The Millikan Experiment: Determining the Elementary Charge

Transcription

1 LAB EXERCISE The Elementay Chage (p. 374) Can you think of a method that could be used to suggest that an elementay chage exists? Figue 1 Robet Millikan ( ) m + q V b The Millikan Expeiment: Detemining the Elementay Chage One of the main chaacteistics of fundamental paticles is thei electic chage. In this section, you will lean about a billiant expeiment investigating natue s elementay chage, namely, the chage of the electon. At the tun of the twentieth centuy, when ou undestanding of electic foces was beginning to incease, two fundamental questions aose egading the natue of electic chage: 1. Does thee exist, in natue, a smallest unit of electic chage of which othe units ae simple multiples? 2. If so, what is this elementay chage, and what is its magnitude, in coulombs? Lab Execise 7.5.1, in the Lab Activities section at the end of this chapte, allows you to calculate the elementay chage. To answe these questions, the Ameican Nobel laueate Robet Andews Millikan (Figue 1) devised and pefomed a seies of ceative expeiments. He easoned that the elementay chage would be the chage on an individual electon. He assumed, futhe, that when tiny oil dops ae spayed in a fine mist fom an atomize, they become electically chaged by fiction, some acquiing an excess of a few electons, othes acquiing a deficit. Although thee was no way of knowing how many exta electons thee wee on any given oil dop o how many wee missing, Millikan hypothesized that if he wee able to measue the total chage on any oil dop, it would have to be some small integal multiple of the elementay chage. To measue this chage, Millikan made use of the unifom electic field in the egion between two oppositely chaged paallel plates. He chaged the plates by connecting each to opposite teminals of a lage bank of stoage batteies whose potential diffeence could be vaied. Millikan was able to use this appaatus, called an electical micobalance, to isolate and suspend chaged oil dops, and ultimately to measue the total chage on each. Once a mist of oil dops is spayed though a small hole in the uppe plate in a Millikan appaatus, it is possible, by caefully adjusting the potential diffeence between the plates, to balance a paticula doplet that has the same sign as the chage on the lowe plate. When the doplet is balanced, the gavitational foce pulling it down equals the electic foce pulling it up (Figue 2). Fo a positively chaged dop of mass m and chage q, the electic foce acts upwad if the lowe plate is positively chaged: q whee is the electic field between the plates. When the doplet is in balance, + F g F g q mg Figue 2 When the total foce on the oil doplet is zeo, the electic foce up is equal in magnitude to the gavitational foce down. But in Section 7.4, we leaned that the electic field in the egion between two paallel plates is constant and has a magnitude given by V whee V is the electic potential diffeence between the plates, and is the sepaation between the plates. 360 Chapte 7 NEL

2 Section 7.5 Consequently, fo an oil dop of mass m and chage q, balanced by a potential diffeence V= V b, q m g mg q V b whee V b is the balancing value of electic potential diffeence between the plates. Thus, it is possible to detemine the total chage on an oil dop if its mass is known. The mass of any individual dop may be detemined by measuing the teminal speed with which it falls when the electic balancing foce is emoved (when the batteies ae disconnected) and only gavity and fiction ae acting on it. By measuing the teminal speed of an oil doplet as it falls unde the foce of gavity, Millikan was able to calculate its mass. Then, by measuing the value of potential diffeence between the plates necessay to balance the doplet, he was able to calculate the total electic chage on the doplet. Millikan epeated the expeiment ove and ove, meticulously balancing a chaged oil doplet, measuing its balancing voltage, and then allowing the doplet to fall unde gavity and measuing its teminal speed. The list of values he detemined fo the total electic chage on each of the dops studied contained a significant patten: all the values wee simple multiples of some smallest value. Many of the doplets had this smallest value of chage on them, but none had less. Millikan concluded that this smallest value epesented the smallest quantity of electic chage possible, the chage on an electon, o the elementay chage. Accuate measuements of the elementay chage have yielded values close to Millikan s. The cuently accepted value fo the elementay chage, commonly called e, is, to fou significant digits, e C Knowing the value of the elementay chage enables us to undestand the natue of electic chage on a fundamental level. In Section 7.1, we noted that all electic chages in solids ae due to an excess o deficit of electons. If we now know a value fo the chage on an individual electon, we can calculate the numbe of excess o deficit electons that constitute any obseved electic chage. An object with an excess (o deficit) of N electons has a chage q that is given by q Ne SAMPLE poblem 1 Calculate the chage on a small sphee with an excess of electons. Solution N q? q Ne ( )( C) q C The chage on the sphee is C (negative because of the excess of electons). NEL Electic Chages and Electic Fields 361

