Atomic and Nuclear Physics

Transcription

1 tomic and Nuclar Physics ntroductory Exprimnts Spcific Elctron Charg LEYBOLD Physics Laflts Dtrmination of th Spcific Charg of th Elctron Objcts of th Exprimnt Study of th dflction of lctrons in a magntic fild into a circular orbit. Dtrmination of th magntic fild B as a function of th acclration potntial U of th lctrons at a constant radius r. Dtrmination of th spcific charg of th lctron. Principls Th mass m of th lctron is hard to com by xprimntally. t is asir to dtrmin th spcific charg of th lctron ε = m (), from which th mass m can b calculatd if th lmntary charg is known: n lctron moving at vlocity v prpndicularly to a homognous magntic fild B, is subjct to th Lorntz forc F = v B () which is prpndicular to th vlocity and to th magntic fild. s a cntriptal forc F = m v2 () r it forcs th lctron into an orbit of radius r (s Fig. 1), thus v = (V). m r B n th xprimnt, th lctrons ar acclratd in a fin bam tub by th potntial U. Th rsulting kintic nrgy is U = m 2 v2 (V). Th spcific charg of th lctron thus is = 2 U m (r B) 2 (V) Wit Fig. 1 Dflction of lctrons in a magntic fild B by th Lorntzforc F into a circular orbit of a givn radius r. 1

2 LEYBOLD Physics Laflts pparatus 1 Fin bam tub Hlmholtz coils with holdr and masuring dvic DC powr supply V DC powr supply 0 20 V Voltmtr, DC, U 300 V g mmtr, DC, g Stl tap masur, 2 m Safty conncting lads, 25 cm Safty conncting lads, 50 cm Safty conncting lads, 100 cm additionally rcommndd: 1 Tslamtr xial B-prob Multicor cabl, 6-pol, 1,5 m long Th fin bam tub contains hydrogn molculs at low prssur, which through collisions with lctrons ar causd to mit light. This maks th orbit of th lctrons indirctly visibl, and thir orbiting radius r can b dirctly masurd with a rulr. Th magntic fild B is gnratd in a pair of Hlmholtz coils and is proportional to th currnt in th Hlmholtz coils: B = k (V). Th dpndnc on th acclrating potntial U of th currnt, in th magntic fild of which th orbiting radius of th lctrons is kpt to a constant valu r, follows aftr rcasting quations (V) and (V) U = m 1 2 r2 k 2 2 Th proportionality factor (V). 3 k = n 5 (X) R 0 = Vs : magntic fild constant m can b calculatd ithr from th coil radius R = 150 mm and th winding factor n = 130 pr coil, or b dtrmind by rcording a calibration curv B = f(). ll dtrmining factors for th spcific lctron charg ar now known. Safty nots ttntion: Th fin bam tub rquirs dangrous contact voltags up to 300 V for acclrating th lctrons. Othr voltags that ar connctd with this dangrous contact voltag also prsnt a contact hazard. Dangrous contact voltags ar thus prsnt at th connction panl of th holdr and at th Hlmholtz coils whn th fin bam tub is in opration. Connct th connction panl only via safty conncting lads. lways b sur to switch off all powr supplis bfor conncting and altring th xprimnt stup. Do not switch on th powr supplis until you hav finishd assmbling th circuit. Do not touch th xprimnt stup, particularly th Hlmholtz coils, during opration. Dangr of implosions: Th fin bam tub is a vacuatd glass vssl with thin walls. Do not subjct th fin bam tub to mchanical strsss. Oprat th fin bam tub only in th holdr ( ). Connct th 6-pol plug of th holdr carfully to th glass bas. Rad th instruction sht supplid with th fin bam tub. Stup Not: Prform masurmnts in a dark chambr. Hlmholtz coils may b chargd with mor than 2 for short tim only. Th xprimntal stup to dtrmin th spcific lctron charg is shown in Fig. 2, th lctric connctions in Fig. 3. Disconnct powr supply and turn all rotary potntiomtrs to lft catch position. Connct th 6.3-V input nd of th fin bam tub to th 6.3-V outlt of th DC powr supply. Short-circuit th positiv pol of th 50-V outlt of th DC powr supply with th ngativ pol of th 500-V outlt and connct with th sockt - of th fin bam tub (cathod). Connct th sockt + of th fin bam tub (anod) with th positiv pol of th 500-V outlt, th sockt W (Whnlt-cylindr) with th ngativ pol of th 50-V outlt. n ordr to masur th acclration potntial U connct th voltmtr (masuring rang 300 V ) to th 500-V outlt. Short th dflction plats of th fin bam tub to th anod. Connct th DC powr supply and ammtr (masuring rang 3 ) in sris with th Hlmholtz coils. 2

