Chaptr 11 DUAL NATURE OF MATTER AND RADIATION Intrdctin Light xhibit dal natr - wav natr and particl natr. In Phnmna lik Intrfrnc, diffrctin tc wav natr is xhibitd. In pht lctric ffct, cmptn ffct tc particl natr is bsrvd. Ths light xhibit wav - particl dality. Mattr can als xhibit dal natr. Mving particl lik lctrns, prtns tc can xhibit wav prprtis. What is Phtlctric ffct? Explain th laws f Phtlctric ffct. Phtlctric ffct was discvrd by Hrtz in 1887. Whn light f sitabl frqncy is incidnt n crtain mtals fr lctrns ar mittd frm th mtal. This prcss is calld phtlctric ffct. Gnratd lctrns ar calld phtlctrns and crrnt d t this is calld phtlctric crrnt. Ordinary mtal shws this ffct whn UV rays falls n thm. Bt alkali mtals lik Ptassim, Sdim tc xhibit this ffct vn with visibl light. Laws f Pht lctric missin 1. Fr a givn mtal thr is a minimm frqncy calld thrshld frqncy fr incidnt radiatin, blw which thr is pht lctric missin, hwvr high th intnsity is 2. Fr a givn mtal, th phtlctric crrnt dirctly prprtinal t intnsity f incidnt radiatin prvidd frqncy is highr thn thrshld frqncy 3. Th KE f th phtlctrns dpnds n th frqncy f th incidnt radiatin. 4. Phtlctric missin is an instantans prcss. i thr is n tim lag btwn incidnt radiatin and missin f phtlctrn. 5. KE f pht lctrns almst indpndnt f intnsity. What is satratin crrnt? What is stpping ptntial? Ds it chang with intnsity f light. Maintain th and A at sm acclrating ptntial and cathd C is illminatd with light f intnsity I 1. Whn th acclrating ptntial incrass th pht lctric crrnt als incrass and bcm maximm. This maximm val f phtlctric crrnt is calld satratin crrnt fr that intnsity. This satratin crrnt incrass with incras in intnsity. Nw apply rtarding (-v) ptntial t and A with rspct t C. Whn this rtarding ptntial incrass, th pht crrnt dcrass and bcms zr at a particlr rtarding ptntial (V ). C A
Th minimm rtarding ptntial givn t and fr which phtlctric crrnt bcm zr is calld stpping ptntial (V ). Stpping ptntial is th sam fr all intnsitis. It dsnt dpnd n intnsity f light. KE max = V (Max KE if pht lctrns) Einstin s Pht lctric Eqatin Einstin gav xplanatin t pht lctric ffct basd n qantm thry f light. Th missin f lctrn is as a rslt f intractin f singl phtn with an ltrn, in which th phtn is cmpltly absrbd by th lctrn. T rmv an lctrn frm th mtal, a crtain minimm nrgy calld wrk fnctin ( ) is rqird. By law f cnsrvatin f nrgy Enrgy f incidnt phtn= Wrk fnctin + KE f mittd lctrn i. h = +½ mv 2.... (1) ½ mv 2 = h - Whn =, KE = ½ mv 2 =O O = h - i. = h qn (1) bcms h = h + ½ mv 2 r ½ mv 2 = h( - ) This is Einstin s Pht lctric qatin. Says (1) Kintic Enrgy f Pht lctrns dpnds n frqncy ( ) (2) < Pht lctric missin is impssibl. Nt : c l 1 2 c c mv h( ) 2 2 mv hc 2 c l 1 1 1 ( ), Pht Elctric Emissin (PEE) in trms f wavlngth. p h t crrnt I 3 I 2 I 1 I 3 >I 2 >I 1 -V Rtarding Ptntial Acclrating Ptntial
What is th ffct f frqncy f incidnt radiatin n stpping ptntial? Fr a particlar intnsity f light, th stpping ptntial is mr ngativ fr highr frqncy f incidnt radiatin Pht crrnt I 1 3 2 1 Satratin crrnt - v 3 - v 2 - v 1 Rtarding ptntial Acclrating ptntial Blw is th graph shwing th variatin f stpping ptntial with frqncy f incidnt radiatin. stp ptntial( ) mtal A 1 mtal B O 1 incidnt f r q ( ) Nt : If V is th stpping ptntial ½mv 2 = V Einstin s Pht lctric qn V = h ( - ) h h r V = Cmparing with y = mx+c
