Charge f an Electrn EX-9929 Page 1 f 12 EQUIPMENT Charge f an Electrn 1 Millikan Oil Drp Apparatus AP-8210 1 Basic Digital Multimeter SE-9786 1 High Vltage Pwer Supply SF-9585A 1 Large Rd Base ME-8735 1 45 cm Steel Rd ME-8736 1 Banana Plug Crd - Red (5 Pack) SE-9750 1 Banana Plug Crd - Black (5 Pack) SE-9751 INTRODUCTION The electric charge carried by a particle may be calculated by measuring the frce experienced by the particle in an electric field f knwn strength. Althugh it is relatively easy t prduce a knwn electric field, the frce exerted by such a field n a particle carrying nly ne r several excess electrns is very small. Fr example, a field f 1000 vlts per cm wuld exert a frce f nly 1.6 X l0-14 Newtns n a particle bearing ne excess electrn. This is a frce cmparable t the gravitatinal frce n a particle with a mass f l0 -l2 (ne millin millinth) gram. The success f the Millikan Oil Drp experiment depends n the ability t measure frces this small. The behavir f small charged drplets f il, having masses f nly l0-12 gram r less, is bserved in a gravitatinal and an electric field. Measuring the velcity f fall f the drp in air enables, with the use f Stkes Law, the calculatin f the mass f the drp. The bservatin f the velcity f the drp rising in an electric field then permits a calculatin f the frce n, and hence, the charge carried by the il drp. Althugh this experiment will allw ne t measure the ttal charge n a drp, it is nly thrugh an analysis f the data btained and a certain degree f experimental skill that the charge f a single electrn can be determined. By selecting drplets that rise and fall slwly, ne can be certain that the drp has a small number f excess electrns. A number f such drps shuld be bserved and their respective charges calculated. If the charges n these drps are integral multiples f a certain smallest charge, then this is a gd indicatin f the atmic nature f electricity. Hwever, since a different drplet has been used fr measuring each charge, there remains the questin as t the effect f the drp itself n the charge. This uncertainty can be eliminated by changing the charge n a single drp while the drp is under bservatin. An inizatin surce placed near the drp will accmplish this. In fact, it is pssible t change the charge n the same drp several times. If the results f measurements n the same drp yield charges that are integral multiples f sme smallest charge, this is prf f the atmic nature f electricity.
Charge f an Electrn EX-9929 Page 2 f 12 THEORY An analysis f the frces acting n an il drplet will yield the equatin fr the determinatin f the charge carried by the drplet. Finding the Relatinship between Velcity f Oil Drp and the Electric Field Figure 1 shws the frces acting n the drp when it is falling in air and has reached its terminal velcity. (Terminal velcity is reached in a few millisecnds fr the drplets used in this experiment.) In Figure 1, F f represents the frce f frictin and F g represents the frce due t gravity. Where, Ff F f = -kν F g = -mg ν is the terminal velcity f fall (its value is negative and cnstant), k is the cefficient f frictin between the air and the drp, m is the mass f the drp, and g is the acceleratin f gravity. F f + F g = 0 Figure 1 Fg -kν + -mg = 0 -kν = mg k mg = (Equatin 1) υ Figure 2 shws the frces acting n the drp when it is rising under the influence f an electric field. FE F f = -kν F g = -mg F E = qe E is the electric field, q is the charge carried by the drp, and ν is the velcity. F f + F g + F E = 0 Fg Ff -kν + -mg + qe = 0 Figure 2 qe = kν + mg mg qe = ν + mg ν cmbining with Equatin 1 abve yields rearranging gives
Charge f an Electrn EX-9929 Page 3 f 12 mg ν = qe mg ν slving fr ν prduces qν = ν (Equatin 2) mg ν E + Finding the Mass T find m frm equatin 2, ne uses the expressin fr the vlume f a sphere: 4 m = π a 3 ρ (Equatin 3) 3 where a is the radius f the drplet, and ρ is the density f the il. T calculate a, ne emplys Stkes Law, relating the radius f a spherical bdy t its velcity f fall in a viscus medium (with the cefficient f viscsity, η). 9ην a = (Equatin 4) 2gρ Stkes Law, hwever, becmes incrrect when the velcity f fall f the drplets is less than 0.1 cm/s. (Drplets having this and smaller velcities have radii, n the rder f 2 micrns, cmparable t the mean free path f air mlecules, a cnditin which vilates ne f the assumptins made in deriving Stkes Law.) Since the velcities f the drplets used in this experiment will be in the range f 0.01 t 0.001 cm/s, the viscsity must be multiplied by a crrectin factr. The resulting effective viscsity is: 1 n eff = η (Equatin 5) b 1+ pa where b is a cnstant, p is the atmspheric pressure, and a is the radius f the drp as calculated by the uncrrected frm f Stkes Law, equatin ( 4 ). Substituting η eff in equatin (5) int equatin (4), and then slving fr the radius a gives: a = b 2 p 2 9ην 2gρ b 2 p (Equatin 6)
