JOURNAL OF PHYSICAL AND CHEMICAL SCIENCES. A Review of Determination of Charge to Mass Ratio of an Electron by Thomson's method Belachew Desalegn

Transcription

1 JOURNAL OF PHYSICAL AND CHEMICAL SCIENCES Journal hompag: Rviw Opn Accss A Rviw of Dtrmination of Charg to Mass Ratio of an Elctron by Thomson's mthod Blachw Dsalgn 1 Dpartmnt of Physics, Wolaita Sodo Univrsity, PO box 138, Wolaita Sodo, Ethiopia * Corrsponding Author: Blachw Dsalgn; blachwdsalgn76@gmail.com Rcivd: Fbruary 18, 018, Accptd: March 05, 018, Publishd: March 05, 018. ABSTRACT Th orbit of a chargd particl in a uniform and constant magntic fild is a circl whn th initial vlocity of th particl is prpndicular to th magntic fild. Th radius of th orbit dpnds on th charg to mass ratio of th particl, q/m, th spd of th particl v, and th strngth of th magntic fild B. Whn th strngth of th magntic fild and th initial spd of th particl ar known, a masurmnt of a radius of th orbit dtrmins q/m. This principl was usd by J.J. Thomson to masur th charg to mass ratio of th lctron, /m, in In this xprimnt I hav usd a commrcially availabl CRT-8SJ31J with 70mm diamtr scrn siz to rpat th Thomson s xprimnt and dtrmin /m of th chargd particls. Elctronic charg to mass ratio (/m) is dtrmind by subjcting th lctron bam to lctric and magntic filds. This xprimnt backs up that th masurd valu of charg to mass ratio is in clos agrmnt with th standard valu of this ratio. Kywords: Charg to mass ratio, lctron, Cathod Ray Tub, Thomson's mthod INTRODUCTION Th orbit of a chargd particl in a uniform and constant magntic fild is a circl whn th initial vlocity of th particl is prpndicular to th magntic fild. Th radius of th orbit dpnds on th charg to mass ratio of th particl, q/m, th spd of th particl v, and th strngth of th magntic fild B. Whn th strngth of th magntic fild and th initial spd of th particl ar known, a masurmnt of a radius of th orbit dtrmins q/m. This principl was usd by J.J. Thomson to masur th charg to mass ratio of th lctron, /m, in 1897[,3]. Th rason for a circular orbit can b undrstood by th fact that a chargd particl xprincs a forc at right angls both to th instantanous vlocity and to th dirction of th magntic fild. Th particl thrfor movs undr th influnc of a forc whos magnitud is constant but whos dirction is always at th right angls to th vlocity[,3,5] Basd on his xprimntal rsults, Thomson providd convincing vidnc that th X-rays consistd of lctrons. H masurd th ratio of thir charg to mass and stimatd that th mass of th particl was about 1/1800 of that of a hydrogn atom[1,7]. Thomson ray tub has thr parts, namly th cathod assmbly consisting of a filamnt which on hating mits lctrons, th anod which is kpt at high potntial acclrating th mittd lctrons, and th grid which focuss th lctron bam. Th scrn is coatd with a fluorscnt matrial which glows whn th lctrons imping on it. Thr ar two dflction anods; th first is th X-plat and th scond consists of a pair of two Y-plats, P and Q. By applying an lctric- and/or a magntic- fild to this pair of plats, th dirction of movmnt of lctron bam can b altrd. By using th commrcially availabl 8SJ31J cathod ray tub (CRT), I dtrmin lctronic charg to mass ratio (/m) by subjcting th lctron bam to lctric and magntic filds. Th purpos of this articl is to show that th xprimntally masurd valu is in clos agrmnt with th standard valu of this ratio. Concptual Dscription If an lctric fild, E, is applid btwn th two plats prpndicular to th dirction of lctron bam passing through th spac btwn th plats, th forc acting on an lctron in th upward dirction of motion is givn by[1,4] invstigatd th natur of th mittd radiation by subjcting th radiation to an lctric fild and a magntic fild and found that it F E...1 gts dflctd by both th filds proving that th cathod rays consist of chargd particls[4,7,9]. Employing a vacuum tub, th