Clogs-12” NCE eee Ace: to New Syllabus. Structure of ATOM Thomson’s model of an Atom» + fhe First mocel oF atom was Proposed b e FJ Thomson tn 1898 + shee fo thie mode + tt the postive charge of the atom “Ig uniformly t distr? butecl throughout the volume of atom Gnol negatively chayged electrons are embedded fn it Uke seeds in a water melon. Jhis moclel was Calieed plum pudding model of the atom - The mutudl repulsion between tne electron are balanced by their altraction with the positively charged matter. Thus the atom asa whole fs Stable and Neutral Fofluve of Thomson's Model Thomson's model was failed 'n ex planing the o-particle Scatter’: expetment proposed oy Rutherfore and hater performed by Hans Geiger and Ernest Marsden Alpha-Tarticle Scattering &xprlment £2@) At the suggestion Of Rutherford fn 1911 Geiger and Marscen performed ac— particle tterfng €xperiment- ai ae They divected o- beam of 5:5 MeV a- particle emitted froma Br vadio active Source ata thin metol Foll made of Gold. ie The beam wot allowed to fait on a thin Fotl of gokl oF thickness 21xi6 m: Alpha particles Umilted by radioactive Source were collimated Into a Narrow btam by passing through lead bricks» he scattered Opho. Particle were yeceivec by a rotabie cktector with zinc Sulphide screen and a microteope Dichet bubion oF the Number Of Lcattered by flashes oF Scintiilations produced by Striking «- particles onthe zine sulphide screen. Alpha - Particle +> Alpha particle, also Colied alpha royr or alpha radfatton pconsist of two protons Od two neutron bound together Into o particle Ydentical to a helium-4 nucleus: They are Qinerally produced In the process ofalpha decay, but may alto be produced tq other ways: RutherForel's Observations and Recutts* I. Most OF the w- particle pass oead the gold Foil without any deflection: thie Shows that — Pani Most of the space in an atom fs empty: ‘Nucleus 2). few a- particles got Scattered deflecting at Various angles from 0 to xt: Shits Shows that atom has a Small positively chargecl core Calied ‘nucleus’ at centre of atorh, which deFlecks the positively charged a Particles at alifferent angles depending on their distance from “Centre ‘ot nucleus. BD very few x particles (1 tn 8000) suffers deflection oF Igo". Jhte shows that size oF Nucleus fs very Jmall, Nearly 1/€o00 times the Stze ot atom # Rutherfora's o- Scattering formulae Number of al vticle scattered per unit areq Neos or ‘Scattering angie 9 varies taversely as Nco)« | Sin*( 9/2) a4 1 5 Ny ba | T ° Scaticring angle 9 Gin degree © 20 40 60 6 100 120 140 100 180 Number of scattered parties detected # Impact Parometer Cb): (P¥O) . 9t Is cleFined as the. perpendicular distance of the tnital velocity vector of the @tpha particie from the Centre of the nucleus , when the particle ts Far away from the nucleus of the atom be Zecotl /2) | ke Kinette energy Teen” Saecmc YreK of the particle Z=alomic no- of nucleus 9 Seatter?ng le, Qu a Distance of clocect approach(evay At 0 certatn distance Y, from the Nucleus , the o particle stops fora moment ord then begin to retrace tts path The distance v, fs Called the al’stance of Closest approach ° Tyr azer yxek At the elfstance of Closest Gpproach whole Kinetic energy of the alpha particle {s converted fnto Potential energy»9 let; inftiod Kinetic. energy of a- particle = K = Lm —~t > electrostatic PE of X~ particle and * won [4,7 \ Nuckus Ot distance % U=49, 5 deze cuenta Wey Ye 4nd, At afstance %, KeU]) > K=2ze* 9 Unto 4 Electron Orel / Uetng Rutherford’s model of +he atom, Find total energy of electron jin Rucoten atom. Cra) Pn dectron revolving fn an orbit