ATOMIC STRUCTURE. Gas at low pressure (10-4 atm) Production of a shadow of the solid object by cathode rays

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1 CATHODE R AYS (Discove y of e - ) ATOMIC STRUCTURE V > 0,000 volts Gas at low pessue (0-4 atm) - Catode + Aode vaccum pump (Ivisible ays) (Catode ays) I 859, Julius plucke stated te study of coductio of electicity toug gases at low pessue i a discage tube. We a ig voltage of te ode 0, 000 volts o moe was impessed acoss te electodes, some sot of ivisible ays moved fom te ve electode to te +ve electode. Sice te ve electode is efeed to as catode, tese ays wee called catode ays. Pope ties of Catode ays () Tey tavel i staigt lies away fom catode wit vey ig velocity agig fom 0 7 to 0 9 m/sec. () A sadow of metallic object placed i te pat is cast o te wall opposite to te catode. Poductio of a sadow of te solid object by catode ays (3) Tey poduce a gee glow we stick te glass wall matte. Ligt is emitted we tey stike te zic-sulpide scee. (4) We a small pi weel 0.0is placed i tei pat, te blades of te weel ae set i motio. Tus te catode ays cosist of mateial paticles wic ave mass ad velocity. Rotatio of ligt paddle weel by catode ays (5) Tey ae deflected by te electic ad magetic fields. We te ays ae passed betwee two electically caged plates, tese ae deflected towads te positively caged plate. It sows tat catode ays cay -ve cage. Tese paticles cayig egative cage wee called egatos by Tomso.

2 Te ame egato was caged to 'electo' by Stoey Deflectio of catode ays towads positive plate of te electic field (6) Tey poduce eat eegy we tey collide wit te matte. It sows tat catode ays posses Kietic eegy wic is coveted ito eat eegy we stopped by matte. (7) Tese ays affect te potogapic plate. (8) Catode ays ca peetate te ti foil of solid mateials. (9) Catode ays ca ioize te gases toug wic tey pass. (0) Te atue of catode ays is idepedet of (a) Te atue of catode ad (b) Te gas i discage tube. MEASUREMENT OF e/m FOR ELECTRON : I 897, J.J. Tomso detemied te e/m value (cage/mass) of te electo by studyig te deflectio of catode ays i electic & magetic fields. Te value of e/m as bee foud to be coulomb/g. By pefomig a seies of expeimets, Tomso poved tat wateve gas be take i te discage tube ad wateve be te mateial of te electodes te value of e/m is always te same. Electos ae tus commo uivesal costituets of all atoms. DETERMINATION OF THE CHARGE ON AN ELECTRON : Te absolute value of te cage o a e - was measued by R.A. Milika i 909 by te Milika's oil dop expeimet. Oil dops Spay gu (atomize) Te appaatus used by im is sow i fig. A oil doplet falls toug a ole i te uppe plate. Te ai betwee te plates is te exposed to X-ays wic eject electos fom ai molecules. Some of tese e - ae captued by te oil doplet ad it acquies a egative cage. Te metal plates wee give a electic cage, ad as te electic field betwee te plates was iceased, it was possible to make some of te dops tavel upwads at te same speed as tey wee peviously fallig. X-ays Cagable plates telescope to obseve speed of oil dops

3 By measuig te speed, ad kowig tigs like te stegt of te field ad te desity of te oil, adius of oil dops, Milika was able to calculate te magitude of te cage o te oil dops. He foud tat te smallest cage to be foud o tem was appoximately C. Tis was ecogised as te cage o a e -. Te mode value is C. MASS OF THE ELECTRON : Mass of te e - ca be calculate fom te value of e/m ad te value of e 9 e. m e / m g o kg Tis is temed as te est mass of te electo i.e. mass of te electo we movig wit low speed. Te mass of a movig e - may be calculate by applyig te followig fomula. Mass of movig e - est mass of e bv / cg Wee v is te velocity of te e - ad c is te velocity of ligt. We v c mass of e - v > c mass of e - imagiay POSITIVE R AYS - (DISCOVERY OF PROTON) : Te fist expeimet tat lead to te discovey of te +ve paticle was coducted by 'Goldstei'. He used a pefoated catode i te modified catode ay tube. Poductio of Aode ays o Positive ays It was obseved tat we a ig potetial diffeece was applied b/w te electodes, ot oly catode ays wee poduced but also a ew type of ays wee poduced simultaeously fom aode movig towads catode ad passed toug te oles o caals of te catode. Tese ays wee temed caal ays sice tese passed toug te caals of te catode.tese wee also amed aode ays as tese oigiated fom aode. We te popeties of tese ays wee studied by Tomso, e obseved tat tese ays cosisted of positively caged paticles ad amed tem as positive ays. Te followig caacteistics of te positive ays we ecogised : (i) (ii) Te ays tavel i staigt lies ad cast a sadow of te object placed i tei pat. Like catode ays, tese ays also otate te weel placed i tei pat ad also ave eatig effect. Tus, te ays passess K.E. i.e. mass paticles ae peset.