whr rays wr collimatd into a bam by two mtal slits (lctrods). Th first of ths slits was th anod and th scond was connctd to th arth. Th bam was thn subjctd to an lctric fild that was producd btwn two paralll aluminum plats connctd to a battry. Th nd of th tub was mad in th shap of a larg sphr whr th bam would impact on th glass, crating a glowing patch[1,6,10]. Thomson pastd a scal on to th surfac of this sphr and masurd th dflction of th bam. Whn th uppr F is th forc acting on an lctron, is th lctronic charg 1.6x10-19Coulomb, and E is th applid lctric fild. Bcaus of th applid lctric fild, lctrons travl in a smicircular path and strik th scrn at th point M1. By rvrsing th polarity of th voltag applid to th plat, lctrons can b movd in th downward dirction in a smicircular path as shown in Figur-1. plat was connctd to ngativ pol of th battry and th lowr plat to th positiv pol, th glowing patch movd downwards. Whn th polarity was rvrsd, th patch movd upwards[4,8,11]. In this xprimnt I hav usd a commrcially availabl CRT- 8SJ31J with 70mm diamtr scrn siz to rpat th Thomson s xprimnt and dtrmin /m of th chargd particls. Th cathod 1

2 prpndicular lins OC and RC ar drawn to mt at C which forms th circl of radius r. OC and CR ar two prpndicular lins drawn to mt at C. From th gomtry on can writ OCR ATM θ Tanθ AM AT OX OC r OC ATxOX AM Figur-1: Dflction of lctron bam by an lctric fild [7] Instad of lctric fild if w apply a magntic fild prpndicular to th dirction of lctron flow, similar dflction of th bam taks plac by rvrsing th magntic fild in which cas also th dirction of th bam gts rvrsd similar to th dflction causd by th lctric fild. If r is th radius of th smicircular path travrsd by an lctron in th magntic fild, th forc acting on th lctron is givn by[4,7 Bv (mv^)/r... whr B is th applid magntic fild, v is th vlocity of th lctron at th point whr it ntrs th magntic fild, and r is th radius of th circular path travrsd by th lctron. From Equation-, /m is givn by...3 v Br In ordr to dtrmin th ratio /m, on nds to know th valu of th magntic fild applid, th vlocity of th lctron, and radius of smicircular path tracd by th lctron. (a) Dtrmination of lctron vlocity (v) With th application of lctric fild, th lctron bam movs to position M1 as shown in Figur-. Now th magntic fild is applid so that th bam dflcts back to its original position at O. Whn th magntic forc is qual to th lctric forc, th bam coms back to its original position. Hnc on can writ[1] Bv E v E B E B r...4 Thus th lctron vlocity is qual to th ratio of th two applid filds which is known. Hnc v can b dtrmind. (b) Dtrmination of radius (r) of th smicircular path tracd by th lctron bam In ordr to dtrmin th radius, r, on nds to considr th gomtry of lctron path as shown in Figur-. An lctron ntring btwn th pair of plats PQ at O will trac an arc and lav th plats at R and thn mov in a straight lin path and strik th scrn at th point M. OA is th path tracd by th lctron whn thr is no applid fild. Th lin joining th lctron path aftr laving th plats is xtrapolatd to mt th OA lin at T. Two Figur-: Gomtry of th lctron path[4] If L is distanc btwn th scrn and cntr of th two paralll plats, AT L OX is th lngth of th paralll plats OX l LM y is th distanc th spot movs on th scrn, which can b masurd on th graduatd scrn of th CRT. Hnc r Ll y Substituting for radius and vlocity, /m is givn by ye LlB If V is th voltag applid btwn th two paralll plats and d is th sparation btwn thm, thn E v d Hnc m dllb...5 (c) Masurmnt of magntic fild (B) Th magntic fild at th cntr of th two plats P and Q, cannot b masurd using a gauss mtr bcaus th magntic fild producd by bar magnts is of th ordr of 10 3 Tsla which is quit