of “H-atom, has both kinetfe. energy ancl clectroctatic potential energy « She electrostatic force of attraction, between the Nevolving electrons and. the Nucleus provicles the Yequisite centripetal Force & to keep them én orbit- it Fes fe teem 9 fe — UD. Ung? or 4n8mv* | Relatfon between the Orbit vodfus and the electron velocity The kinetic Energy CK) anol the electrostatic potential energy Cv) at the electron tn hyclrogen aton ave ke dmvt=t x t2 2 2 Unér negative sign Indtcates thal’ the eieclroctatt force fs fn the —¥ atvectfon. Jhus total energy E ot the Ueclron In a hydrogen atom iS k=k+u 9 er — ef Bnbt 4n8Y The total energy of the electron '% negative: wt ]ante Pmpttes the Fact that the electron & bound to the Nucleus. if E were positive, an dectvon will not foltow a Closed orbit Qround the Nucleus.Limttations of Rutherford’s Atomic Model i) Abou the Stability of atoms Ace to Maxnlell’s electromagnetic wave theory eiectron should emit energy ln the form of electromagnetic wave durlag its ovbttal motion- Therefore , vactius of orbit of electron wit! cleereace gradually and ulH— — mately it will fall in the Nucleus. i): Abouk the Line Spectrum) 1 Ruther Ford atomic Medel cannot explatn atomic Une Spectrum BOHR MODEL OF THE HYDROGEN ATOM PPottulates|: This model , algo called Planetary model of the atom, tc basect on the foitowing postulates: ) Nuclear Concept +> An atom consists of a malt and masstye central core, Called Nucleus around which planetory wectvon revolve: The centripetal force vegutved for tnety rotation fe provided by the electrostatics alrvactton between the electron and the nucleus. (2 Quantum Condition s> oF alt possible cfreular orbit Are allowed by the Classical theory, the electrons are Permitted to Circulate only fn those orbit, in which the angular momentum af on electron Is an integral multiple of b- ax ie n= 1,2,3, ---. N= principal Quantum numbers. G Gatiet Bohr's quantisation Conel*tion. h= plank’s constant Wd Stattonary Orbits? While Yesoiuing fn the permfcs?bie orbits, an electron cloes not rodfate energy » Thete non- radfattng orbit are Called stationary orbit: (iv) Frequency cond’ton:> An atom can emit or absorb Yadfation tn the Form oF discrete energy Photons Only when an eectron jumps from a higher to Lower orott or from a bower to a higher orbit , respectively whee y fs Faparey of rodiation emi ttecl, Er 2 Ep are the tnugie Asoctated with stattonary orvit of principal quantum Number MW, and ng respectively C where ,>n,)BOHR’S THEORY OF HYDROGEN ATON) cra _Radltys of ai Orble > In H-atom, an electron hovtng charge -€ revolves Qyound the nucleus oF charge +e fn a Cfrcwor orbit ‘of mdius G such that necessary centripetal ‘force is provided by the electrostatic force of attraction anc nucleus re my?= 1 ee D [mvs 1 e*| —W) Y Ung, y= ume, ¥ from Bohy'e guantization_condition. mvrzenh or Ve bb |_ (i), at amy ustr tion (ii) tn eg, U7, we yo ising tguation (i!) in eq Lt) » we get man une 2, or mph’ = 1 et or| = thee Uainr® Und, Fume | where n=1,2,3,---- fe principal quantum number: ie [gan Roctlus of n'” orbtt of H-atorn Sucn atoms gen one electron Uke Hydrogen atom, put the charge of thefr nucleus ig +Zey where Z is their Atonfic number. So thal fn this Case , radius oF n‘? orbit of such atom becomes Ye thé of [v= néxo-529an mZme* Zz Speed of Electron inn Orbit of Hydrogen atom from Bohr's quantization condition: mvrz hh or ve nb using value of 1 here » we get ar me ve nh or ve te Sve et xe orlve Ke eae a (nth’ts anh€o aheep n BIN remey Where x= €> = 1 ,Callecl Fine structure constant ahct, 137 PQ) Using Bohr's atomic model , derfve