4 (iii) Te ays ae deflected by electic ad magetic fields towads te egatively caged plate sowig teeby tat tese ays cay +ve cage. (iv) Te ays poduce flases of ligt o ZS scee (v) Tese ays ca pass toug ti metal foil. (vi) Tese ays ca poduce ioisatio i gases. (vii) Positive paticles i tese ays ave e/m value muc smalle ta tat of e -. Fo a small value of e/m, it is defiite tat positive paticles possess ig mass. (viii) e/m value is depedet o te atue of te gas take i te discage tube, i.e. +ve paticles ae diffeet i diffeet gases. Accuate measuemets of te cage ad te mass of te paticles i te discage tube cotaiig ydoge, te ligtest of all gases, wee made by J.J. Tomso i 906. Tese paticles wee foud to ave te e/m value as coulomb/g. Tis was te maximum value of e/m obseved fo ay +ve paticle. It was tus assumed tat te positive paticle give by te ydoge epesets a fudametal paticle of +ve cage. Tis paticle was amed poto by Rutefod i 9. Its cage was foud to be equal i magitude but opposite i sig to tat of electo. Tus cage o poto columb i.e. oe uit +ve cage Te mass of te poto, tus ca be calculated. e Mass of te poto e / m Mass of poto i amu amu N E U T R O N g kg I 90, Rutefod suggested tat i a atom, tee must be peset at least a tid type of fudametal paticles wic sould be electically eutal ad posses mass ealy equal to tat of poto. He poposed te ame fo suc fudametal paticles as euto. I 93, cadwick bombaded beyllium wit a steam of -paticles. He obseved tat peetatig adiatios wee poduced wic wee ot affected by electic & magetic fields. Tese adiatios cosisted of eutal paticles, wic wee called eutos. Te uclea eactio ca be sow as + -paticle Be-atom Cabo atom Neuto Cage + Atomic No. 4 Atomic No. 6 Cage 0 Mass 4 amu Mass 9 amu Mass amu Mass amu [ 4 He Be 6 C + 0 ] Tus a euto is a sub atomic paticle wic as a mass g appoximately amu, o ealy equal to te mass of poto o ydoge atom ad cayig o electical cage. Te e/m value of a euto is zeo.

5 ATOMIC STRUCTURE : Atom is actually made of 3 fudametal paticles :. Electo. Poto 3. Neuto F u d a m e t a l Discoveed By Cage Mass cage m ass paticle (Specific Cage) Electo J.J.Tomso coloumb kg C/g (e o ) esu g Uit amu Poto Goldstei coloumb kg (P) esu g (Ioized H amu C/g atom, H + ) + Uit Neuto James Cadwick kg ( 0 ) g amu IMPORTANT POINT :. esu electostatic uit ( cb esu) amu atomic masss uit amu g kg. Ode of Mass m e < m p < m Ode of Specific Cage e m INTRODUCTION : < e/m < e/m p mass of poto m p mass of electo 837 m e e Atom A Not Tom (Geek wod) Divisible Not divisible (Accodig to Dalto) Atom is a Geek wod ad its meaig Idivisible i.e. a ultimate paticles wic caot be fute subdivided. Jo Dalto ( ) cosideed tat " all matte was composed of small paticle called atom.

6 ACCORDING TO DALTON'S THEORY : () Atom is te smallest idivisible pat of matte wic takes pat i cemical eactio. () Atom is eite ceated o destoyed. (3) Repesetatio of atom : Z XA. Wee : A Mass umbe, Z Atomic umbe, X Symbol of atom. Mass Numbe : It is epeseted by capital A. Te sum of umbe of eutos ad potos is called te mass umbe. of te elemet. It is also kow as umbe of ucleos because euto & poto ae peset i ucleus. A umbe of potos + umbe of eutos Note : It is always a wole umbe. Atomic Numbe : It is epeseted by Z. Te umbe of potos peset i te Nucleus is called atomic umbe of a elemet. It is also kow as uclea cage. Fo eutal atom : Numbe of poto Numbe of electo Fo caged atom : Numbe of e Z (cage o atom) Z umbe of potos oly Fo Eg: 7 Cl 35 8 p 7 e 7 Two diffeet elemets ca ot ave te same Atomic Numbe Numbe of Neutos Mass umbe Atomic umbe A Z (p + ) p Metod fo Aalysis of atomic weigt eg. 6 C P + 6 Weigt of Poto Weigt of Neuto e 6 Weigt of Electo Weigt of C atom.0 a.m.u. Mass o. of C atom [P ad ] Note : Mass o. of atom is always a wole o. but atomic weigt may be i decimal. Q. If o. of potos i X is 6. te o. of e i X + will be () 4 () 6 (3) 8 (4) Noe No. of poto i X is 6 No. of electo i X + is 4

