor plate

Aligning the Optical System brightest (in highest contrast compared to the center ofthe wire).

2. While viewing the focusing wire through the viewingscope, turn the vertical filament adjustment knob untilthe light is brightest on the wire in the area of thereticle.

3. Return the focusing wire to its storage location on theplatform.

2. Unscrew the focusing wire from its storage place onthe platform and carefully insert it into the hole in thecenter of the top capacitor plate (Figure 7).

Note: The thorium source and theelectrical connection on the lower capacitor plate fitinto appropriately sized holes on the plastic spacer.

Check to be sure that the transformer is thecorrect voltage: 100, 117, 220, or 240 V).

4. Bring the reticle into focus by turning the reticlefocusing ring.

5. View the focusing wire through the viewing scope,and bring the wire into sharp focus by turning thedroplet focusing ring.

ionization ON position

droplet viewingchamber housing

ionization OFF position

ionization lever

IONIZATIONSOURCE

IONIZATIONSOURCE

SPRAYDROPLET

POSITION

ON

IONIZATIONSOURCE

IONIZATIONSOURCE:

THORIUM 2320.008 Ci

spray droplet position

Figure 8. Ionization source lever settings

focusing wireupper capacitor

spacer

lower capacitor

Note: Viewing will be easier forexperimenters who wear glasses if the viewingscope is focused without using the glasses.


7

Adjusting and Measuring theVoltage1. Connect the high voltage DC power supply to the

plate voltage connectors using banana plug patchcords and adjust to deliver about 500 V.

2. Use the digital multimeter to measure the voltagedelivered to the capacitor plates.

Determining the Temperature of theDroplet Viewing Chamber1. Connect the multimeter to the thermistor connectors

and measure the resistance of the thermistor. Refer tothe Thermistor Resistance Table located on theplatform to find the temperature of the lower brassplate. The measured temperature should correspond tothe temperature within the droplet viewing chamber.

Experimental Procedure1. Complete the reassembly of the droplet viewing

chamber by placing the droplet hole cover on thetop capacitor plate and then placing the lid on thehousing. (See Figure 5.)

Introducing the droplets into the chamber

1. Put non-volatile oil of known density into the atomizer(for example, Squibb #5597 Mineral Oil, density: 886kg/m3).

2. Prepare the atomizer by rapidly squeezing the bulbuntil oil is spraying out. Insure that the tip of theatomizer is pointed down (90 to the shaft; see Figure9).

3. Move the ionization source lever to the Spray DropletPosition to allow air to escape from the chamberduring the introduction of droplets into the chamber.

4. Place the nozzle of the atomizer into the hole on the lidof the droplet viewing chamber.

5. While observing through viewing scope, squeeze theatomizer bulb with one quick squeeze. Then squeezeit slowly to force the droplets through the hole in thedroplet hole cover, through the droplet entry hole inthe top capacitor plate, and into the space between thetwo capacitor plates.

6. When you see a shower of drops through the viewingscope, move the ionization source lever to the OFFposition.

Note: The droplet hole cover prevents additionaldroplets from entering the chamber once theexperiment has started.

2. Measure and record the plate voltage and thethermistor resistance (temperature).

Figure 9. Correct position of the atomizer tip

tip

shaft

Measure the voltage at the plate voltageconnectors, not across the capacitor plates.There is a 10 megohm resistor in series witheach plate to prevent electric shock.

Although the dichroic window reflectsmuch of the heat generated by the halogenbulb, the temperature inside the dropletviewing chamber may rise after prolongedexposure to the light. Therefore, thetemperature inside the droplet viewingchamber should be determined periodically(about every 15 minutes).


8

Collecting Data on the Rise And Fall of the OilDroplet

1. Measure the rise (plates charged) and fall (plates notcharged) velocities of the selected droplet about 1020 times. Maneuver the droplet as needed using theplate voltage switch.

Note: The greatest accuracy of measurement isachieved if you time from the instant that the brightpoint of light passes behind the first major reticleline to the instant bright point of light passes behindthe second major reticle line. (These lines are 0.5mm apart.)

2. When you find an appropriately sized and charged oildroplet, fine tune the focus of the viewing scope.

Note: The oil droplet is in best focus for accuratedata collection when it appears as a pinpoint ofbright light.

