Thomson Moclel of Atm Rutherford 's X- vou Scattering. Distemce of Closest Approach Impact Poramedter Rutherford'!s Atom Mockef Limi tation ob Rutherford 's Atom model Boh mock} of hyclrogen Ahm Radius of Bohr's Stedionary Orbits Velocity of eleehon fn Bohr's Stotionanp orbit Freguen of electron in Behr's Stodiondny Ft Total ener: of; elechor, in Bohr's Stodionory orbi + Onigin Of Spectyal Lines Bohy's Explanction of specs-roul Series. of Hydsegen — cutem Enagy Level Lagram De Byogtie's Explancition of Bob's second postulede ot Quantizodion Very. FEmportent QuestionsIn this Unit, we. Shall discuss the models of atoms in Some cletoi). The first Contr bution in Wis regarcl come from Deabion, who proposect that matter is mace of atoms, een are indivisible I.I. Themen proposes! a See foy the atom, which JS mooalifieo! by Rutherford amd Later by Niels Bohy- Thomsen Model of Atom- Accorcling to (ely “change moole}, every, atom comist of @ positively chy s phone of ACKUA Of the orc of To!’m in mgeel pe entire. mars anol positive change of the cutom ake Uniform, iatributted, Tnsiole. this sphare, the -elechons ane embeded Like seady in a woteameln.or Uke plums in a pudloling. The number of electron is such thet +Hhreiv n o ee 4b eortol to the positive. charge m. Thus the atom dd elechically tt a of Thomson Atom moolel - (1) It Could not explain te Owigin of Spectre Serer of iy and other atoms, obseaveal experimentally. Gi) Tt Corl not explain He ane scoHfering of x- particles” from thin “meted foils, a4 observed by Rutherford.Rutherfordis d-ray Scattering Experiment : The cepenimendn| Setup used by Ruther ford and hia Collaborators, Geiger and Marsden +s Shown in Pig - ~s ~ ‘ COLLIMATOR [=] \ OLD FOIL), (10-8m thick) 4—» MOST-o anne 4 pass ~Je “> STRAIGHT 7 ay / y 7 SCREEN CAVITY J i] SS ABOUT 1 in 8000-c a econ IS REFLECTED BACK GerectORy S 38 @ pleca of radioactive Source (es87'") Contained in a deadl Covity. The X- particles emitted by the Source are Collimated into a narnowo beam with the help of @ lead slit ( Collimator). The Collimated beam Gs allowed to fall om a thin gold foil of thickness of the oxder of 2IxIOm. The a particles Scottered in ifferent clivections are. observed trv Q vrotetable. oletector Consisting of a zine sulbh Screen and a micwscepe: The A- particles produce bright flashes on the ZnS Screen. These are observed in the microscope and Countes! at U angles from the clirection of incidence of the beam- Tre angle © of cteviation of an a- particle from dts original olivection is Called JAS Scocttering angle. e.Observations ~ a graph ud plotted between the Scattering angle @ and the number of X- particles N, Scattered at £0 for a large number of A- particles, we find that - ' i) Most of the &- particles {s pars shralginr throu ‘c! the gold foil. Tt means 2 olo not Suffer any , 3 caliision with gold atoms. 5 (ii) about 014% of git ind a- particles statler 20 40 60 80 100 120 140 160 180 by more. than I. SCATTERING ANGLE (0°) =emmo- Wii) About one A- particle in every Bo00 porticles aftects by move than 3¢- Ex planation - ' ————_ Am a- partie 44 over Too mohe massive than an elechon, and vin this experiment, A- particle is travelling ot a high speed ; thureppre, vey Ateong fore alone” could hove oleflected Hed Lage angres. Tws Led Ruther foro] to postulate that the entire positive che af the atom must be Concentretecl In a tiny centyol Cove of the abm This ding central Core of each atom was Calleol atomic Hucleus. An &-particle Carries two units of positive and has mass of a@ helium atom, Cc on gold “nucleus = ze, whe Z of golol iu 79, As gold nucleus is about So dimes heavier than an x- particle , we aXsume thot it wold remain stable in the Scattering Process.Thinepove, the yecto of ~-particle Gan be Compute uain New ete D haw of motion amd Coulomb force of repulsion between A~ cle and gold nucleus ive. whre ¥ iA the Mistance of A- povcticte tom the centre of the nucleus. The mi ituole and olivection of the force on an x~ particle cha Continuously ab Jt approaches the nuctens first ond then moves away from at. —o 8518, ATOMIC , a NUCLEUS a { tt 1 to a lo 1 INCIDENT & PARTICLES ON an wo a 1 As shown in fig an - particle (1) tending to Collide with the nucleus, slow down clue to repulsive force of the nucleus, finally stops anal As then repelleof back. This o- jche. thers fore vetrar ots peth , Scodterimg prough 180". The d-paxticles 2 and 2! tendling ao Wit the nucleus ot ths peeiphiny, experience Shong vepulaive force andl qe 1 eadtened through lange angles (67390). The &- particles Zand 2, which pass at a stance from the nucleus experience small repulsive forts ond get scattered trough small lea.The x-porticles which pars at Large olistances fem the nucleus gr almost undeviated. We Can show that the number af x - Particles Scattered per unit awa NCO) cb Scattering angle @ varies inwersely or Sint (2): NW) % —SntCEy Distance of Closest Approach - tohen & - particle 4k divectec! towards the nucleus , the Kinetic energy of A- particle goes on olecreasing and mm twen electrical p lod es on increasmg due 40 Coulomb’s repulsive force between nucleus and oX- particle. At a cartein clistance v from the nucleus, KE. ef o- particle reduces to ) Impact Payameter ( b) - ines] AA the Perpendicular distance Tt js of the inital velocity of « “porticie | & from tHe Central Une of tre nucleus , when the particle 4h for Cuno pom the nucleus. VELOCITY VECTOR OF @ PARTICLE fe cenRACONE ~~ 0 DISTANCE (fm) =m TARGET NUCLEUS: When the im pact eee As Jonge 5 an A - particle wil) cleviots a much smaller angk- pear when impact p 48 Amal , force perienced aa | and the a- particle oil Scatter Hough a dange angle. Rutheforol Coleuloted ana ically the velotion between the im pact Fete fs Scattering angle 8, which wu given by- 1 z t 8 a b = aes ES Cot fr [Re= amv ]Rutherforels Atom Model - CL) Every atom Consist of a tiny central Core, Called tre atomic nuceus In which the entire positive charge and almost entire mars of the atom are Concentrated. @) The size of the nucleus ws of tre order of 10, which 2s Amal a& Com parsol fo the size of the atom whith is of the oreler of Jom. @) The atomic nucleus is a number of electon’. As atom ids electric: neutral, the total negocive change. of elechons Aurrounding He nucleus 4s equa} to toted positive. change ox the nucleus, (4.) These elechons revolve around the nucleus in Various civeuteord orbits. Tae cercripeted force required by elechon for revolution is provided by the electrostectic force ef attracton between eechonA and the nuclens. Enevay of the electyon in orbit - Let Fe? Centripetal force requires) 4O Keep Q revolving elechon in orbit fe = elechostactic foree of cttraction behven the revolving eaeckon and the nucleus then for a narically Stoble orbit in @ hygchogen ete. Fe — Fe mv2>_._e-e > a. 22 ¥ ATC Y= UA Amer KrE. of the electron in the orbit = Le myv>Hence KE =e? Be ¥ Potential encrgy of electron in orbit- U = ece - -e2r 4N EY 4TLeG.