Distance. of Closest Approach Impact Posameter Rutherford 's Atom Model Limitation ef Ruther fored's Atom moodlef Bohr mock of hydeogen Atom Racius of Bohy's Stochonary Orbits Veloetty of electron in Behris Station orbit Frequency of elechon in Rohr's Stoctionoray Orbit Total energy © elector, in Bob's Stationary Lah Oxigin Of Spectral Lins Bohi's Explanation ef spectre Series of Hydrogen atom Eneay Lured chiogram Be Byogtiels Explanation Bohé's Second postulede ef Quant Tora} Very Fenportemt QuesthonsTa this unit, we Shall cacuss the models ef atems in seme. olttel). The first Contribution in Hus resatad come from Dalton, who proposed thot matter 18 meole of atoms, which are indivisible J.J. Thaemsan proposed @ shuctusr for He atom, which Ls meali fies! by Rutherford ond Later by Niels Bohr: Thomsen Model of Atom -— Accorcling ato +e, Thomsen moolel, ew ater comsiat of a petivet el Sphare ely radius of the orolen of Iol’m ty which entive mas amo pesitive change of the cotom ane Uniformh, isthbuttid, Trsiole His sphart, the electons are embeded Like seeds in a wateamelon. or Ake plums in a pucloling., The number. ef electron is such that Hair ve Ch 4b equcl to the positive ch of He tom. Thus the cofom 2 electically neuteal, Limite+ions of Thomson Atom moodle} - (t) Tt Could not explain Ha oa of Spectrol series of hag eer ond other atoms, observed experimentally. ci) Tt Cotdd not explain Hee angie scattering of x particles” from thin metal foils, 25 observed by Rutherford. Rutherford's a-ray Scattering Experiment : The experimental setup usec) by Rutherford and hit Collaborators, Gelger cond Marsden is Shown in fix - COLLIMATOR [7] ‘ 4 OLD FOIL +—+> i MOST-a@ C1 on te "pane <> STRAIGHT a a | -~6 - Tey, f2ns avin / SY SCREEN / oo NS @icro- | -* * SCOPE ABOUT 1 in 000-a_ 1S REFLECTED BACK (ROTATASLE BETECTOR) S iso plece °f vacdtonctive Souken (eB?) Contained In a Atal “Camty. The o- particles ented by the Source ake Collimated imfo a narrow beam oath the helb of a Lead slit ( Collimedor). The Collimateo beam A allowed sto fall a thin gold foil of thickness of the order of Zixitm. The a Particles Scattered in cli clivecHons are observed Ho a rotatable detector Consisting of a zine 5 ) Screen and a microscape- The A-perticles produce bal flashes on the ZnS screen. These are sical h Hae microscope and Countesl at cti angles from the olirection of inciclence of the m- The. angle © of cteviation of an a- particle from wuts original civection is Called Be Scattering angle. 8. tObservations ~ . ————__ A graph 8 plotted between He Scattering angle @ and the number ef o(- particles N, Scattered at LO for a large number of a particles, Wwe find Mad - Ci} Most of the o- particles | ars stra thro it tne gold ft It wes 4 Callision) twitn geld atoms. : (ii) Onty about 014% of g Inetolént a- particles statler by more than I. elo not suffer any i 9 a0 40 80 80 100-120 140 160. 180 SCATTERING ANGLE (@*}rmete Gi) About one A- particle In everry Booo of perticles clbtects by move than 3c. Explanation - , Oso particle 4A over. Tooo more massive. than an elechon, and in tia experiment A- particle is travelling ata hk “peed Ine vera} Afreng pre alone” coutd hove cleft ected Hered idnge angles. This tel Rutherfore| 40 poss e that the enhre positive change of the atom mudt be Comeantredtsl tn a Any central Core of the atm: This Ainy central Core of each atm wat Called atomic Yucleus. Ain a&-Ppardicle Cannes two units of positive. and has mass of a helium atom. ch on gold “nucleus = ze, there Z of gold is 79. As gold nucleus 4 about So dimes Aeavier than an &- particle