3 low. Hnc convntional mthods ar usd for this. Th magntic fild strngth, B, can b calculatd knowing th pol strngth and dimnsions of th bar magnt or by th wll known mthod using a magntomtr which dos not nd information on any dimnsional paramtrs of th magnt. In this mthod th bar magnts ar placd prpndicular to th arth s magntic fild, as shown in th Figur- 3. Th CRT is alignd paralll to th arth s magntic mridian in which cas th lctron bam travls paralll to th magntic mridian. on th physical paramtrs of th tub is not supplid by th manufacturr, w had to cut opn th tub for masuring thm. Th masurd valus of ths paramtrs ar: Th lngth (L) distanc from th cntr of th Y dflcting plats to th scrn L 1.3cm (This can also b masurd without braking th tub, bing th lngth of blacknd portion of th CRT which is visibl from outsid.) Ovr th yars du to th chang in tchnology, th CRT dsign has also changd. Th Y-and X- dflcting plats ar no longr paralll plats but ar horn shapd. Figur-4 shows thir dimnsions for 8SJ31J CRT. Th X-plats ar connctd to voltag sourc and thr is a non-uniform lctric fild insid horn shapd X-plats. Th lctric fild dcrass along th horn lngth. Th lctric fild is a constant whrin th lctron maks ntry in to th X-plats bcaus of its uniform sparation (10mm lngth of th X-plats ar paralll). Hnc thr is an avrag lctric fild throughout th lngth of plats. Or th lctric fild is prsnt along th lngth of th tub and hnc[1,4,7] Lngth of th X plat l 3.1cm Th magnts ar placd prpndicular to th Y-plats. Hnc insid th two Y-plats thr is non-uniform magntic fild. This fild is prsnt throughout th width and lngth of th Y plats. Hnc width of th Y-plat is takn as plat sparation d Width of th Y plat d.8cm Figur-3: Magntic compass usd for masuring magntic fild[1] Th magntic fild strngth at th cntr of th compass du to a bar magnt is givn by[1] B H tanθ whr H is arth s magntic fild T at Wolaita, and θ is th angl of dflction of th compass ndl. Th prmability of vacuum (μ o ) dos not com into pictur in this cas, bcaus th magntic fild producd by a moving lctron or vic vrsa is not bing considrd hr[1,4,7]. Hnc, B H tanθ K lld, Hnc dllb kb ktan θh...6 From this quation if on draws a straight lin graph taking along Y-axis and tan θ along X-axis, th slop of th straight lin will b th avrag valu of K 1.3x3.1 x cm 106.7x10 6 m 3. Figur-4: Structur and dimnsions of CRT[7] Matrials and Mthods (a) Apparatus usd Th apparatus usd to dtrmin /m is shown in Figur-5. It consists of 1000V powr supply, dflction voltag ± 5V, X-shift, focus and intnsity controls. A dflction magntomtr with U- shapd stand and a st of bar magnts. Slop tan θ which can b substitutd in Equation-6 to obtain th valu of /m ktan θh Slop kh...7 As indicatd abov, K lld is known as CRT constant. As th data Figur-5: Exprimntal st-up for dtrmination of /m Th magntic mridian, giving th dirction of arth s North- South magntic fild, has bn markd on th cntr of a study tabl. 3

4 Th U-shapd stand has bn placd on th tabl and its two arms hav bn mad prpndicular to th magntic mridian. Th CRT has now bn placd in th arms of th U-shapd stand. In this position th axis of th CRT has bn paralll to th arth s magntic fild. Th CRT has now bn connctd to th powr supply kpt away from th CRT and has bn switchd on. Th brightnss and focus knobs hav bn adjustd to gt a bright spot on th CRT scrn. With X- and Y- dflction voltag knobs turnd to th minimum position, th position of th spot on th scrn has bn notd. Initial position of th spot has bn rckond as 0.0cm Th two bar magnts hav bn placd on ithr sid with opposit pols and at qual distanc from th tub on th two arms of th U-shapd dflction magntomtr stand. Th distanc, D, has bn rad from th scal D 3cm on th lft arm and 3cm on th right arm Th spot has movd up or down (Y-dirction) dpnding on how th bar magnts hav bn placd. Th distanc movd by th spot on th scrn has bn notd. This is th y dflction y 3.3cm Th Y-dflction voltag has now bn applid and so spot has com back to its origin position at 0.0. Th dflction voltag has