3 In a Millikan-type expeiment, two hoizontal plates ae 2.5 cm apat. A latex sphee, of mass kg, emains stationay when the potential diffeence between the plates is 460 V with the uppe plate positive. (a) Is the sphee chaged negatively o positively? (b) Calculate the magnitude of the chage on the latex sphee. (c) How many excess o deficit electons does the sphee have? Solution SAMPLE poblem cm q? m kg N? V 460 V (a) The electic foce must be up, to balance the downwad foce of gavity. Since the uppe plate is positive, the latex sphee must be chaged negatively to be attacted to the uppe plate and epelled by the lowe plate. The electic field is downwad, giving an upwad foce on a negative chage. (b) When the sphee is balanced, F g q mg But V. Theefoe, q V mg q m g V ( kg)(9.8 m/s 2 )( m) 460 V q C The magnitude of the chage is C. (c) N q e C C N 5 The sphee has 5 excess electons (since the chage is negative). Answes electons N N/C; 14.0 V Pactice Undestanding Concepts 1. Calculate the numbe of electons that must be emoved fom a neutal, isolated conducting sphee to give it a positive chage of C. 2. Calculate the foce of electic epulsion between two small sphees placed 1.0 m apat if each has a deficit of electons. 3. A small object has an excess of electons. Calculate the magnitude of the electic field intensity and the electic potential at a distance of m fom the object. 362 Chapte 7 NEL

4 Section Two lage, hoizontal metal plates ae sepaated by m. A small plastic sphee is suspended halfway between them. The sphee expeiences an upwad electic foce of N, just sufficient to balance its weight. (a) If the chage on the sphee is C, what is the potential diffeence between the plates? (b) Calculate the mass of the sphee. 5. An oil dop of mass kg is balanced between two lage, hoizontal paallel plates 1.0 cm apat, maintained at a potential diffeence of 510 V. The uppe plate is positive. Calculate the chage on the dop, both in coulombs and as a multiple of the elementay chage, and state whethe thee is an excess o deficit of electons. 6. Delicate measuements eveal Eath to be suounded by an electic field simila to the field aound a negatively chaged sphee. At Eath s suface, this field has a magnitude of appoximately N/C. What chage would an oil dop of mass kg need in ode to emain suspended by Eath s electic field? Give you answe both in coulombs and as a multiple of the elementay chage. Answes 4. (a) V (b) kg C; 6e; excess C; e Chage of the Poton The poton and the electon ae believed to have chages equal in magnitude but opposite in sign. Moden expeiments have evealed that the atio of the magnitudes of the two chages is essentially 1, since the diffeence in coulombs does not diffe by moe than 10 20, an extemely small numbe to say the least. But this is not obvious fo paticle physicists. One eason fo the cuiosity is that, othe than the similaity in the chage of the two paticles they ae quite diffeent. Unlike the electon, the poton does have a complex stuctue. And like most othe heavy subatomic paticles, it is compised of othe fundamental entities called quaks. Quaks themselves have chages of ± 1 e and 3 ± 2 e. Howeve, this does not change ou view of what the fundamental chage should be 3 since quaks have not been found to exist in a fee state unde odinay conditions. All known fundamental paticles do have chages that ae integal multiples of e. (Quaks will be studied futhe in Chapte 13.) At fist, one might think that Millikan just discoveed the magnitude of the chage on the electon that happens to be the same as the chage on the poton. Howeve, his discovey has geate implications. In fact, evey subatomic paticle that has been obseved to date (only a small numbe exist) has a chage that is a whole numbe multiple of this tuly fundamental chage. It appeas that chage is quantized, meaning it appeas in specific amounts, whethe positive o negative. This might not seem so supising when we emembe that matte also comes in specific packages (paticles), so why not the chage associated with those paticles? Howeve, unlike mass, which can be changed into enegy (which is eally anothe fom of mass) o vice vesa in chemical and nuclea eactions, chage is always conseved and cannot be changed into anothe quantity. SUMMARY The Millikan Expeiment: Detemining the Elementay Chage Thee exists a smallest unit of electic chage, called the elementay chage, e, of which othe units ae simple multiples; e C. NEL Electic Chages and Electic Fields 363