Hint: A drop that requires about 15seconds to fall the distance between the majorreticle lines (0.5 mm) will rise the samedistance, under the influence of an electric field(1000 V/cm), in the following times with the

If repeated squirts of the atomizer fail toproduce any drops in the viewing area butproduce a rather cloudy brightening of thefield, the hole in the top plate or in thedroplet hole cover may be clogged. Referto the Maintenance section for cleaninginstructions.

Selection of the Drop

1. From the drops in view, select a droplet that both fallsslowly (about 0.020.05 mm/s) when the platecharging switch is in the Plates Grounded positionand can be driven up and down by turning on thevoltage.

Note: If the entire viewing area becomes filledwith drops, so that no one drop can be selected,either wait three or four minutes until the dropssettle out of view, or disassemble the dropletviewing chamber (after turning off the DC powersupply), thus removing the drops. When theamount of oil on the parts in the droplet viewingchamber becomes excessive, clean them, asdetailed in the Maintenance section. Remember:the less oil that is sprayed into the chamber, thefewer times the chamber must be cleaned.

Note: The exact technique of introducing dropswill need to be developed by the experimenter.The object is to get a small number of drops, not alarge, bright cloud from which a single drop can bechosen. It is important to remember that the dropsare being forced into the viewing area by thepressure of the atomizer. Therefore, excessive useof the atomizer can cause too many drops to beforced into the viewing area and, more important,into the area between the chamber wall and thefocal point of the viewing scope. Drops in this areaprevent observation of drops at the focal point ofthe scope.

Note: If too many droplets are in view, you canclear out many of them by connecting power to thecapacitor plates for several seconds.

Note: If you find that too few droplets have netcharges to permit the selection of an appropriatelysized and charged drop, move the ionization lever tothe ON position for about five seconds.

2. Calculate the charge on the droplet. If the result of thisfirst determination for the charge on the drop is greaterthan 5 excess electron, you should use slower movingdroplets in subsequent determinations.

3. Introduce more oil droplets into the chamber using theprocedure previously described and select anotherdroplet.

4. Measure the rise and fall velocities of the selecteddroplet about 1020 times or until the charge changesspontaneously or the droplet moves out of view.

following charges: 15 s, 1 excess electron; 7 s, 2excess electrons; 3 s, 3 excess electrons. (Note:these ratios are only approximate.)


9

5. Bring the droplet to the top of the field of view andmove the ionization lever to the ON position for a fewseconds as the droplet falls.

6. If the rising velocity of the droplet changes, make asmany measurements of the new rising velocity as youcan (10 to 20 measurements).

7. If the droplet is still in view, attempt to change thecharge on the droplet by introducing more alphaparticles, as described previously, and measure thenew rising velocity 1020 times, if possible.

8. Repeat step (7) as many times as you can.9. Record the plate potential, the oil density, the viscosity

of air at the temperature of the droplet viewingchamber, (see appendix A), and the barometric pressure for each set of velocity measurements.

Note: It is desirable to observe as many differentcharges on a single drop as possible.

Computation of the Charge of an Electron

1. Use the formula derived in the Introduction tocalculate the the charge of an electron*:

*The formula is derived from equation 10 (page 2),using SI units as defined below.

The definitions of the symbols used, in SI units:

q

charge, in coulombs, carried by the dropletd separation of the plates in the condenser in m density of oil in kg/m3g acceleration of gravity in m/s2

viscosity of air in poise ( Ns/m2) (Appendix A)b constant, equal to 8.20 x 10-3 Pa mp barometric pressure in pascalsa radius of the drop in mvf velocity of fall in m/sv

r velocity of rise in m/s

V potential difference across the plates in volts

Note: The accepted value for e is 1.60 x 10-19coulombs.

2. Substitute a from the above equation to find the mass(m) of the oil droplet:

Suggested Procedure for Computation of the Chargeof an Electron:

1. Using equation (7) (page 2), calculate the radius (a) ofthe oil drop:

3. Substitute m from the calculation above into equation(3) (page 2) to find the charge carried by the droplet(q):

Note: Equation (10) ( page 2) is equivalent to theabove equation, since

E (e.s.u.) = V (volts)300d (cm)

q = 43gb

2p2

+9 v f2g

b2p

3vf + vr

Evf

m = 43a3

=43

b2p

2+

9 vf2g

b2p

3

q =mg (vf + vr)

Evf

=43g

b2p

2+

9 vf2g

b2p

3(vf + vr)

Evf


10

Using a Projecting Microscope withthe Millikan Oil Drop Apparatus

To demonstrate Millikans experiment for an entireclassroom on a TV screen or computer monitor, use aprojecting microscope, such as the Ken-A-VisionVideoFlex Microscope (PASCO Model No. SE-7227).