bn rad from th digital mtr. This givs th valu of V as V 7.3 Volt This has compltd th first trial. Th Y-dflction voltag has now bn brought back 0.0V and th magnts hav bn positiond at 4cm on both th arms to rpat th xprimnt. Th distanc movd by th spot y.6cm V1.5V hav bn notd Th trial has bn rpatd by kping th two magnts at diffrnt distancs on th arms and applying voltag to bring th spot back to 0.0 positions. Th radings obtaind hav bn tabulatd in Tabl-1. In th scond part of th xprimnt th position of th magnts has bn rvrsd so that th dflction of th spot has bn on th opposit sid. Th polarity of th dflcting voltag has also bn rvrsd by turning th switch to th rvrs position. Th radings of dflction y, and dflcting voltag for diffrnt positions of th magnt hav bn rcordd in Tabl-. Th CRT has now bn rmovd without disturbing th arms and a compass has bn placd in its plac with its pointr rading along th magntic mridian and prpndicular to th magntic mridian. Th two bar magnts hav now bn placd at a distanc of 3cm on both th arms and dflction in th compass is notd (rading of any on of th two pointrs is nough for this purpos). For various positions of th magnt givn in Tabl-1, th dflction angl has bn notd and rcordd in Tabl-1. Valu of th tangnt of th angl has also bn rcordd and tan θ is calculatd and prsntd in Tabl-1. Th magnts hav bn rvrsd in thir positions and th dflction angl, θ, of th compass ndl has bn notd for various positions of th magnt and rcordd in Tabl-. Tanθ and Tan θ hav also bn calculatd and prsntd in th Tabl-. A graph has bn drawn with Tan θ on X-axis and th product Vy on Y-axis, as shown in Figurs-9 and 10 for th forward and rvrs cas rspctivly. Dflction Data and Data Analysis Tabl-1 Dflction of th spot and voltag applid in forward (upward) dirction Position of th Spot dflction Y- dflcting Tanθ Tan θ magnt (D)cm y(cm) voltag (V) V y θ Tabl- Dflction of th spot and voltag applid in rvrs (downward) dirction. Position of th Spot magnt dflction (D)cm y(cm) Y- dflction Dflction θ Tanθ Tan θ voltag(v) V y

5 ii) For th cas of rvrs voltag Thn, ktan θh slop kh ( )( ) Kg/C Avrag valu of charg to mass ratio of an Elctron Figur-6: Tan θ vrsus Vy curv with forward voltag Th slop of th straight lin is dtrmind as Slop cmV mV 1 30 charg to mass ratio for th cas of forward voltag+charg to mass ratio for th cas of invrs voltag Avrag valu of / Kg/C Kg/C Kg/C 1.76 Elctron charg to mass ratio, /m is found to b Kg/Coulomb, which is vry clos to th currntly accptd valu Kg/Coulomb. Acknowldgmnt I am profoundly thankful to Adama Scinc and Tchnology Univrsity(ASTU), Physics dpartmnt staffs for kindly ltting m in to thir laboratory to us all matrials and quipmnts that ar hlpful for data collction. Figur-7: Tan θ vrsus Vy curv with rvrs voltag Th slop of th straight lin is dtrmind as Slop RESULT AND CONCLUSION.730cmV mV Th avrag charg to mass ratio of an lctron can b calculatd by considring for both cass of voltag(forward voltag and rvrs voltag): i) For th cas of forward voltag ktan θh slop kh ( )( ) Kg/C REFERENCES 1. Jthndra Kumar P K and P Sharma, Elctron and its charg, Lab Exprimnts, Vol-11, N0-3, Sp.-011, Pag mson_m_ratio.pdf 3. f 4. C L Arpra BSc Proactical Physics, 19th Edn., S Chand and Company Ltd, 000, pag r%0m.pdf 6. o%0mass%0ratio.pdf 7. Exprimnt to show that cathod rays could b dflctd lctrically, n.wikipdia.org/wiki/j.j. Thomson mass.pdf Lilly J., Nuclar Physics: Principls and Applications, John Wily, (001) Citation: Blachw Dsalgn (018). A Rviw of Dtrmination of Charg to Mass Ratio of an Elctron by Thomson's mthod. j. of Physical and Chmical Scincs.V6I-01. DOI: /znodo Copyright: 018 Blachw Dsalgn, This is an opn-accss articl distributd undr th trms of th Crativ Commons Attribution Licns, which prmits unrstrictd us, distribution, and rproduction in any mdium, providd th original author and sourc ar crditd. 5