Charge f an Electrn EX-9929 Page 4 f 12 Finding the Charge Observe equatin 2: qν = ν (Equatin 2) mg ν E + A plt f ν versus E yields a slpe (s) f: qν s = (Equatin 7) mg Rearranging fr the value f the charge (q) gives: smg q = (Equatin 8) ν Cmbining equatin 8 with equatins 3 and 6 prduces: q 2 b 9ην 4 b πgsρ 3 2 p 2gρ 2 p = (Equatin 9) ν 3 q = charge carried by the drplet g = acceleratin due t gravity = 9.80 m/s 2 s = slpe f ν versus E graph as measured in the lab by equatin 2 ρ = density f il = 886 kg/m 3 b = cnstant = 8.22 X 10-3 Pa*m p = barmetric pressure = 101.3 X 10 3 Pa η = viscsity f dry air (see graph in appendix A) ν = terminal velcity f fall (its value is negative and cnstant) as calculated as the vertical intercept f equatin 2 r as measured directly thrugh the Millikan Oil Drp Apparatus.
Charge f an Electrn EX-9929 Page 5 f 12 SETUP Adjusting the height f the platfrm and leveling it 1. Place the apparatus n a level, slid table with the viewing scpe at a height which permits the experimenter t sit erect while bserving the drps. If necessary t achieve the prper height, munt the apparatus n tw supprt rds (ME8736) n the large rd stand (ME-8735) (Figure 1). Dne. D nt mve the machine! 2. Using attached bubble level as a reference, level the apparatus with the leveling screws n the rd stand r the leveling feet f the platfrm, as is apprpriate fr yur setup. Dne. Check carefully! Re-d if machine was mved! Figure 1a: Equipment Set-Up Adjusting the envirnment f the experiment rm 1. Make the rm as dark as pssible, while allwing fr adequate light t read the multimeter and stpwatch, and t recrd data. Use desk light fr reading and writing dwn data! 3. Insure that the backgrund behind the apparatus is dark. Dne. D nt mve the machine! 4. Select a lcatin that is free f drafts and vibratins. Dne. D nt mve the machine! Figure 1b: Equipment Set-Up
Charge f an Electrn EX-9929 Page 6 f 12 Measuring Plate Separatin Disassemble the drplet viewing chamber by lifting the husing straight up and then remving the upper capacitr plate and spacer plate. (See Figure 2.) Nte: The thrium surce and the electrical cnnectin n the lwer capacitr plate fit int apprpriately sized hles n the plastic spacer. Measure the thickness f the plastic spacer (which is equal t the plate separatin distance) with a micrmeter. Be sure that yu are nt including the raised rim f the spacer in yur measurement. The accuracy f this measurement is imprtant t the degree f accuracy f yur experimental results. Recrd the measurement. Figure 2: Disassembly f Viewing Chamber Aligning the Optical System Fcusing the viewing scpe 1. Reassemble the plastic spacer and the tp capacitr plate nt the lwer capacitr plate. Replace the husing, aligning the hles in its base with the husing pins. (See Figure 2) F i Figure 3: Insertin f the fcusing wire int the tp capacitr plate 2. Unscrew the fcusing wire frm its strage place n the platfrm and carefully insert it int the hle in the center f the tp capacitr plate (Figure 3). 3. Cnnect the 12 V DC transfrmer t the lamp pwer jack in the halgen lamp husing and plug it int a wall scket. Check t be sure that the transfrmer is the crrect vltage: 100, 117, 220, r 240 V). Dne. 4. Bring the reticle int fcus by turning the reticle fcusing ring. 5. View the fcusing wire thrugh the viewing scpe, and bring the wire int sharp fcus by turning the drplet fcusing ring. Dne. Check carefully! Re-d if machine was mved r if the alignment is distrted! 6. Nte: Viewing will be easier fr experimenters wh wear glasses if the viewing scpe is fcused withut using the glasses. Fcusing the halgen filament 1. Adjust the hrizntal filament adjustment knb. The light is best fcused when the right edge f the wire is brightest (in highest cntrast cmpared t the center f the wire).