Procedure:1. Put a white paper screen in the droplet viewing

chamber to reflect more light:a. Prior to focusing the viewing scope (step 1

under the Equipment Setup section, Aligningthe Optical System), place a white paper screenin the droplet viewing chamber as illustrated inFigure 10.

b. Proceed with step 1 of Aligning the OpticalSystem.

2. Align and focus the projecting microscope:a. Set up the projecting microscope as directed in

the manufacturers instructions.b. After completing the setup and focusing of the

Millikan Apparatus on the oil droplets, carefullyslide the eyepiece of the projecting microscopeover the eyepiece of the Millikan Apparatus.

c. Focus the projecting microscope as directed inthe manufacturers instructions.

Figure 10. Placing a white paper screen in thedroplet viewing chamber to increase the brightnessof the oil drop image

Place thepaper screenso the lightpath is notblocked andso the light isreflectedtowards thelens of theplasticspacer.

Cut a 32 x 6 mmstrip of whitepaper and bendback tabs of6 x 6 mm.

lens

Top View

path oflightsource

scope

paper screen

cross-section of thedroplet chamber housing plastic

spacer


11

HISTORICAL NOTESThe Greeks were the first to report the effects ofelectricity when they recorded that rubbed amberattracted light objects. However, theories explaining thisphenomenon did not emerge until 1747, when BenjaminFranklin proposed that an electrical fluid or fire existed incertain amounts in all matter. An excess of this fluid inmatter would produce a positive charge and a deficiencyof this fluid would produce a negative charge. A slightlydifferent theory was put forth by the physicist Symmertwelve years later. He proposed that matter in a neutralstate shows no electrical properties because it containsequal amounts of two weightless fluids, which werecalled positive and negative electricity respectively.Franklin also postulated the existence of an electricalparticle small enough to easily permeate matter.Faradays experiments in electrolysis, whichdemonstrated that when a current is passed through anelectrolyte, the masses of compounds deposited atopposite electrodes are in proportion to the chemicalequivalent weights of the compounds, also supportedFranklins concept of an elementary electrical particle.The fluid theories, along with a theory explainingelectricity as a state of strain in matter, were the primeexplanations of electrical phenomena until late in the19th century.

EARLY DETERMINATIONS OF eThe word electron was first suggested in 1891 by Dr.G. Johnstone Stoney as a name for the natural unit ofelectricity, namely, that quantity of electricity that mustpass through a solution in order to liberate at oneelectrode one atom of hydrogen or any univalentsubstance. It would follow that the charge of the electronmultiplied by the number of molecules in a gram molewould give the amount of electricity required to depositone gram mole by electrolysis. This quantity had beendetermined by Faraday to be 9650 absoluteelectromagnetic units of electricity. Using this method,Stoney obtained a value of 0.3 x l0-10 e.s.u. (The KineticTheory provided the basis for Stoneys estimation ofAvogadros number).The first experimental attempt to measure the chargeof an ion was made by Townsend in the late 1890s.He had observed that during electrolysis of sulfuric

acid, positively charged hydrogen and oxygen gasseswere produced (although there were one million mil-lion neutral molecules to every charged one). Thismethod was used to produce an ionized gas that wasthen bubbled through water to form a cloud. For hisdetermination of e Townsend proceeded in the follow-ing manner:

1. He assumed that in saturated water vapor each ioncondensed moisture about it, so that the number ofions was the same as the number of droplets.2. He determined with the aid of a quadrantelectrometer the total electrical charge per cubiccentimeter carried by the gas.3. He found the total weight of the cloud by passing itthrough drying tubes and determining the increase inweight of these tubes.4. He found the average weight of the water dropletsconstituting the cloud by observing their rate of fallunder gravity and computing their mean radius withthe aid of a purely theoretical law known as StokesLaw.