the expressfon for the madfus of nih = ovblé of tne revolving electron tn a hydrogen atom. CAT toto? Solution ¢= Gnswer fn notes:Enugy of Electron fn n'® Orott Hydrogen atom fin electron revolving fn Gn orbit of H-atom, has both kfnetic energy ond eectrostatte potential energy. Kinetic energy of the electon revolving 'n @ Circular orbit of rodtus ris using equation (£2 fn te Uectrostatic pet ntiod energy of electron of charge -€ yevolvPng around the nucleus of Charge +2 th Qn orbtt of jus y fs So, total energy of electron fn oreit of radius 1 is Br Keps = ie" - 2 unegey ling ustng value of r we gee E= ae rune”, [1ev- 16 x10" 7} Totes U) -ve sign of energy of electron fncicates that the electvon and nucleus together form'a bound system + ie Ulectron fs bound to the nucleus: WG) energy of electron fo ths orbfr vartes Enversely wth negative of ri + ie [E sasey — ne tneroy Level dfaxvam ot nyatrogen Beals " Energy (@¥) quantum numbers 13.6 ev —_21und lve 4In the Qround state of Hydlrogen Gtom , {tS Bohr radius Is given as 53 xi6"'m+ She atom {s excited ‘such that the radius becomes didxid'm- Find the value of the princfpal quantum number ancl (ii) the total energy OF the atom in this excited State: (DelhP2o13C) Solution: L W) since ren net © en 5 praaianp 9 nz da 9 nes [nee % I> (3x 15" 53 =Gi) ue know that = E= 1366 = -13-6 = -3-4ev re 4 Nnwey —-THE LINE SPECTRA OF THE HYDROGEN ATOM --— TF Es ond Ef ore eege associated with the vadfus of H-alom of prfncipal quantum number n; ancl ng recpectively (n;> ng) , Hen On jumping of electron From orbit n- tony , the difference energy associated with these orbit Ig emitted as a photon of Frequency’)? “ushase energy Is given by E=E--E, of hy= —me 4 me Serce-mel a BG nH Bee CoS) or 9= metf a - 4 c= met [het ne nf. 8h » Beh deme! fi -1 ot i gear [np np one Ry= me" = +097x08 mi! BE ch? 's Glea 8yd berg's Constant- 1 = wave number. Spectral Series of Hydlrogen Atom when the electron in & H-atom jumps From Higher energy Level to Lower energy level, the difference of energies of two energy levels fs emitted as radiation of particular wavelength » Called spectral Line- Spectral Lines of different wavelengths Gre obla?ned for transition of electron between two cufferent energy levels , which Gre Found to far! fh @ number OF spectral serfer given by Wyman certs: V=1= % PL -L ] MNEs np3,4,---20 Emer RETR ies Lyman seuiea Yet th U-v region: Ci) Balmer Seriess2 D=L=R, [#4 ] nye2 nj 3,4,5,-- © a 2 ne Bolmer Sevies Let fn the Balmer yegton+ Gi) Poschen series? ete Ry [ a 1] ngs yrU,S_--20 Poschen sevies Lies IR vegion i of em. waves. (WW) Brackett Series > Lae ®[ho 4] MyrY y= S,6,-- 20 Brockett series Lies % IQ region of waves. () Pund seritsis V=1L=R [eo ] nye nyt b7,--- 0 fund Series x ewe Pfuncl series also Lies fn TR region OF em waves:Piund far infrared 16 me \ Brackett far infrared = seh Paschen Near infested mak Hable Balmer Visible region maid 400k s000h 60004 70004 Tyman Energy level dfagrom for Spectral Series of Hydrogen. Transition of Electxon W).Emtsston Spectrum $2 when an electron jumps from h’gher energy slate to Lower energy state, it emits eneigy fn the form oF Madfation whfeh produce @ spectrum’ Cotted emfssfon of spectrums UD-Absorplion Spectrum’ when an electron jumps from Lower energy state to higher enugy state, tt absorbs eneugits of the photons of cevtain Frequencies » OF the white Ught passecl through the hydrogen gas. The resulting spectrum then produced consist of bright background with some dark Unes Corresponding to the Frequencies absorbed by the Ulectron. This Pattern of dark Lines Is Caled absorption spectrums