we aArsume treat Jt wold remain stable mM the Scattering prows. Thinegove, the yecto of a-portide can be Compute: using, weds of of metim and Coulomb force of repulsion between A- Park cle. and gold nucleus te. = ae (ze >C2e) +7 €, yz ohne ¥ 4d the distance of x- particle from the Certre of the nucleus. The m ituole and olivecton of the force on On o&~ particle changes Continuously as Jt approaches the nucleus first amd then moves awe from 4. INCIDENT a PARTICLES WN aN w As show in fig an x- particle (1) tending to collide with the nucleus, slow down clie +o repulsive force of the nucleus, finally stops anol 4 : » This at- idle ; vetrace ats Path, Scodfering through 18c'. The @-panticles 2 and 2! tending Ao hit the nucdeus at its PUSIPhiry , experience. Shong repulsive forte ancl qea eathehad through lange onqles a @ra0)- The a- particles Band 3, which pass at a Aistance from the nucleus experience small repulsive forts amd Jet scatlered tHrough small eA,TRe A-partces hich pass at loage cishances Fem the nucleus go edmest uncleiactid. We Can shew that the number gf o- Particles Scattered pera unit axa NCO) et Scattering angle @ varies rwerseliy ars Sint (2): NO) & Sint (By Distance of Closest Approach - tohen %- particle tb Arectec} towards Ha nucleus, the Kinete energy of a- particle gees on ole creasing and my two electrical potentfat goes on incresting duc 40 Coulombs vepulsive force bettoeen nucleus and a- particle. At a cantain clutane % from the nucleus, KE. of &- particle veduces to zexsp. The Particle Stops and at comnot qo, closea 30 the nucleus. It is wpelled by the nucleus and , at veto, Sts path, tiening How Io. Thu isimee Yo is Known a the clistance of closest PP reach - Electrical potential at olittinie vo cue to nucleus Potential Enengy of X- particle at distance % fiom the nucews = Potential x Chonge Pe. = _Z€ _xze As ot tHe olistance of Closeat approach - KE. = PE. amv = =e a 2e = ATT Eo Ne or %; si we x 2e . 4ne, (Ime Impact Parameter ( b) - TE is ineol AK the per penciicular distance of the imal vehocity of A- poticle from the Centre}l Une of He nucleus » when the particle ak for aun auy proms the nucleus. VELOCITY 100) VECTOR OF @ PARTICLE 3 a a as | be a ee Zi CENTRALLINE z= Ban euss DISTANCE (tm) == TARGET NUCLEUS when the impact parameter iB > an A-parhcle will oleviate tro & much smaller angle. However, , When tempat Pars 4&8 Amall , force experienced ih lange andl the o- Particle util Scatter Hreough a dange angle. Ruthaforel colculoted analytically the relation between the impact Parameter Sper Scatiering. angle 8B, which 4s given by [Re = gm] bs = ot Ze™ Cot O/r 4ne KE.Rutherfore’s Atom Model - CL) Every atom Consist of a tiny central Core, Called “the atomic nucleus In which the entre positive, charge. onc} almost entire mass of the edom ane Conconpratecs. (2) The size of the nucleus uh of Hue orden of 16%, which as Amall ah Com do the size of the atom whith ib of the orelra of Jol?m. (3) The otemic nucleus ib a number of electrons. As edom ids electric: neutral, He total negodive change. of elechons Aurmounding Hae nuclens i4 equal do teted postive change on tht nucleus, (4) These electons revelve around the nucleus in Various ciyeulem orbits. The Cexcripetod foree required by electron fer revolution 4s provided by tre electrostatic force of attraction between eaechonsA ond the nucleus. Enevay of the electvon in orbit - Let Fe > Centyipetal force require] 40 Keep a ie ee 3 elector in orbit fe = electwstoctic force of athaction behveen the seuolving. elechon and the nucleus then for a Aynamically Stoble orbit In @ hgclogen atom (t=) - Fe = Fe mv> __e-e€ = 2. % ¥ ATE: ¥™ mvs ATG KE. of the electron in the orbit = Aemyv> Hence. Ke = 22 Ber PotenHol energy of elector in orbit — us £680 - -er 4x 4Il@.