Charge f an Electrn EX-9929 Page 7 f 12 2. While viewing the fcusing wire thrugh the viewing scpe, turn the vertical filament adjustment knb until the light is brightest n the wire in the area f the reticle. 3. Return the fcusing wire t its strage lcatin n the platfrm. This part was dne. Check carefully! Re-d if machine was mved r if the alignment is distrted! PROCEDURE Adjusting and Measuring the Vltage 1. Cnnect the high vltage DC pwer supply t the plate vltage cnnectrs using banana plug patch crds and adjust t deliver abut 500 V. 2. Use the digital multimeter t measure the vltage delivered t the capacitr plates. Measure the vltage at the plate vltage cnnectrs, nt acrss the capacitr plates. There is a 10 mega-hm resistr in series with each plate t prevent electric shck. Determining the Temperature f the Drplet Viewing Chamber 1. Cnnect the multimeter t the thermistr cnnectrs and measure the resistance f the thermistr. Refer t the Thermistr Resistance Table lcated n the platfrm t find the temperature f the lwer brass plate. The measured temperature shuld crrespnd t the temperature within the drplet viewing chamber. Althugh the dichric windw reflects much f the heat generated by the halgen bulb, the temperature inside the drplet viewing chamber may rise after prlnged expsure t the light. Therefre, the temperature inside the drplet viewing chamber shuld be determined peridically (abut every 15 minutes). Experimental Prcedure 1. Cmplete the reassembly f the drplet viewing chamber by placing the drplet hle cver n the tp capacitr plate and then placing the lid n the husing. (See Figure 2.) Nte: The drplet hle cver prevents additinal drplets frm entering the chamber nce the experiment has started. 2. Measure and recrd the plate vltage and the thermistr resistance (temperature). Intrducing the drplets int the chamber 1. Put nn-vlatile il f knwn density int the atmizer (fr example, Squibb #5597 Mineral Oil, density: 886 kg/m3). 2. Prepare the atmizer by rapidly squeezing the bulb until il is spraying ut. Insure that the tip f the atmizer is pinted dwn (90 t the shaft; see Figure 4). Figure 4: Crrect Psitin f the Atmizer Tip
Charge f an Electrn EX-9929 Page 8 f 12 3. Mve the inizatin surce lever t the Spray Drplet Psitin t allw air t escape frm the chamber during the intrductin f drplets int the chamber. 4. Place the nzzle f the atmizer int the hle n the lid f the drplet viewing chamber. 5. While bserving thrugh viewing scpe, squeeze the atmizer bulb with ne quick squeeze. Then squeeze it slwly t frce the drplets thrugh the hle in the drplet hle cver, thrugh the drplet entry hle in the tp capacitr plate, and int the space between the tw capacitr plates. 6. When yu see a shwer f drps thrugh the viewing scpe, mve the inizatin surce lever t the OFF psitin. Nte: If the entire viewing area becmes filled with drps, s that n ne drp can be selected, either wait three r fur minutes until the drps settle ut f view, r disassemble the drplet viewing chamber (after turning ff the DC pwer supply), thus remving the drps. When the amunt f il n the parts in the drplet viewing chamber becmes excessive, clean them, as detailed in the Maintenance sectin. Remember: the less il that is sprayed int the chamber, the fewer times the chamber must be cleaned. Nte: The exact technique f intrducing drps will need t be develped by the experimenter. The bject is t get a small number f drps, nt a large, bright clud frm which a single drp can be chsen. It is imprtant t remember that the drps are being frced int the viewing area by the pressure f the atmizer. Therefre, excessive use f the atmizer can cause t many drps t be frced int the viewing area and, mre imprtant, int the area between the chamber wall and the fcal pint f the viewing scpe. Drps in this area prevent bservatin f drps at the fcal pint f the scpe. Selectin f the Drp 1. Frm the drps in view, select a drplet that bth falls slwly (abut 0.02 0.05 mm/s) when the plate charging switch is in the Plates Grunded psitin and can be driven up and dwn by turning n the vltage. Chse a drplet that is nt t bright. Chse a drplet that des nt react t suddenly t the change in plarity. Nte: If t many drplets are in view, yu can clear ut many f them by cnnecting pwer t the capacitr plates fr several secnds. Nte: If yu find that t few drplets have net charges t permit the selectin f an apprpriately sized and charged drp, mve the inizatin lever t the ON psitin fr abut five secnds. 2. When yu find an apprpriately sized and charged il drplet, fine tune the fcus f the viewing scpe.