5. He divided the weight of the cloud by the averageweight of the droplets of water to obtain the number ofdroplets which, if assumption 1 is correct, was thenumber of ions, and he then divided the total chargeper cubic centimeter in the gas by the number of ionsto find the average charge carried by each ion, that is,to find e.1

Townsend achieved results in the range of 3 x l0-l0 e.s.u.for e. J. J. Thompson, in 1900, used a method similar toTownsends and obtained a value of 6 x l0-l0 e.s.u. Inboth of these methods, however, the first assumption(each droplet formed around only one ion) proved to beonly approximately correct, and the experimental methodswere not adequate to provide a precise determination of e.H.S. Wilson improved upon Townsends andThompsons work by adding two brass plates which couldbe connected to a 2000 volt battery. A cloud was formedbetween these plates (not charged) and the falling velocity

1 condensed from Robert A. Millikans book, TheElectron (University of Chicago Press, Chicago, 1993,pp. 45-46) and used with permission of the publishers.

Historical


12

of the cloud recorded. A second cloud was then formedand its falling velocity observed in an electric field (theplates being charged). Since the two velocities areproportional to the forces acting on the drops2, and thevelocity of the cloud with the plates uncharged determinesthe size and mass of the drops by Stokes Law, Wilsonwas able to obtain a value of 3 x 10-10 e.s.u. for e. SinceWilsons measurements were always made on the top ofthe cloud, or the drops with the smallest charge (the moreheavily charged drops being driven downward faster inthe field), the assumption of one ion per drop wasvalidated.

MILLIKANS DETERMINATION OF eMillikan improved upon Wilsons design by using ahigher potential across the plates so that the fallingvelocity of the cloud could not only be impeded, butactually reversed. Some charged drops moved upward,some moved rapidly downward, while the unchargeddrops were unaffected and continued to drift downward.A few drops, which carried a charge of the propermagnitude so that the force of gravity on the drop almostequaled the force of the electric field on the drop,remained in view. By varying the potential of the plates,Millikan could just balance these drops. This situationproved to be a significant improvement for it permitted allmeasurements to be made on a single drop. By using thisbalanced drop method, Millikan was able to observe theproperties of individual ions and to determine whetherdifferent ions carry one and the same charge.In the following passage, taken from the PhilosophicalMagazine for February, 1910, Millikan describes theactual procedure of the experiment.The observations on the rate of fall were made with ashort-focus telescope placed about 2 feet away from theplates. In the eyepiece of this telescope were placed threeequally spaced cross-hairs. . . . A small section of thespace between the plates was illuminated by a narrowbeam from an arc light, the heat of the arc being absorbedby three water cells in series. The air between the plateswas ionized by 200 mg of radium of activity 20,000

placed from 3 to 10 cm away from the plates. A second orso after the cloud was produced3 the radium was removed. . . and the field thrown on by means a double-throwswitch. If the drops were not found to be held suspendedby the field the potential difference was changed . . . . Thecross-hairs were set near the lower plate, and as soon as astationary drop was found somewhere above the uppercross-hair, it was watched for a few seconds to make surethat it was not moving and then the field was thrown offand the plates short-circuited by means of the double-throw switch, so as to make sure that they retained nocharge. The drop was then timed by means of an accuratestop watch as it passed across the three cross-hairs, one ofthe two hands of the watch being stopped at the instant ofpassage across the middle cross-hair, and the other at theinstant of passage across the lower one. It will be seenthat this method of observation furnishes a double checkupon evaporation; for if the drop is stationary at first, it isnot evaporating sufficiently to influence the reading of therate of fall, and if it begins to evaporate appreciably beforethe reading is completed, the time required to passthrough the second space should be greater than thatrequired to pass through the first space. It will be seenfrom the observations which follow that this was not, ingeneral, the case.

It is an exceedingly interesting and instructive experimentto watch one of these drops start and stop, or even reverseits direction of motion, as the field is thrown off and on. Ihave often caught a drop which was just too light toremain stationary and moved it back and forth in this wayfour or five times between the same two cross-hairs,watching it first fall under gravity when the field wasthrown off and then rise against gravity when the fieldwas thrown on . . . .

Furthermore, since the observations . . . are all made uponthe same drop, all uncertainties as to whether conditionscan be exactly duplicated in the formation of successiveclouds obviously disappear. There is no theoreticaluncertainty whatever left in the method unless it be anuncertainty as to whether or not Stokes Law applies tothe rate of fall of these drops under gravity.Experiments with the balanced water drop produced thevalue of 3.422 x l0-l0 e.s.u. for e. The most importantaspect of these experiments, however, was the observationby Millikan that a rising drop would suddenly change itsvelocity. This phenomenon could easily be produced byplacing a radioactive source near the drop. Thisdemonstrated that the drop had captured an ion, thuschanging the charge of the drop and its respectivevelocity.