¥ Tote enkgy of elechon in hylragen atom — E= KE +tU ec «_e% _ e® anéy Arter or E+ “2 aileor Hence te total energy 0 electron In orbit of hayctro atom tA noe eae eae. elechon ts bound do the nucleus Ce the electon +a not free to heave the erbit around the nucleus, Limitation of Rutherford Atom Model - (1D Accoveling to the classicod EM Hwory, the revolving alechons, must Yoollotr e im Fhe. form 7 of Em Waves. As vewolving elechon Loses Continuously 9 It must — wo inwards and fin habs the nucleus, aoe 4A Atoble,; we. cannot expect the odoms to Collapse. Gi) As He revolving elechons spiral fnwords, Heir an velocihes “amd hence their frequencies af vexolution would chenge Continuously - Therefore, preauency of EM WaveA emtted must ConFinuowsly -Thirefore , erfomrs should emit cortinupus spectrum but wwe observe only a dine Spectrum. Bohy Model of Hyelvogen Atom- Thine ane three basic postulates of thia model— (1) Ev. odom consist of A cenhal core Cattecl nucleus, in which entire positive co and almost ernrtive sass of the adem ane concentrated, A suiteble. number of -elechrons revolve anound the nucleus in clive orbits. The cerbipetal fore required fos revolution it provided by the elechostatic forte of attraction between the elechm and the nucleus. Centripeal fore = Electustatic force of attraction mv se (zee) zh ie aie, re a ile ve mv> . Kze x= Hameo a ee zeal (2) A ceoroling ao Bohr, elect can revolve. ay im certain “chsereds non radiating ovbits , Cotte Stedion orbits, for Which btal a of the Awolvin eleefron i4 an integral multi ple_ of Wan, Whae” h da plank's Canstart. Thus the arppadan. momentum of 4 orbiting electron 44 Quantised: mvr = mh Z Li a1 me 12,3... Here YL vA Collect principle Puantum number. * The ehecton , while venslving in such orbits, Shall not tose. ering Ce: ads energy. wowel Sta Covustant- (2) The emission / absorbtion of ye occlutes only when oy elechon jumps fsom one of ts specified non - yack ovbit 40 another. The cli oe in the total enon of elechon in the two orbits js absorbec! cohen" the electon jumps from an inner #0 On outer. orbit and emitied whin electon jumps frome outer. Jo the inner ovbit- Lohere WP is the prequancy of macketion emitted on Jumping from outer, doo finer orbit of entrge E, ond &; respect vely- Rackius of Gehr's Stationary ovbits— We Know Heb fox Atation wu orbjts - > vw =_4h_ 2Tr mr mvy = mh 27 sr putting. the valuc of v in ay = Kzet 7 > m eke = Kze2 2 al im re =a vs nth for hydrogen atom 4it'mke we om It shows trot — ran* Hence the yackus ef stedion oAbits ohe in the vatio 17:2:28: and so om ve Liui9)... Cleandy tae stocbionanay orbits are not enuoally Spaced.Velocity of electron in Gohr's Stationary Orbit - As we Know thet - _mv* = Kze> Y Fo or y = kzer — WW) mye and also y 2_nh = te aiimVv by equadlion (1) and (2) we get — Kte> =. onth or Vs 2 keer mye 2irmv La yv s_zmke> foe haychogen atom, 2=1 nh As Voto hence the orbital velodty of election in outer orbits Jy smaller as comparsol do its value In the inner orbits. Frequency of electron in Bohr's Stationary orbit - It 4s the number of yevolutions Cempleteo! per Second by the electron in 4 Stationary orbit, arelme the nucleus. It id represented by v. As Ve YW = yr(amv) ysl = 2tkte® = KzeX 2mur nh: 2itr nhy for huyatrogen The frequency of electron in subsequent stationary orbits i 4malka ab vi xt: Total Energy of electron in Gohr's Stationary