¥ '. Total energy of eleehon in hurohagen atom — E+ KE tU ce =e et SM En¥ ATILGoY ov e = -<& BMleor Hence the Jotal energy of electron in orbit of hydro atom is negotive. Hence, the electon ta bound do the nucleus fe. the elechon +s not free to eave the orbit around the nucleus. Limitation of Rutherford Atom Model- OD Accorcling to the Classical EM theory, the revolving. Gechons must yaoliokr energy in the fom of EM Waves. As vewolvin elechon, Loses continuously . it must é spivod inwards and fin into the nucleus but as” mattir 4A Atoble, we Cannot expect the atoms sto Collapse- Gi) As +e revolving elechons spival inwards, Heir angular Velockties “ond hence tiv frequencies of yewolution would chomge Continuously - Theredpre frequency of EM Waves emitted must change Continuowsly.re , efoms shoud emyt continuous spectrum but we observe ony a dine spectrum. Bohyv Moeel of Hyclrogen Atom- There ane three baaje postulates of +hia modif— Q) Ev ator Consist of & cental core Coho! nucleus, In which entire positive chi ond almost entire mass. of the atom aw concentrated. A surtoble number of “electrons revolve around the nucleus in cive orbits. The cenhipehal fore required for revolution is provided by the elechrostatic forte of attraction between the Elechnn and the nucleus. Centripetal fore = Electrostatic fore. of attraction my = LL. (222) r a ad ve mv= . Kzer k= Yaneo ~~ Oe zeLl (2) A ccoroling ao Bohs, electron Can evelve. only in certain ‘chscrets non radiating oxbits 4 Stodionareg orbits, for Which total angulor momentum of the Awolving electron is an integral muttiple of ham, whare” h ia plank's Constant. Thus the argular momentum of a orbiting electron 44 quantised, Here 1 ud Callecl principle Puantum number, * The ehechon, while vevolving in such orbits, Shell not tose enwrgy C-2- dts enngy woutel Ste Constant.(3) The emission / absorbtion of vy ccs only when an elechon PS form one $ ts S Specified non - Yactlaking ‘ae Another - Hi fferance in the ‘otal enon: oy elechon in nthe tuo orbits JA absorbec} cohen" the elechon jumps from an immer #0 an outer. orbit amd emitted whin eketon jumps from outer 4o the inner orbit. hv = &-& OCWAL VY As the uLn ° f yaciotinn emitted on Jumpin: mm outer do! Inner orbit of eng E. oa fr respectively. Radius of @Behr's stationary Orbits— We Know that for Atotion oy orbits - = mh =n Case ia oor, By puting, the value of v in ray = ze? > Mx We = Kzer vr arch m* > ye = nthe = for hyehogen adem 470 mKe’ Ze Tt shows tot - ran” ce the raclius of stocionary, orbits ane in a yatio 13 2S and so on be LiWi Glow. cleanly the stodionany, orbits are not equally spaced.Velocity of electron in Bohr's Stationary Orbit - As we Know that - _mv> = kze? Yr re ov y = kze> — ) mv> and also y =_nh — ©) atmv by equation U1) and (2) we get — Kze> =. nh 2 21kzer mv? 2ITmMV or v nh ana As Vx+> hence the ovbited velocity of electron in outer. orbits is smaller as compartol “do its Value in the inner orbits: Frequency of electron in Gohr's Stationary orbit - Tt is the number of vewolutions completeo! per. Secor by the ekcton In a Stationary orbit, araumd the. nucleus. It is represented by vy. As Vz rw = r(oanv) ype = 2m kte2 = KzeX ane rth: 27tr nhr Kze® > |v The frequency of election in subsequent stationary orbits 4s smallA as v «xt -Total Energy of electron in Gohr's Stationary Orbit Kinetic. energy of election revelving ina stedionasy, orbit is - 1 - 2 by .mv>. kze™ KG. of electron = Smv* = Se [*s ie Potential energy of elechon = Potential x Change PE. of electron = Kzex(-e) = —Kze> Yr Y Tote energy of electron in the orbit - E = KE. + PE. Ee: Lkze* _ Kze> = ~ kee? 2 -> + ar