Charge f an Electrn EX-9929 Page 9 f 12 Nte: The il drplet is in best fcus fr accurate data cllectin when it appears as a pinpint f bright light. Cllecting Data It is suggested that tw individuals cllect data. One persn bserves the drplet while changing the plate vltage in ne hand and manipulating a stp watch with the ther hand. The ther persn reads the stp watch, changes the vltage, and recrds the data. 1. Change the plate vltage s that the drplet is "driven" t the tp f the viewing area. 2. Set the plate vltage t neutral and time the drplet as it falls a distance f 1.0 mm r 2 majr divisins. D this several times t find an average fr the terminal velcity, ν. 3. Adjust the vltage t 500 V. Drive the same drplet t the tp f the viewing area. Set the plate vltage s that the drplet is driven dwnward. Recrd the vltage with the plarity required t drive the drplet dwnward. (Either -500V r +500 V) 4. Find the time it takes the drplet t mve dwnward a distance f 1.0 mm r 2 majr divisins. Recrd this value in the data table (include a negative sign fr the dwnward mtin). 5. Change the plate vltage s that the drplet is driven upward. Recrd the vltage and plarity required t drive the drplet upward. 6. Find the time it takes the drplet t mve upward a distance f 1.0 mm r 2 majr divisins. Recrd this value in the data table. 7. Repeat steps 3-6 with vltage values f 400 V, 300 V, 200 V, and 100V. Data Table Vltage (V) ΔT (s) 8. Repeat the same measurements fr anther drp.
Charge f an Electrn EX-9929 Page 10 f 12 ANALYSIS 1. Calculate the value f the terminal velcity, ν. 2. Enter yur values f vltage and change in time frm the Data Table abve. 3. Chse the first rder plynmial functin t fit the data. 4. Recrd the values fr the Slpe and the Vertical Intercept. 5. Calculate the value f the radius using Equatin 6. 2 b 9ην b a = 2 p 2gρ 2 p where a = radius b = cnstant = 8.22 X 10-3 Pa*m p = barmetric pressure = 101.3 X 10 3 Pa η = viscsity f dry air (see graph in appendix A) ν = terminal velcity f fall (its value is negative and cnstant) as calculated as the vertical intercept f the graph r as measured directly thrugh the Millikan Oil Drp Apparatus. g = acceleratin due t gravity = 9.80 m/s 2 ρ = density f il = 886 kg/m 3 6. Calculate the value f the mass f the drplet using Equatin 3: 4 m = π a 3 ρ 3 where m = mass f the drplet a = radius f the drplet ρ = density f il = 886 kg/m 3 7. Calculate the value f the charge f an electrn using Equatin 8: smg q = ν where q = charge f an electrn s = slpe f ν versus E graph as measured in the lab by equatin 2 m = mass f the drplet g = acceleratin due t gravity = 9.80 m/s 2 ν = terminal velcity f fall (its value is negative and cnstant) as calculated as the vertical intercept f equatin 2 r as measured directly thrugh the Millikan Oil Drp Apparatus. Remember t Cmpare yur value t the accepted value f the charge f an electrn: 1.60 X 10-19 C
Charge f an Electrn EX-9929 Page 11 f 12 Appendix A
Charge f an Electrn EX-9929 Page 12 f 12 Appendix B