Orbit Kinehc enogy of election reveling in a stationany orbit is - = dat. BEEP by my? kee™ K€ of elechon = dmy*= Kee! [' my Kee Potential energy of elechon = Potential x Change. PE. of elector = Kzex(-e) = ~Kze> ¥ ~¥ Tote energe of electron tn the orbit - E& = Ke. + PE. Es: dt Kze* _ kee = ~Kee* 2” yy ¥ ay we gu - E = — 20m K*22¢+ we by Substihting the Standercl values, we ge = — 13-6 Hence. the dota) of dechon in a stats orbyt ad ive, which muans thet the electron is bel to the Srucleus amd wa not free #o ftoave at- K when n=l then this state of doweat enngy of the atom ib Coble ground stote. Trae enrgy of this state E, = -I3-6eyv- ® Therastore, the minum enw yequived do fy electron from the und Stele of hydsegen adom 1A 13Ceu. This #3 Called jonisatien energy of hydrogen odpm. by pudding +r =_nth 4mm kze> ead ee. the* As mn ineveases, the value of negative energy clecreasea be energy ia Progressively danger or the outer. orbits. Origin of Spectral Lines - ote, most of the bydrogen atoms At rom Qhe in ground state. When a ro adem recaives eh bi corsets Auch as eléchth Collisions or heat, the ateni mi require. sufficient ty rvaise the electron to haghon aura ste be from n=l 4 n22, 3,4,.-. The atom vs said to be in an excited Stote- E2 _ —+PHOTON F> v A: From Hure excited states, the electron can fale back 4o a State of tower and emitting 4 hatin ie ee energy (= olifference Ly eneagien of the Let Ey; and €, ane the +totol energy of elechon. in the immer and outer orbit reapecchyely. bohen an electon jumps an outer do an Inner ovbit the entrgy of wadiotion emitted Ja giren by hvo= €,-€, Av = 2m?m ket Fa _ ee E: ale Al he = _ammeztet fi _ A re ne an 4a . _an*mekretz? [i _ 4. A ce nro Now x =D, whae ous te wave. number of vv Yooliation emitted fe numba of Complete wave in unit ema atmket = R (Rydberg Constant ) a (Rydberg or R = 1-097 x10" m4 Hence =. ale & ¥ + Rl ae a] Above. equation ss colled Rydberg formula for the Spectrum of hyehogen otom. * By above formule tt Ja Clean that sesh frequencies / wave numbers of radiations emrtted by the exertect hychogan atom ane net Continuord. Wi have. specific valurs clipending upon the volus n, and Nos For hydrogen mel * Frequen of rackiation diag when the atom makes transition om the aes energy State (ni) to the fou energy Atote 11) — ver S > +t-4L v nz me | ~ = RCFind the satin of enngies of photms proctuad EE hue An teaniition of om electon of huptrogen octem from its (9) Setorned peumitiect erangy Luuel 0 the fivsk Live! (b> the height pesmitherl energy. del do He pivst permitted Luvel. _Sol. (a) Enengy of Pholon reltased = E,-E, = -34 = (-13-6) =lo.2ev (b> The heighest peamittec! energy Luel to the fivat prem Lowel = Ex- E, # = 6 - (-13-6) = sé ev Rotin o A of hole ss jo2 - 3 b d b " 13-6 a L What is the ratio of racius of the orbits cS* Corvesponeling to fest excited stots and ground Stole in a hapelvogen atem 7 Sal. For first excited Staite Ae ow Sok Gromd stot occurs for n= t é ¥Y¥ an Hence Yi =fnmpP = zr th Te L Tie os Bie al TRe woclius of innermost elect oxbit of cee hydro atom ts 63010" mm, What id te ractins of orbit in the second excited stot ? Sek The radius of atom whote Principle. quantum number, Js 1, Gs given Yanh Hore. % JA Yadlius of Mmnermost’ (n=!) ovbrt . fer second exdted stats n=3 Y = (33 « 53x so! = 4-77 x10! m, Bohr!s Explanation of spectral series of Hydyogen Atom - tohon an atomic 4s excited us oy vopous af Low Pressure, by mg. an electric. Cuiunt thi at, the [vapour emits yadietions of certain Specific | wa S onky - This Kind ef spectum ud ‘Aine emission spectrum" and at