2 With the plates uncharged the force is mg where m isthe mass of the drop and g is the acceleration of grav-ity. With the plates charged the force is mg + Ee

nwhere E is the electric intensity between the platesand e

n is the charge on the drop.

3The italicized phrases indicate a slight change inwording, for purposes of clarity, from Millikansoriginal work.


13

THE EXACT EVALUATION OF eIn 1909 Millikan set about building a new piece ofapparatus designed for the observation of single oil dropsfor extended periods of time. Since water drops hadproved inadequate for prolonged observation of this ioncatching phenomenon, Millikan used oil drops, whichwere not affected by evaporation. The apparatusconsisted of two parallel brass plates separated by adistance of 16 mm by ebonite blocks. Non-volatile oilwas sprayed into the chamber above the plates, and smalldrops slowly found their way into the area between theplates through a small hole in the top plate. The dropswere illuminated by a beam from a carbon arc lamp andwere observed through a measuring scope. The details ofthe construction of Millikans final apparatus built in1914 (which was basically similar to his earlier devices,and for the purposes of this discussion can be consideredthe same as the earlier pieces of apparatus) attest to theeffort expended in obtaining the most accurate evaluation

of e possible. The following passage is part of Millikansdescription of the apparatus, including a diagram of thedevice.Accordingly, I built two years ago a new condenserhaving surfaces which were polished optically and madeflat to within two wave-lengths of sodium light. Theywere 22 cm. in diameter and were separated by threepieces of echelon plates, 14.9174 mm. thick, and havingoptically perfect plate surfaces. The dimensions of thecondenser, therefore, no longer introduced an uncertaintyof more than about 1 part in l0,000.5

Complete stagnancy of the air between the condenserplates was attained, first, by absorbing all the heat raysfrom the arc lamp by means of a water cell 80 cm. long,and a cupric chloride cell, and secondly, by immersing thewhole vessel in a constant temperature bath of gas-engineoil (40 liters), which permitted, in general, fluctuations ofnot more than 0.02 C during an observation.6

5Millikan, Robert A., p. 115.6Millikan, Robert A., p. 110.

7Millikan, Robert A., p. 116.

Diagram of Millikans Apparatus7

Fig.11.A, atomizer through which the oil spray is blown into the cylindrical vessel D. G, oil tank to keep the tem-perature constant. M and N, circular brass plates, electrical field produced by throwing on 10,000-volt battery B. Lightfrom arc lamp a after heat rays are removed by passage through w and d, enters chamber through glass window g and illu-minates droplet, p between plates M and N through the pinhole in M. Additional ions are produced about p by X-rays fromthe bulb X.

gg c c

A

s

e

to pump

X

G

C

S

D

V

Bm

a

w d

pM

N


14

With this new apparatus hundreds of measurements ondifferent drops were made, for the purpose of both makingan exact evaluation of e and proving or disproving theatomic theory of electricity. The value of e that wasobtained from these five years of work was 4.774 x 10-10e.s.u. This value of e was accepted until 1928 when aprecise determination of Avogadros number by X-raydiffraction measurements on crystals permitted thecalculation of e to be 4.803 x 10-10 e.s.u. The discrepancywas later traced to Millikans too low value for theviscosity of air.

ATOMIC NATURE OF ELECTRICITYThe atomic nature of electricity is best exemplified by thefollowing table taken from Millikans data:

n 4.917 x n ObservedCharge

1 4.917 . . . .2 9.834 . . . .3 14.75 . . . .4 19.66 19.665 24.59 24.606 29.50 29.627 34.42 34.478 39.34 39.389 44.25 44.4210 49.17 49.4111 54.09 53.9112 59.00 59.1213 63.92 63.6814 68.84 68.6515 73.75 . . . .16 78.67 78.3417 83.59 83.2218 88.51 . . . .