5 Section 7.5 Questions Undestanding Concepts 1. Sphee A with chage 3q is 1.5 m fom anothe identical sphee B with chage +5q. The two sphees ae bought into contact and then sepaated by a distance of 1.5 m; the magnitude of the foce between the sphees is N. (a) Find the numbe of electons tansfeed fom one sphee to the othe. Explain which way they moved. (b) Find the magnitude of the electic field and the electic potential midway between the two sphees. (c) Detemine the magnitude of the initial electic foce between the sphees. 2. A small dop of wate, of mass kg, is suspended motionless by a unifom electic field of N/C [up]. (a) Is the chage on the dop positive o negative? Explain. (b) Find the numbe of exta electons o potons on the dop. 3. An oil dop, of mass kg, is suspended between two paallel plates, as in Figue 3. (a) Calculate the chage on the oil dop. (b) Calculate the numbe of elementay chages equied to make up this chage. (c) Does the oil dop have a deficit o excess of electons? Explain you answe cm + 4. Two small, equally chaged objects have the same mass of kg. Find the possible chages on each object if the electic foce cancels the gavitational foce between each object. 5. Sphee A of mass kg has an excess of electons. Sphee B has a deficit of electons. The two sphees ae sepaated by 0.12 m, as in Figue 4. (a) Find the angle between the thead and the vetical. (b) Find the tension in the thead. Applying Inquiy Skills 120 V thead A 0.12 m 6. When Millikan began his investigation, he used wate doplets athe than oil. He late switched to oil doplets because he expeienced poblems when examining the B Figue 4 Figue 3 wate. (He found it difficult to suspend the wate doplets fo any length of time.) (a) Why might it be moe difficult to keep wate doplets suspended than oil doplets? (Hint: Conside changes of state.) (b) Descibe what would be obseved when doing an expeiment of this natue with wate. (c) Anothe scientist might have assumed that othe poblems wee causing the obseved esults using wate. Explain one of these false assumptions. 7. An investigato detemines the chages on seveal diffeent oil doplets with appaatus simila to Millikan s and claims that the data in Table 1 ae accuate to the numbe of digits shown. Table 1 Oil Dop Chage (C) (a) Without using any pio knowledge about the fundamental chage, descibe a pocedue that could be used to find the value of a fundamental chage, assuming that all chages in natue ae integal multiples of this chage. (b) Use the pocedue to detemine the fundamental chage. (c) Can the scientist be cetain that this value is the fundamental chage? Explain you answe. (d) We know the value of the fundamental chage. Discuss the expeimental esults and explain any poblems. Making Connections 8. Eath actually has an electic field of N/C at its suface pointing towad the cente. (a) A unifomly chaged sphee poduces an electic field outside the object exactly the same as the field that would be poduced if the chage is concentated at the cente of the field. Assume Eath is unifomly chaged. What is the type and magnitude of the chage on Eath? (b) Compae Eath s electic field and gavitational field in tems of (i) diection and shape, (ii) effect on objects, and (iii) how it changes as height inceases. (c) What is the lagest mass that can be suspended by the electic field of Eath if the paticle has the elementay chage on it? (d) Could the electic field of Eath be used to suspend (i) a poton and (ii) an electon? Explain you easoning. 9. In still ai unde diect sunlight, tiny dust paticles can often be obseved to float. Explain how this happens. How could you test you answe? 364 Chapte 7 NEL