by putting = _nth™ we. _ d 4 477m kze> at E = -_20mk*zet we by Substituting the Standard values, we get € = -13-6 ey eat n rn Hence the toto) enrgy of elethon in aq stati orbit ad ive, whith means thet the electron is beled to the nucleus and ia not free to teave it * when n=L then this state of lowest enngy of the. atom Jb Cotbed groundl stoke. The enngy of this stat. HSE, = -I3-6ey. * > the minimum enngy required do pree, the electron from the ground stote of hydrogen atom 48 I3Gev. This id Called ionisation energy of hydrogen odom.* As n increases, the value of negective energy clecreased be encrgy Ks progressiv' Jangex me the outer orbits. es preg “y Origin of Spectral Lines — At room Lumperoture., most of the hyetrogen atoms axe in ground state. when a hyclogen ator Yeevives erurgy q proasses Auch as aldcheh ‘collisions or heat, the atom mou require sufficient energy to yaise the elechon to heghor @ stots Le from nel do n=2, 3,u,.-.. The atom CD Abn said tv be in an extited state - E2 —> PHOTON ~ Ay From Hure excited statis, the elechon can fall hack 40 a state of tower energy and emitting a photon of particular energy (= olifference t enurgies of, the fe stoter )). 7 tf 7 ong 4 Let E, and €, are the total of elechon in the inner and outer orbit reapectivelyy When an elechon jumps pom an outer. 40 an innex orbit , the enrigy of radiation emitted Js giren by hv = €,-€, hv = _27?mk72et Fa a we ne 7 | he = _an?me eet Ft a re nooor 2 2 _anmektete? PL A on ne ne Now avs Where VY Ub te wave numb of radiation emitted -e. number of Complete wave in unit Langth. stim whet and = 2nmke = R (Rydberg Constant’) or R = 1037 x10" m* = zi _i Hence P:R at” ve] For hydrogen fo ne =n Above. equation us called Rydberg formula for the Spectrum of hyerogen otem. *% By above formula tt ia Clear that wavelength / frequencies [weve numbers of yadichions emith by the excitedt hyelrogan atom ore not Continuous. Thay hove specific valu» cupending upon the values of Yn and no. * Frequency of radiation emitted cohen the atom makes transition from the higher ena gy Stote (m2) +o the bwer energy. Atodz C1) — vr &£& > 14 a v= Rela a3][Q) Find the watio of enngies of photons produad SEE clue 40 teamition ef am electon of huplrogen acm abs (a) Setond permittect energy Lvel 40 the fist Loved (b> the halghust peemittes| energy Lavel “to Hie pirat permitted Jewel. Sel. (4) Enengy of Photon released = E,-E; = -3.4 = (-13-6) =lowev (6b) The heighest permitted ei dwel to the first wget es URSA fis peemrtt = Ea- E, = © - (13:6) = Iséev Rokio o enuagies ek Photon = 1Je2 = @ b b 13-6 q What is the ratio of radius of the ovbits S§Er Coreaponoling to fist excited stat. and Grund Stoke In a hyelrogen atem 7 Sol. For fivst excited stole N= 2 Groumd stot occuns for n= 1 y an? Henee Y1 sf{mP = (zy % (Ft) (+) Wiw = 4tl Gl Re wdiws of innermost elechon orbit of 4 CBE hydro atom 3s $:3K10" m, Wheat Js the mmdius of orbit in the Second excited sto ? Sek The radius of atom whose PHnciple Guantum number JA v1, us given Yann Hore ¥% Jb Yaclius of Mnermost’(n=1) orbit . Fer second excited state n=3 Y = (39x 53x 101! = 4-77 x10 !?m,Bohr's Explanation of spectral series of Hydyogen = Atom - bohon an atomic. ox vopour at dow Pressure, 4s excited uasuodly bg ne an electric. Cuiiurt thw at) the / vapowe emits yadictions of certain Specific wor 6 This Kind of spectum dd caltel “Line emission spectrum" and wt consists of 4 few Laight Airts on a clark background. Detector photographic plate) High voltage Hydrogen gas discharge tube 410nm = 434nm 