Millikan makes the following comments about this table.In this table 4.917 is merely a number obtained . . . fromthe change in speed due to the capture of ions and onewhich is proportional in this experiment to the ionic

charge. The column headed 4.917 x n contains simply thewhole series of exact multiples of this number from 1 to18. The column headed Observed Charge gives thesuccessive observed values of the rising velocity of thedrop plus the falling velocity. It will be seen that duringthe time of observation, about four hours, this drop carriedall possible multiples of the elementary charge from 4 to17, save only 15. No more exact or more consistentmultiple relationship is found in the data which chemistshave amassed on the combining powers of the elementsand on which the atomic theory of matter rests than isfound in the foregoing numbers.Such tables as theseand scores of them could begivenplace beyond all question the view that anelectrical charge wherever it is found, whether on aninsulator or conductor, whether in electrolytes or inmetals, has a definite granular structure, that it consists ofan exact number of specks of electricity (electrons) allexactly alike, which in static phenomena are scatteredover the surface of the charged body and in currentphenomena are drifting along the conductor. Instead ofgiving up, as Maxwell thought we should some day do,the provisional hypothesis of molecular charges, we findourselves obliged to make all our interpretations ofelectrical phenomena, metallic as well as electrolytic, interms of it.9

Although the values of the charge on a specific drop werefound to be exact multiples of a certain value (e), the valueof e varied for drops of different masses. Thisdiscrepancy was traced to the breakdown of Stokes Law.Through experimentation the law was found to fail whenthe size of the drop approached the mean free path of airmolecules. When this situation occurs, the medium inwhich the drop falls is no longer homogeneous in relationto the drop. This contradicts one of the assumptions uponwhich Stokes Law is based. Through his work on theelectron, Millikan was able to determine a correctionfactor for Stokes Law.By performing the experiment with mercury drops anddrops of other materials, Millikan demonstrated that theelementary electrical charge was the same for insulators,semi-conductors, and conductors. He also demonstratedthat the beta particle had the same charge as an electron(indeed, it is an electron) and that positive and negative

8Millikan, Robert A., p. 74.9Millikan, Robert A., pp. 7475.


15

electrons (the positive electron referring to a proton andnot a positron) are equal in charge. The experiment alsoproduced insights into the study of ionized gasses.Few experiments that are so simple in principle haveprovided such a wealth of experimental evidence toconfirm the atomic theory and measure an importantphysical constant.

Suggested ReadingShould the student desire a more detailed back ground inthis classic experiment, the following references aresuggested:1. Millikan, Robert A., The Electron, (Chicago, TheUniversity of Chicago Press, 1917 (reprinting inpaperback form, 1963).2. Millikan, Robert A., The Isolation of an Ion, APrecision Measurement of its Charge, and the Correctionof Stokes Law, The Physical Review, Vol. 2, No. 2, pp.109 143, June 1913.3. Millikan, Robert A., On the Elementary ElectricalCharge and the Avogadro Constant, The PhysicalReview, Vol. 32, No. 4, pp. 349 397, April, 1911.4. Shamos, M.H., Great Experiments in Physics (Holt-Dryden, New York, 1959), pp. 238 249.


16

Maintenance Notes

Cleaning

1. The housing of the droplet viewing chamber, thecapacitor plates, the plastic spacer, and the droplethole cover should be cleaned with water anddetergent, with particular attention to the droplet holein the top capacitor plate, the glass observation portcovers on the housing, and the droplet hole cover.

2. The plastic spacer should be polished with a soft, lint-free cloth to remove any oil, finger prints, or lint.

3. The lens on the plastic spacer should be cleaned onboth sides using a Q-tip.

4. Apply a thin film of oil to the capacitor plates to helpprevent corrosion.

5. Dry all parts completely before reassembly.

Always handle the plastic spacer and capacitorplates carefully to avoid scratching them.

Solvents that might attack the plastic should beavoided.

Adjusting vertical reticle and viewing scopealignmentsIf the alignment of the reticle or viewing scope is alteredduring rough handling, realign it using the followingprocedure:

1. Loosen the set screw in the viewing scope holder(Figure 12).

Replacing the halogen light bulb

1. Disconnect the apparatus from all power sources.2. Remove the four screws on the halogen lamp housing

and lift off the top cover. Gently pull the halogen bulbout of its socket.

3. Replace with a GE #18426 halogen bulb (12 V, 5 W,T3 type with 2-Pin G4 base, C6 straight filament).Carefully insert the pins at the base of the bulb into thesocket and press firmly to seat the bulb securely.

2. With the focusing wire in place and while lookingthrough the eyepiece, rotate the viewing scope untilthe vertical reticle lines are vertical to the focusingwire.