consisds of 4 few bright Lines on a clark background, Detector photographic plate) Prism 5 ai “) IL High : ‘| ) x voltage :| | = ‘ Hydrogen gas discharge tube Er I r | 410nm = 434nm 468nm 656nm tohen the white Ae 44 parsed through the foe [Vapour., we observe a ‘bri ka mo cress by a fen aank Lines signi ing the misst a or “the wavelengths One ne by As - They form a “Line absovption spectum! It was ounal that missing wav i he He Same a4 the wavelength patsenctt In “the emission spectrum of the gas / vapour. Bohr ve. his theory © ro ahem about ctrof ceaee whch he bt eekly ened a Hheoretcot by veel ows Acientists. Bohr explarotion of thease spectro! series as follows :1. Lyman Series — Bohr postulatia that Lyman series is obtained tohen an electron jumps do the first orbit Cn, =1) from any outer orbrt (ras 2,3,4....) Wave numbers of spectral Lines | an Serres west Calculated J fe b - These values of ae die in the “ultra violet region” of the Spectrum. 2. Balmer Series - Accercling 4o Rehr, Balmer Series 48 obtameot when an electron jumps to the secercf orbit (,=2) from any outer. orbit (72 = 3,4,5,---- have number op these Ape ct vod dines were Cotculedeo fh = L L vo af en a] (na = 3,45-+--) TAs Sef of spectral limes Lie in the visible part of the spectrum. 3. Paschen Series — According 40 Bohr, Paschan series ~s obteimtcl when an electron Jumps Jo the Sx Orbit (n= 39 from any outer ovbit (ma = 4,5)6,--)- Bohr colctlated the wave number of spectra} Amer of Paschen series from the reletion : The Veduc Of TF Lie in the infroved region of the a. fe T 4. Brackett Series- According do Bohr > Brackett Series Ah Obtained when an clecho jumps do the 4% orbit Crys 4) pom oma outer orbit (n= $\6,7---) Wave number | W = ald ~# | (= S16 Ty.) Brackett series Wor chacoversel Im the Infrened region of the Spechum, S- Pfunel Series - According. to Bohr Pfunal Semjes Ad obtained When on electron jumps ao tHe S* orbit (n,-s) from any ovdter, orbit (n,* 6,7,8,.--) [te - de] Na? 6,7 By Pfund Serius wos cliacoverd in the infrared region of the spectum, Wave number. weEnergy Level Diagram ~ A Alagram vohich represents the doted enngies of elector in clifferent stationary orbits of an atom wa Called the energy Level cbiaguram of thet achm. In this olla, m, total ies of electron ented by the in) various Atacionany orbits ake horizontal Lines drawn aceorcling 46 Some Suitable enangiy scale Toted ery of electron In nth orbit of hyolrogen odor iA - putting n21,2,3,---- we the energies of biesies ivy Wardous steele orbits ae ee eee os Ee, = Im.éegeyv 5) 6, SIs. . -Syey 2 Eg = -!I86 J ipciev Ey, obese = -O-BseVv - -/3:6 9. ee eB: a: ce Ee = Prone ew Ey ea = cearey Clearly aS nn increasea Ex, becomes Luss negathi've undil Neo , Enso. Tre energy level Ciagram Js shown fh ‘ fer ha dleo atom." The heightst enorgy ig Seedigtels’ n= 99 ond has eneagy €= ce Thin Sa the of the atom, when the elechon is vemoyed (Y= 00) from the nucleus and the eeeton 4s Test - Or see eee eee pene REP + at Prundseries W=8 a Brackatt series at =20 -_ Paschen series. 1 -3-0)}— ' ee Balmer series —14-0! Lyman series * As n Increases energies of the excited stots Come Closer together. TQ) calculate Has wavelen cB\ im Balm series of hydvo adem , ren ” Ryelbens Constant R= 1037 x10? mt # Sel, For Galimer Aekies, wavelen 44 given by tnt a] thy, Ek lit A 2 ca for Hx Ling M2 =3, 56 thot 1 = i FO he de 1.097 Xfo [2 ae} A A= olszy xiv” A of Ha Line (nz 3) A =-—1 - = 6562 4° ISD X}ofal Photons , with @ cordinupus yange of frequencies PES ane made 4 pars tho 9 Serepll of yelper The transitions = —- Shown , incicode thee oF the spectyol absorption Lines in the Continuonds spectrum. nee nes n=y -2 = n-=2 z naa fev) ~# —& ie Ir -10 12 nek (A) Telent the. chal seajea of the ro: delete lumens, to which a. ie ee Linss Corres s. (b) Which of these Lines Cavresponds 4o the absorption of Yadiation of maximum tuavelenath P So}. So). Ca) Tse spectrum Yepresenct Lyman Sercjes because. in this Spectrum, elechon jumps Bem nal te ne2., dine Spectrum vepresert Bolmar Series because fen this spectrum , electron jumps fom n=2 40 n=3. IDvd Spechum yveprrsents aS thre electon jumps this Spectrum. Poschen Series frm n=2 to n= 4 in (b) Spectred Line OT ( Poschen Series) Grreponds o the absorption of radiation ak Maximum worelensth. GS) Te eran dwiels of an atom ane Shown cee ” fig: vohich of Haem esill reaubt Tn the 2 emission of a Photon of wavelength 275 nm? Ue) tohich transition Corresponds to emission of tadiation of maximum wavelength ? A Ow £ D -2ey -45 ey lle Sok (a) When Az 2ISnM = a7TsxIcIM ten e: hv che = Gexie24x axio* A 27S x10 Ee = a5 ev Tramition @& will reautt in cthe emission ef photon of As 275 nm, (6b) Maximum wavelength has oimimum Transition A provioles energy of 2ev, cohic 4d paimimum,. De Broglie's Explanation of Rohr's Second “postulate of Quantization The Second postulode of Behe model sa¥s thal: angular Momentum of electron orbiting aound the nucleus 44 quarttized ¢ fe. omvr=e Th éohere = 41,2,3..) 3a Lou cde Broglie expainec Hid purale. Accoveliny to cle ‘ie, the elechon inits crreuln orbit, a& proposed by” Bohr, must be Seen as a particle wave.We Know thet cohen a shin fined ot tut ends 4s plucked, a | Number of, wavelen ane. excited. But o these “waves which have nodes at the two ends from the Standing Waves ancl Survive. It means that in q string, Standing wscres form when total olistance travellec} by a wave down the Ating and back as ang. integer mutt ple. of the meget th ved with other a inter} ere with Hem selves upon reflection and r athe varush quickly. a stationary Contains ari viegral number of Hence, accorclin ng fo ole Byo Key ovbt ia that which de Broglie waves attociatzel with the reveling. electron, For an electron rewolving in nt circular orbit of YooUus ¥ , For the permissible ovbit , amr =na According +o cle : = g to ole age A ae Gohtre Vid speeol of olecton revolving In vi orbit anv = nh => mvy = th 2It Angular. Mementum omyy = n(be Hence om momentum oh electron eet nth orbit “must be an ¢ multiple of ns which Js tha Qquandum Ceneition proposcl by Bolw in second pashtate. Limitation of Bohr's Theory - (1) This trsory as icoble St St ar Oe Aike drogen , with 221. fails in Case of otms of oHun, cae dee re Zr. (2) The theovy oes not explain thy orbits o} elechons ane taken as circular, cohile ellipHeol orbits ane alao possible. (3) Bohr's Hae does not 3 a ng about Hae telodive | federisidlen of special ee + (4+) Bohr's theory clue not take into account the wave properties of electrons.Very Impertant Questions L Mork Questions- Ql. Wate the exprersion fer Bhor's radius in ygolrogen otorn Crelhi aio , 01) Q2. Stede GBhor's quantisation cenditon for olefining -stetion orbits, 3 on (Rese 208,°R36 2510, 03) GB. In the Rutherford scoctter experiment, He aatena of aes Aperaden Pi a particle 1S co. Tf c-particle is replaced by a proton, hove | much | KineHe enigy in ysorn to Ae perncle will at require’ so have tre same duatance of Closest approach cle ? Hint: Prefon CH"), a-panhcle(Hé*) Cease aeog,2000) Qu. In agen atom ik the lechmn is replaced by o~ eee sshdeh b nob ened te but hos the Sama change, how wuld Obs radius Change . CCBSE 2002, 08) &.S- The energy of the electron im the und State of Mgalrogen odom is -13-6 ev. - (a) Whot coed the negocive sign signify ? (6) How much 4s reguiresl to take an electron in Mea hn toned the ground state, to the first excited stat ? (ease 2009) 2 Mark Questions - Ql. The ground stede entrgy of byclvogen atom 4b -15.gev. The Photon emitted clini the tromaiton of electron from na2 to n=l Stati, is inciclant on the photosensitive moterioad of unknown Work function. The photoelectrons onc emitted frm modertiels with a maximum Kinetic enuagy of 8 ev. Cade ate Hye Hesheld wewelensty of the material usec, Praweh - As S6UL5 nm. Q2, Using, Bohr's postulates hychogen adem) show “Hat the dohal eneagy (Ee) of the electron In the stoction stot, Con be expressec| ak the Sum of KineHe energy (kK) and potentol enagy (U), Whine K = —2U. Hente cleduee the expression for tre sotal erurgy Tin the mn energy Auvel of- hagahogen oem. (e@SE 202, 12) Q.3.0 Using Bhor's secomcl poshtate ef quan~ tizediby, of exbrial angulor memertum show trod the Crreum ferme of the electon In Cease 2008) the nth orbital tode in hygolee, ofom is rn times the ae- brogtie wav: assouated wit ah. (6) The ekecthon In in Hae thc) excited sinti. Whe 4d tae maximum, number ef spectral Lines cohich can be ernittec| when it finally moves se the qround stoke 9 ( deh, aoa, RBse aan) Prawns - (by n=3Qu, Re unc state energy of hydro adom ds ~1e ev. Tp an slack contina! » cate from om energy Awel -o. Bs ev Fo -1Sl ev, Codcutecte the tuavelen ity of the Spectral Ling arittect. To which Series ef hyclregen spectum aloes this crewelength belong ? (case a0ooi, 12) Qs. Ina Geiger Marsden experiment calculate He Adtemn ce of Closeat approach to the nucleus of Z=Bo, When on a-particle of BMev enngy Incictent on it bebpre at comes reat and reverse its direction: How will the clatance of closest approach be. affected woken the Kinelre enrgy of the A- particle is cloubled 2 a Pmawer- Te = 2-88 X10 py ©-6. Sede the basic assumption s oh the Rutherford modef ef the atom. Explain in bef val Ais mookl con not account for the Stability of ‘an atom ? (Delhi 200 2,10) the Bohr'ls postulodes , olerive. He rerssior fox the — (a) speecl of the electron () radius of the wth orbit im hyelregen oxtora. CRGse 2007, 1°} Gee. Tae Of the electon in the qreunel Stott 6 Ja -1%6ev, Coleulode the enneay. ef He. haton thot utoutd be emitted ih the elechon wee do make a tomsHen Corcesponcling 40 the emission ek the fiat Ling of the (> Lyman series (b) Bode sens of Hye hychrogen m7 Ariwer— (a) Jozew (bd 1-9 ey (€ ©@se 2209) QT Usin m the mth ovbit, of Hae elechem QS. Re tind Steck. eninay of hyslroger ocom 4s aa “y a la) Wohot 4a the KE. of an electron in the 274 excites| stecte ? (b) Tf tHe electron jumps to the ground Stodte, the 2nd excited state, Codewlate the wovelen of the spectral Lng emitted. Prmawer f) sev (Cb) A= los0# (¢ese 2003, 08) @lo- The enna Juvals of an oom ate cs shou in Figure belovo: = oev & D -~aey -4Sev -loev le) which of pum wall wesault in the -hansition of A photon of wavelengaty zis nm ? (&) which transition Corresponds to emission of radiation of maximum wavelength ? Answer: Cer) -tramiton & CeBse Deel) 09 ) Ce) transifion 4. Su Ca) Using Peatulates ef Bhoris theory af 0 otom, show that — Co) The tains ef obits increase a4 n> Gi) The total energy of the elechor Increases O4 n* wohlire on JS the paincipal quantum number of the ohm. (b> Coden the wavelength of Ha dine in Balmer series of hychogern ahm, given thot Ryolberg Constant = mn 1097 x107 mi rnswer- (by) A = 6s63 A (case 2002, 06)