Slp f frqncy ( ) - Stpping ptntial V graph is, m = h, Slp x = h, Planks cnstant. V y intrcpt c = h What will b th max. KE f pht lctrns mittd frm magnsim ( 3.7 V ) whn v f = 1.5 1 15 th is incidnt. h = 6.6 1-34 1.5 1 15 = 9.9 1-19 J Evalatin = 3.7 V = 3.7 1.6 1-19 ½ mv 2 m = 9.9 1-19 - 3.7 1.6 1-19 = 3.98 1-19 J = 2.5 V h J Mnchrmtic radiatin f wav lngth 64.2nm frm Nn lamp irradiats a pht snsitiv matrial mad f csim n tngstn. Th stpping vltag is masrd t b.54v. Th src is rplacd by src f 427.2nm irradiating th sam pht cll. What is th nw stpping ptntial. Wav Natr f mattr - Mattr Wavs In 1924 Lis d Brlgli prpsd that mving particl f mattr shws wav - lik prprty ndr sitabl cnditin. This wav assciatd with mving particl is calld mattr wav. D Brlgli wav lngth : Th wav lngth assciatd with a particl f mass m mving with a spd v is givn by h h p mv Whr h is planks cnstant. This wav lngth is calld d Brlgli wav lngth assciatd with mattr wav. D Brgli wav lngth f lctrn Cnsidr n lctrn f mass m acclratd frm rst thrgh a pd f V vlts. Th KE f lctrn, K= V 2 P bt K =½mv 2 = 2m P 2mk 2mV D Brlgli wav lngth f lctrn h h p 2mV Sbstitting h,, n, m 1.227 nm V
Dfin wrk fncitn f a mtal Th minimm nrgy rqird t librat an lctrn frm th srfac f th mtal. w = h whr h = 6.63 1-34 JS. - Thrshld frqncy - Frqnty f th incidnt radiatin fr which lctrn missin jst starts. What is th nit f wrk fnctin - Elctrn Vlt (V) What ar th mthds sd fr spplying wrk fnctin. Thrmnic missin Elctric fild missn, Pht lctric missin (Spplying Hat nrgry) (Spplying lctric fild) (Incidnting Light) Wrk fnctin f A is 1.92 V and B is 5V which f thm is pht missin fr a radiatin wavlngth 33 A. Nt :\ - th mtal is pht missiv = 9 1 14 g 8 c 3 1 = 33 1 1 = 14 9 1 Hz (A)= w 19 h = 1.92 1.6 1 J 34 6.63 1 (B)= w 19 h = 5 1.6 1 J 34 6.63 1 = 14 5 1 Hz, Pht missiv = 14 12 1 Hz, nt pht missiv Cnditin fr Pht lctric missin - r Alkali mtals ar sitabl fr Pht lctric mmissin Wrk fnctin f alkali mtal is small. Which phtn is mr nrgtic Rd r Vilt - Jstify. Vilt sinc KE, f vilt is gratr than that f Rd. Explain Pht lctric Cll : Dvic which cnvrts chang in intnsity f lgiht int crrspnding chang in lctric crrnt. C A B light B - Evalatd Glass blb C - Emittr - A mtallic platd catd with pht snsitiv matrial G (sdim xid) A - And (Nickl Rd)
Pht lctric cll is calld "Elctric Ey" - It rspnds t th light falling n it, lik y. Uss f pht lctric cll. 1) Usd t masr intnsity f light (Masrs rat f flw f Phtns) 2) Atmatic switching f strt light. 3) Cnvrsin f slar nrgy int lctrical nrgy (Slar cll) Explain mattr wavs r d-brgli wavs. Wavs assciatd with matrial particls. Eg.: Elctrn, Prtn, Ntrn. Exprss th rlatin fr d-brgli wav lngth. Cnsidr a phtn f mass m mving with th vlcity c Enrgy f phtn, E = mc 2 = h w h r - frqncy phtn. h m = 2 c Mmntm f phtn P = mc = h h = c d-brgli wavlngth f phtn = h p In gnral, th d-brgli wavlngth assciatd with a matrial particl f mass m mving with vlcity. = h p = h m - It cnncts mmntm (P) and wav lngth D-Brgli wavs ar always assciatd with a mving particl. If v= thn d-brgli wav l n g t h =, infinity. Writ th applicatin f wav natr f mattr Elctrn micrscp having high rslving pwr dsignd by Ernst Rska. Why d-brgli wavs assciatd with a mving train is nt visibl. Sinc. = h m, 1 m Mass (m) f th train is larg is vry small.
Davisn and Grmr Exprimnt Davisn and Grmr in 1927 sccdd in masring D Brlgli wav lngth assciatd with an ltrn. A bm f lctrns mittd frm a hatd filmnt F is acclratd by applying p.d V btwn th filmnt and cylindr. Th bm is nw narrwd by passing it thrgh tw slits s 1 & s 2 and striks th targt T f Nickl crystal. Th lctrns ar scattrd in all dirctin by th targt. Th intnsits f scattrd lctrn bm in a givn dirctin is masrd by an lctrn dtctr which is cnnctd t a galvanmtr. Th crrnt in th galvanmtr is a masr f intnsity f diffractd lctrn bm. Th bsrvatins ar rpatd fr varis acclrating ptntial and angl f scattring. Th intnsity f diffractd bm is maximm at 54V fr angl =5 Frm lctrn diffractin masrmnt wav lngth f mattr wav was fnd t b.165nm. 1.227 f lctrn sing qn is nm V 1.227.167nm 54 Ths thr is an xcllnt agrmnt btwn thrtical and xprimntally bsrvd val. Ths Davisn and Grmr xpt. cnfirms th wav natr f lctrn and d Brlgli rlatin.