3. Find the center of focus in the adjustment knob on theviewing scope (this will be approximately half-waybetween minimum and maximum focus).

4. Manually move the viewing scope in and out throughits holder until the focusing wire comes into focus.

5. Recheck the reticle to assure that it is still in properalignment with the focusing wire (as in step 2).

6. Lock the viewing scope into position by tighteningthe set screw into the viewing scope holder.

Figure 12. Location of viewing scope set screw

set screw

Handle the new halogen bulb only with tissuepaperoil on the hands may damage thebulb.


17

Touching up the black painted surface on theplastic spacerAfter prolonged use and repeated cleaning, the black paint(Figure 14) that absorbs refracted and reflected light onthe plastic spacer may begin to wear off. In that event,touch up the surface with a thin coat of flat black acrylicpaint such as that available at hobby stores. Do not use alacquer or oil-based paint.

Figure 14. Area on the plastic spacer that should bepainted black

Adjusting the horizontal reticle alignmentIf the horizontal alignment of the viewing scope is alteredduring rough handling, realign it using the followingprocedure:

1. Loosen one of the two socket head cap screws on thebottom of the platform shown in Figure 13.

2. With the focusing wire in place and while lookingthrough the eyepiece, gently tap the viewing scopeuntil the focusing wire is centered in the reticle.

Only a very small adjustment will berequired. Use care to avoid losing sight ofthe focusing wire.

3. Lock the viewing scope into position by tightening thetwo socket head cap screws into the viewing scopeholder.

Figure 13. Location of the socket head cap screwsthat anchor the viewing scope

Do not allow paint to get on the top andbottom flat surfaces of the plastic spacer,since that would change the plate spacerthickness.

bottom of platform

socket head capscrews for scopeadjustment

black-painted area


18

Notes


19

Appendix

Appendix A: Viscosity of Dry Air as a Function of Temperature*

Nsm

-2

x 10

-5

1.8000

1.8040

1.8080

1.8120

1.8160

1.8200

1.8240

1.8280

1.8320

1.8360

1.8400

1.8440

1.8480

1.8520

1.8560

1.8600

1.8640

1.8680-

1.8720

1.8760

1.88001.8840

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Temperature C

Viscosity of Dry Air as a Function of Temperature


20

Appendix B:

Millikan Oil Drop Apparatus Thermistor Resistance at Various Temperatures


21

Teachers Guide

Note: It is best that students work in pairsone to observe the drop and one torecord the experimental data.

Note: Leveling will be most accurate if the bubble level is observed fromdirectly above during leveling.

As an example of typical experimental results, the following pages list one teachers data, using thealternative method for calculating the charge on an electron that is presented on page 9. Theteacher measured the velocity of the drop moving down with the plates charged and used themethod listed below to organize the data for computation.

For each different charge event for a drop the following was done:

1. Measured the velocity of the falling drop with the plates not charged, the velocity of the risingdrop with the plates charged, and the velocity of the falling drop with the plates charged;

2. Assigned a charge letter to each event of differing charge for each oil droplet; for example, fordrop 1: 1A, 0 (velocity of the falling drop with the plates not charged), 1B, u (velocity of therising drop), 1B, d (velocity with the plates charged of the falling drop), 1C, u, d, and 1D, u, d ;for droptlet 2: 2A0, u, d, 2B u, d, 2C u, d, and so on.

3. Averaged all measurements for a drop falling with the plates not charged, for use to determine a;4. For each charge letter, averaged the measurements for the cases of the drop rising or falling with

the plates charged;

5. Calculated the average charges on each droplet for each charge letter (averaging the charges forthe cases with the droplet rising and with the droplet falling while the plates were charged);

6. Listed the average charges for the charge letters in order of increasing size and calculated the av-eragedifference between charges;

7. Calculated the number of e for droplet under each of the charge conditions by dividing the aver-age charge for each charge letter by the average difference in charge from step 5, above.

The data and calculations for measurements on one droplet are listed on the following pages.

Note: If more accuracy with leveling is needed to prevent the oil droplets fromgradually drifting off to one side during prolonged observations, perform the level-ing operation using a two-dimensional level or ball bearing placed directly on thebottom capacitor plate.