468nm 656nm bohon the white Lé 4A parsed through the Same. [Vapour., we observe a ‘bri Lack#round Cross by a few dark Ling signi ing the: missi ee aa or “the wavelensth s that” are ahisotbedl by gs. They form a& “Line absorption Spechum? It was founcl that missing wav s he He Same a4 “the wa murent inthe emission spectrum of the gas / vapour: Bohr gave Wis theo of byclro ahm about spectra] seties which had! observ experimentally by. Voriows Acierttists. Bohr offere| a tHyorelicas exphnotion of these spectro} series as follows :1. Lyman Series — Bohr postulotias that Lyman Series is obtained then an electron jumps to the first orbit Cn, =1) from any outer. orbst (Nas 2,3,4-...) Wave numbers 6 ectral Lints o an seres were Calculodtec de J i 7 ALR-m]] O-28) These valus of ye Lie in the “Ultra violet region” of the spectrum. 2. Galmey Series - Accercling fo Behr, Balmer Aries 3 obtained! when an electron jumps to the secorel orbit (1,=2) from omy outer. orbit (Mm = 3,4,5,---- Wave number of theue spectyol Lines were Caleubiteo| a“ 3 J L vos a[ 7] (na = 3,405----) THA Set of Spectral Lines Lie in the visible part of the spectrum,3. Paschen Series — According 40 Bohr, Paschan series 4b obtedinecl eohen om electron Jumps fo the Sx Orbit (nie 3) from ang outer obit) (n.= 4,5;6,--): Bohr calculoted the wave number of spectra} Anes of Paschen sexier from the reletion: ¥ =R[& ~ 4] (nat sie...) The value Of TF Lie in the infrared region of the spectrum. 4 Brackett Series- According to Bohr, Brackett Serien iB obtained When an eclechon jumps to the 4th omit C= 4) from ong. outer orbit (m= $6,7---) Wave number] FF = R[ a ~# | (y= 5167,---) Brackett Series Was cHidcoverscl Im the infrared region of the Spectum, S- Pfunel Series - Accoroling. Ae Bohr Pfundl senies. 12 obtained When om clechon jumps to the St orbit (n,=s) from any outer. orbit (m= 6,7.8,---) Wave number ve *R[ te = =] Nt 67 Bow Pfund Sertes wos cHscovercl in the Infmrad region of the spectrum,Energy Level Diagram - A clagram which represents the doted tes of electron in Afferent ee orbits of em atom is Coblect the energy eR jagpran In this clagram, total energies of elector in various stationary orbits axe vepreserted by the hofizortal Lines drawn according to Some Surtable. energy Scakt E = -Jja¢ n> putting n=41,2,%,---- We get the ensrgies of electrons in Vardous Ateckiondarey- orbits as? 2 -IB6 2 Li, in Ee, ef = 13 cey 5 EL 136 = -syey 2 = IBC 3s Es see -bsiev 5 Ey = 128 = -OBsev E - —136 2.6. - (126 2. -oO sof == z-OSY CV Eo = Ee ese Clearly ab n increases Ex becomes Luss negothive until ‘at n=o , Enzo. f Tre eae devel lagram Ga shown fn Y fer Ayo! atom.” The height ion Gorceapsrals co n= 2% and has Qeeoy co Ths as the of the atom, when the elechon is vemoyed (v= 00) from the nucleus and the electron is. at vebl- E= OePfund series Brackett series Paschen series Balmer series net =14-0 Lyman series * As n Increases energies of the excited state Come Closer so : TQ) calculate the waveltngth of Ha Line (nz 3) cE i Balm series of hydeo odom, given Rydberg Constant = R= 1.087 X107 m™ Sel: For Balmer Aeries, wavelength is given by- tf" 4) for Hx Line 2223, SO thot eo 77a oa + = 1097 Xto ie 4 4 = os2y x07 a A -—1 = 663 A° OIS2UY Kpo!Ss Photons , with a corctinuows wee of PES ane mace +0 pars tio ra hae The fansitions — Shou hehe 5 diode. Poel the spectyol absoxption Lines in Tha Coa Conus spectrum. ° ne00 nes n=4 -2 x n=3 zr n=2 (ev) ~4 -6 -s I -|0 -12 n=Lb (A) Telentify the ctral sertes ef the ro; emission spectrum, to which each of