3 LEYBOLD Physics Laflts Fig. 2 Fig. 3 Exprimnt stup for dtrmining th spcific lctron charg a Hlmholtz coils b Fin bam tubs c Masuring dvic Elctric connction Powr up th DC powr supply and st acclration potntial U = 300 V. Carrying out th xprimnt Mov th lft slid of th masuring dvic so that its innr dg, mirror imag and scap aprtur of th lctron bam com to lay on on lin of sight. St th right slid for both insid dgs to hav a distanc of 8 cm. Sight th insid dg of th right slid, align it with its mirror imag and adjust th coil currnt until th lctron bam runs tangntially along th slid dg covring th mirror imag (s Fig. 4). Rduc th acclration potntial U in stps of 10 V to 200 V and choos th coil currnt so that th orbit of th lctron bam has a diamtr of 8 cm. Rcord acclration potntial U and coil currnt. Thrmionic mission starts aftr warming up for a fw minuts. Optimiz focussing of th lctron bam by varying th voltag at th Whnlt-cylindr from 0 10 V until it lads to a narrow, wll dfind bam with clar dg dfinition. Connct th DC powr supply of th Hlmholtz coils and look for currnt, at which th lctron bam is dflctd into a closd orbit. f th lctron bam aftr laving th anod is dflctd to th wrong (lft) sid: disconnct both powr supplis. xchang th connctions at th DC powr supply in ordr to chang th polarization of th magntic fild. f th lctrons do not mov on a closd orbit but on a hlical curv lin: Loosn th mounting bolts of both holding brackts (rad th information manual for th fin bam tub). Carfully rotat th fin bam tub around its longitudinal axis, until th lctron bam runs on a closd circular orbit. Fastn mounting bolts. Fig. 4 Masurmnt of th orbit diamtr with th masuring dvic 3

4 LEYBOLD Physics Laflts Calibration of th Hlmholtz magntic fild (optional): Th stup for calibrating th magntic fild is shown in Fig. 5. Th additionally rcommndd dvics mntiond abov ar rquird for making masurmnts. f applicabl disconnct all powr supply units. Rmov th masuring dvic and th Hlmholtz coil at th front sid, loosn th connction to th fin bam tub and th mounting bolts of th two holding brackts (rad th instructions for th fin bam tub). Carfully rmov th fin bam tub and plac it.g. in its original cas. R-assmbl th Hlmholtz at th front sid coil and connct. Connct th axial B-prob to th Tslamtr (masuring rang 20 mt) and calibrat th zro-point (s nstruction Manual for Tslamtr). Mov th axial B-prob paralll to th magntic fild of th Hlmholtz coils into th cntr of th pair of coils. Rais th coil currnt from 0 to 3 in stps of 0.5, masur th magntic fild B, and rcord th masurd valus. ftr conclusion of th calibration: R-assmbl th fin bam tub according to th instructions. Fig. 5 St-up for calibration of th Hlmholtz magntic fild Masuring xampl Tab. 1: Th Coil currnt as a function of th acclration potntial U at constant orbit radius r = 0.04 m U V Evaluation and rsults n Fig. 6 th masurd valus from Tab. 1 ar shown in thir linar form U = f ( 2 ) according to (V). Th slop of th rsulting lin through th origin is = 65.3 V 2. ccording to quation (V), th spcific lctron charg is = 2 m r 2 k 2 Furthr valuation thus rquirs th proportionality factor k. Fig. 6 Prsntation of th masuring rsults from Tab. 1 Tab. 2: Th Magntic fild B of th Hlmholtz coils as a function of th coil currnt (this masurmnt rquirs th abov mntiond additionally rcommndd dvics) B mt U V

5 LEYBOLD Physics Laflts Dtrmination of th proportionality factor k from th calibration of th Hlmholtz magntic fild: Fitting of a straight lin through th origin to th masuring valus of Tab. 2, or of Fig. 7 lads to k = 0.67 mt 1 and furthr = s m kg Calculation of th proportionality factor k: Using (X) on calculats k = 0.78 mt 1 and furthr = s m kg B mt Documntd valu: = s m kg Fig. 7 Calibration curv for th magntic fild of th Hlmholtz coils LEYBOLD DDCTC GMBH Lyboldstrass 1 D Hürth Phon (02233) Tlfax (02233) Tlx LHPCGN D by Lybold Didactic GmbH Printd in th Fdral Rpublic of Grmany Tchnical altrations rsrvd