22

Sample Data for Millikan Apparatus: Voltage = 386 V; Temperature = 28.8 C

Drop# /Charge Letter Distance timed (mm) Time (s) Direction:

0 = no fieldU = going upD = going down

1A 0.5 18.24 00.5 18.56 00.5 19.24 00.5 18.05 00.5 17.23 00.5 15.35 00.5 16.70 00.5 17.99 00.5 15.35 00.5 17.25 00.5 18.38 0

1C 0.5 18.32 01D 0.5 16.56 0

0.5 18.70 00.5 16.56 01.0 33.63 00.5 17.30 00.5 19.06 00.5 18.33 00.5 16.21 00.5 15.36 00.5 15.70 00.5 17.10 00.5 17.30 00.5 17.80 0

Average Time with no field = 17.34 s for 0.5 mm


23

Drop# / Distance timed (mm) Time (s) Direction: Average TimesCharge Letter 0 = no field (s)

U = going up for a distanceD = going down of 0.5 mm

1A 0.5 3.89 U1.5 11.00 U1.5 11.59 U1.5 11.17 U 3.79 U0.5 2.66 D1.5 7.84 D 2.64 D

1B 1.5 8.32 U1.5 8.20 U 2.75 U1.5 6.20 D1.5 6.02 D 2.04 D

1C 0.5 22.16 U 22.16 U1.0 11.56 D1.0 11.64 D 5.80 D

1D 1.0 13.40 U1.5 19.74 U1.0 12.65 U 6.54 U1.0 7.48 D1.5 11.32 D 3.76 D

1E 0.5 21.91 U0.5 22.87 U0.5 21.04 U 21.94 U1.0 11.84 D1.0 12.72 D1.0 12.59 D 6.20 D


24

1. The temperature was T = 0.822 m = 28.8o C, which gives the viscosity ofair = = 1.867 x 10-5 kg/ms.

2. For this droplet, a = 4.9 x 10-7 m 0.2 x 10-7 m.3. The plate separation was 0.767 cm and the plate voltage was 386 V, which gives the

electric field = E = 5.03 x 104 V/m.4. The density of the oil was 886 kg/m3, which gives the weight of the

droplet = mg = 4.26 x 10-15 N.5. The pressure was 1.01 x 105 Pa.

Table of Results

Drop# / Charge for Going Up Charge for Going Down Average ChargeCharge Letter (x 10-19 C) (x 10-19 C) (x 10-19 C) 1A 4.72 4.71 4.72

1B 6.18 6.35 6.27 1C 1.51 1.68 1.60 1D 3.09 3.06 3.08 1E 1.52 1.52 1.52

Table of Final Analysis

Drop# / Average Charge Differences between Number of e =Charge Letter (x 10-19 C) Letter Charges Avg. Charge/Avg. Diff.

(x 10-19 C) 1E 1.52 D-E = 1.56 1 e 1C 1.60 D-C = 1.48 1 e 1D 3.08 A-D = 1.64 2 e 1A 4.72 B-A = 1.55 3 e 1B 6.27 Average diff. = 1.56 4 e

The percent difference between the average difference between charges (1.56 x 10-19 C) and theaccepted value of e (1.60 x 10-19 C) was 2.5 %.

a was 4.9 x 10-7m 0.2 x 10-7m (4 % error). Errors for q were 2 % (1A), 2 % (1B), 0 % (1C), 4 % (1D).

Technical Support

FeedbackIf you have any comments about the product ormanual, please let us know. If you have any sugges-tions on alternate experiments or find a problem in themanual, please tell us. PASCO appreciates anycustomer feedback. Your input helps us evaluate andimprove our product.

To Reach PASCOFor technical support, call us at 1-800-772-8700 (toll-free within the U.S.) or (916) 786-3800.fax: (916) 786-3292e-mail: [email protected]: www.pasco.com

Contacting Technical SupportBefore you call the PASCO Technical Support staff, itwould be helpful to prepare the following informa-tion:

If your problem is computer/software related, note:

- Title and revision date of software;

- Type of computer (make, model, speed);- Type of external cables/peripherals.

If your problem is with the PASCO apparatus, note:- Title and model number (usually listed on the

label);- Approximate age of apparatus;

- A detailed description of the problem/sequenceof events. (In case you cant call PASCO rightaway, you wont lose valuable data.);

- If possible, have the apparatus within reach whencalling to facilitate description of individual parts.

If your problem relates to the instruction manual,note:

- Part number and revision (listed by month andyear on the front cover);

- Have the manual at hand to discuss your ques-tions.

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Millikan Oil Drop 02-06-2009