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# Elementary Modern Physics PHY 215

WFU

GPA 3.91

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This 4 page Class Notes was uploaded by Miss Lucienne Hamill on Wednesday October 28, 2015. The Class Notes belongs to PHY 215 at Wake Forest University taught by Staff in Fall. Since its upload, it has received 11 views. For similar materials see /class/230736/phy-215-wake-forest-university in Physics 2 at Wake Forest University.

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Date Created: 10/28/15

More M likan s O iDrop Experiment M lkm smmm ufdmdmmdm mmsmufdmfzwm ycm w mg 7 w m 31a whmbxywnbysmkzs hw 5sz 311 mlwmusdmcadfmm ufvmmyufdm mdmmasmzmusu hz mmzmmwmmfz md ww Anmmv mzdmycmhemrzdnechumzdmywmhedmy ywmmhxny am zmunemlnvmmwmdawank mime 12 More Droplet a7 Weight mg Fig 35 An oil droplet carrying an ion of charge 6 falling at terminal speed ie mg bv Buoyant force bv 312 see Figure 35 When an electric eld lt8 is applied the upward motion of a charge q is given by dv cg 7 b 7 51 mg v m dt Thus the terminal velocity v of the drop rising in the presence of the electric eld is 158 mg 21 v 313 In this experiment the terminal speeds were reached almost immediately and the drops drifted a distance L upward or downward at a constant speed Solving Equa tions 312 and 313 for q we have mg mngltl l 314 q Wm v 8 Tf T where I Lvf is the fall time and T Lv is the rise time If any additional charge is picked up the terminal velocity becomes v which is related to the new charge q by Equation 313 158 mg 21 V The amount of charge gained is thus m 512 an g gw V Vf 315 M L i lt8 T T The velocities vf v and v are determined by measuring the time taken to fall or rise the distance L between the capacitor plates If we write q ne and q 7 q n e where n is the change in 11 Equations 314 and 315 can be written 11 i 3 346 n T T mng and LltL L lt88 347 n T T mng Continued MILLIKAN s OILeDROP EXPERIMENT To obtain the value of e from the measured fall and rise times one needs to know the mass of the drop or its radius since the density is known The radius is obtained from Stokes law using Equation 312 Notice that the right sides of Equations 316 and 317 are equal to the same con stant albeit an unknown one since it contains the unknown e The technique then was to obtain a drop in the eld of View and measure its fall time 1 electric eld off and its rise time T electric eld on for the unknown number of charges n on the drop Then for the same drop hence same mass m n was changed by some unknown amount n by exposing the drop to the xray source thereby yielding a new value for n and I and T were measured The number of charges on the drop was changed again and the fall and rise times recorded This process was repeated over and over for as long as the drop could be held in View or until the experimenter became tired often for several hours at a time The value of e was then determined by nding basically by trial and error the integer values of n and n that made the left sides of Equations 316 and 317 equal to the same constant for all measure ments using a given drop 39 39 an did experiments like these with thousands of drops some of nonconduct ing oil some of semiconductors like glycerine and some of conductors like mercury In no case was a charge found that was a fractional part of e This process which you will have the opportunity to work with in solving the problem below using actual data from Millikan s sixth drop yielded a value of e of 1591 X 10 19 C This value was accepted for about 20 years until it was discovered that xray diffraction measurements of N A gave values of e that differed from Millikan s by about 04 percent The discrep ancy was traced to the value of the coef cient of viscosity 11 used by Millikan which was too low Improved measurements of 11 gave a value about 05 percent higher thus changing the value of e resulting from the oildrop experiment to 1601 X 10 19 C in good agreement with the xray diffraction data The modem best values of e and other physical constants are published periodically by the Inteniational Council of Scienti c Unions The currently accepted value of the electron charge is e 160217733 gtlt 10 19C 318 with an uncertainty of 030 pars per million Our needs in this book are rarely as precise as this so we will typically use e 1602 X 10 19 C Note that while we have been able to measure the value of the quantized electric charge there is no hint in any of the above as to why it has this value nor do we know the answer to that question now Hardly a matter of only historical interest Millikan s technique is currently being used in an ongoing search for elementary particles with fractional electric charge by M Perl and coworkers PROBLEM The accompanying table shows a portion of the data collected by Millikan for drop number 6 in the oildrop experiment a Find the terminal fall velocity V from the table using the mm fall time and the fall distance 1021mm b Use the density of oil p 0943 gcm3 943 kg m3 the viscosity of air 7 1824 X 10 5 N smz and g 981 ms2 to calculate the radius a of the oil drop from Stokes law as expressed in Equation 312 e The correct trial value of n is lled in in column 7 Determine the remaining correct values for n and n in columns 4 and 7 respectively d Compute e from the data in the table Continued 13 14 More Rise and fall times of a single oil drop with calculated number of elementary charges on drop 1 2 3 4 5 6 7 8 Tf T 1T 1T n 1n 1Tl1Tr 1Tf1Tr n 1n1T1Tf 11848 80708 009655 18 0005366 11890 22366 003234 6 0005390 012887 24 0005371 11908 22390 11904 22368 11882 140566 003751 7 0005358 009138 17 0005375 11906 79600 0005348 1 0005348 009673 18 0005374 11838 34748 001616 3 0005387 011289 21 0005376 11816 34762

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