these Hee Lints Corresponds. (b) Which of these Lines Covrespord s to the absorption of yadiation ef maximum wavelength 2 Sol. Sol. Ca) Lst spectrum epresert Lyman series because, in this Spectrum, elechorn jumps $OM N=aL Ao N=2, Inc spectrum epresert Balmar Serits because im this Spectrum, electron jumps fom n=2 +o n=3,. IDvrd Spectrum veprarsents Padchen series aS tre elechon jumps pam n=% to n=4 in this Spectrum. Ce) Spectrod Line Ot (Paschen Series) Grvesponds to the absoxption of radiation of, Maximum warelergtin.G) @) Te erengy dwiels of an atom ore Shown cE in fig. vahich of Haem coil result In the 2) emission of a Photon of wavelength 275 nm? Uo) thich transition Corvesponds 4o emission of vadiation ef maximum wavelength ? A ow © cs -2ey -tse —loevy Sol, (Q) When A= 2TISNM = 27TSKITFM ten es hv che = 6exisS4x anio® A 27s x16? Ee = aS ev + Transition B& will veautt in the emission of photon of Az 27S nm, (6) Maximum wavelen hos mimimum Transition A provicles energy of 2ev, coh 4 mynrnum. De Brg sey Explanation of RBohr's Second “postulate of Quantization TRe Second postulate of Bohr model sags thal: an, momentum of electron orbiting anound the nucleus iA quardizecl Le. mvy = Th fohtre = 1,2,3..1 Lous cle Broglie expainec| Hus purale - Accorcling to de ie, the elechon inits civcular orbit, a proposed! by Bohr, must be Sean as a particle wave.We Know thet when a shing hixed ad tun ends 4s plucked, a lenge Number of wavelen are. excited. But only those “waves which have nodes ot the two ends from the ‘tondling Waves and Survive. It means that in Q string, Standing wees eae when fotal chistance travellicof by a wave down Atring and back Us ami integer mule ple. of the pave ¢ Waves With othr wavetengins inters eve With them- selves upon reflection and r ontbectes vanish quickly. Hence according to of Broghke, a stationary orbit is that bohich Gcortaina arr a fegtol number’ of de Broglie waves arsociaticl with the revolving. clechon, For an electron revolving in nth circular orbit of Yadius Y, For the permissible oxbit , anv =n According +o ole Brogli = bh cco" g to cle rage A 7 tohere. V dd speeol. of clechon revolving In vith orbit any = nh = =z nh rm 7 > mvy = nh 230Hence om momentum of elechon revolving in nth orbit “must be an | multiple of West » which Js the quantim Cenclition proposes! by Bele in second postulate. Limitation of Behr's Theory - (LD This theory is icoble 40 Simplest atom dike drogen Noi cl. The ne ells in Case of atoms of otur elements for cahigh ark. @) The theory oes not explain why orbits of elechons one taken as circular , while eMipteal orbits are also possible» GB.) Bohr's theo doe not s oO ing about tHe relodive akersl Hee of spect tal gins +) Bohr's Hwory coer not take Into account the wave properties of electrons,Very Important Questions L Mark Questions- Ql. Weaibe the expreasion for Bhor's raclius In WWyetregen outorn Cretki ante , 01) Q.2. Stote Bhor's quantisation cenditon for oLapining Stahionory orbits, C Rese 2008, CBSE 2olo, 03’) @.3. In the Rutherford scodttering experrment, the stance. of Closest Approach for an a-particle is ce. Th x-particle 1s veplaced by a proton, hovo much Kinetic envrgy in Comparison to 4~ portcle will at require“ to have the. same distance. of Closest approach clo ? Hint + Proton CH"), A-Particle (Het) CcBs€ 2003 2000) Qa. In hyeleo cutom , if the elechon is replaced by a Pp cle. which 2 206 times heavier bub Os the Same change, how would rts radius Change ia CeBSE 2002, 08) Qa.s- TR mengy of the electron im the und ‘stoke ‘of 3 a odom is +136 ev. a (er) Whot hoes “the negoctive sign signify ? (6) How much 4s reguireol to take an electron in Hate ben Growl the. ground state to the first excited stat ? eee2 Mark Questions - QL. The und stode ener. of; dvogen atom AA -15.6ev, The Photn emitted clu the tromition of electron from n=2 to net Stodh is inciclant on the photosensitive Moterial of Unknown work functOn. The photoelechons ane emrtted from materials with a maximum Kinetic energy of Bev. Codcutake the thitsheld weveltngy of the materiel used, Answer - As Séles nm. Cease 2008) Q2, Using. Bohr's postulates for chosen atom, shove SHhat the -totol eneagy (Ee) of the electron In the stocion stot, Con be expresses] ak the Sum of KineHe energy (K) and potertHed CU), Where Ks -2uU- Hence oledute the expression for te total energy In the nth enengy devel ob- bugalrugen chem. (cRSE 2002, (2) @.3. CA Using Bhor's seconcl postulate ef quan tizedon of orbital angutor mementum show thod the Civeum ference of the eleckon in tne nto ovbital ctote In hgolro odom is n dimes the Az-broglie wavelength arxsouated with th. (b) The ekectron In agen oto ld inthally in the third! excitect stat... whet 2b the maximum number of Spectro Lines vcohich Car be emitteco| when it finally moves to the ground Stoke ? ( Pelt 20/2, RBSE 2006) Answer: (6) 1-23Qu Me und state energy of hydro: octomn is eee If an checked pleas! Q@ Srransrtion fom om e Aurel ~0- 85 ev Fo -1S1L eV, Codculete the ~ wavelen, of the Spechal Une emitter To which Series of hyolregen spechum aows this woavelengty belong ? (casE 2001, 12) Qs. Ina Geiger Marsden experiment colcutate tre Autonce of Closeat approach to the nucleus of Z=Bo, When om o- particle of Bmev enngy Incident on it befpre Jt Comer reat and reverse. its direction: How udll the dustance of closest approach be. affect-ed when the Kinehic energy of the a- partde is cloubled Cense 2003, 09) Anawer- So = 2-88 K10!2 mm ' Qb, Stedt the baste assumptions of the Rutherford model of the otom. Explain in brief why +Hhis mock con not account wv the Stability of “an atom ? CDelhi 200 2,10) @-1 Using the Bohr's postulotes, olerive He expression for tHe — (a) Speect of the electron im the nth orbit, (eo) radius of the nt arbit of tHe elector in Wydregen dom, CR@se 2007, 10) G8. Tae OF the elechon in the groundl Stott of Ja 136 ev, Coleutode the energy of He p trod woutd be emitted if} the elechon weu do make a transition Corresponeling. to the emission of the fivat Link of the (a) Lyman series (b) Bodmer seniera of Hw hydro; ectrum Arswe- (a) lozev (bd 1.9 i) aa eae 20eg)@8. Re Und stock. ©. dx otom Te ts emenyd of leystregen Ca) Lohot 4a the KE. of an elect in the 24 excites| stecte? (b) Th the elechon jumps to the ground stotte the 2nd excited stote, colewlate the wavelenety ef the spectral tine emitted. Pmawer ©) Sev (b) A= 10304 (cease 2003, 08) Blo. The energy duels of an atom ate @ shoon jn Sige beled 2 oev £ D -2ev -4-s5ev -loev lei) Which of trem will weautt in the transition of a photon of wavelength 21s nm 2? () which transition Covvespors to emission of radiation of maximum wav 2 Answer: (a4) tramiton B Ce@se 2eol; 09) (od transition A. Qu Ca) Usin Atulotes of Bhoris Heo Q hyetrogen hee, show ies me ot Ci) The tadius of obits increase as n> Gi) The total energy of the elechon Increases Ob Sm vole n Js the pAlndpal quantum number of the atm. (6) Codeulode the wavelength of Ha dine in Balmer series of hydro: otom, given that —l Ryolberg Constant = 1-097 x107 m7. Amswe- (b) A = 6563 AY ‘(case 2002, 06)