7 Q. I C atom if mass of e is doubled ad mass of poto is alved, te calculate te pecetage cage i mass o. of C. 6 C P + 3 e Q. e P A 3 6 A 9 % cage % Assumig tat atomic weigt of C is 50 uit fom atomic table, te accodig to tis assumptio, te weigt of O 6 will be :- amu 50 amu 50 6 amu Uit Atomic Weigt : Te atomic weigt of a elemet is te aveage of weigts of all te isotopes of tat elemet. A elemet ave tee isotopes y, y ad y 3 ad tei isotopic weigts ae w, w, w 3 ad tei pecetage/possibility/pobability/atio of occuace i atue ae x, x, x 3 espectively te te aveage atomic weigt of elemet is wx w x w 3x 3 ave. wt x x x 3 Cl 35 Cl 37 Pobability atio 7 5 % 5 % Q. 35 B79 : 35 B8 : 3 : Q. A elemet ave tee isotopes ad tei isotopic weigt ae,, 3 uit ad tei pecetage of occuace i atue is 85, 0, 5 espectively te calculate te aveage atomic weigt of elemet Aveage Atomic weigt Aveage wt

8 Q. Aveage atomic weigt of a elemet M is 5.7. If two isotopes of M, M 50, M 5 ae peset te calculate te pecetage of occuace of M 50 i atue. M 50 M 5 x + x 00% x (00 x ) wt w x x w x x 50 x 5 x 5.7 x x Q x 5( 00 x) x ( 00 x ) x x 570 x x 30 x 5 M 50 5% M 5 85% Calculate te pecetage of Deuteium i eavy wate. D O ( H ) O (Molecule weigt) As 0% Isotopes : Give by Soddy Tey ae te atoms of a give elemet wic ave te same atomic umbe (Z) but diffeet mass umbe (A) i.e. Tey ave same Nuclea cage (Z) but diffeet umbe of Neutos (A Z). Fo Eg. 7 Cl35 7 Cl e 7 e 7 p 7 p 7 Isotopes ave same cemical popety but diffeet pysical popety. e Numbe of electo Isotopes do ot ave te same value of m because mass vaies. mass (No. of electo ae same but mass vaies). Fo Eg. (Poteium Deuteium Titium) H H H 3 e e e p p p 0 e/m / / /3 H is te oly omal ydoge wic ave 0 i.e. o uetos Deuteium is also called as eavy ydoge. It epeset by D Eg. 6 C 6 C 3 6 C 4 e 6 e 6 e 6 p 6 p 6 p

9 Isobas : Give by Asto Tey ae te atoms of diffeet elemet wic ave te same mass umbe (A) but diffeet Atomic umbe (Z) i.e Tey ave diffeet umbe of Electo, Potos & Neutos But sum of umbe of eutos & Potos i.e. umbe of ucleos emais same. Fo Eg. H 3 He 3 p p e e p + 3 p + 3 Isobas do ot ave te same cemical & pysical popety Tey do ot ave te same value of e/m Fo Eg. 9 K40 0 Ca40 Isodiapes : p 9 p 0 +p 40 0 e 9 e p 40 Numbe of Nucleos same +p 40 Tey ae te atoms of diffeet elemet wic ave te same diffeece of te umbe of Neutos & potos. Fo Eg. 5 B 6 C3 p 5 p 6 6 p 7 e 5 e 6 Fo Eg. 7 N5 9 F 9 p 7 p 9 8 p 0 e 7 e 9 Isotoes/ Isoeutoic species / Isotoic : p p Tey ae te atoms of diffeet elemet wic ave te same umbe of eutos. Fo Eg.. H 3 He 4 p p e e Fo Eg.. 9 K 39 0 Ca40 e 9 e 0 p 9 p Isostes : Tey ae te molecules wic ave te same umbe of atoms & electos. Fo Eg. CO N O Atoms + Atoms Electos Electos e e

10 Fo Eg. Ca O K F Atoms Electos e 8 e Fo Eg. 3 OF HClO Atoms 3 3 Electos e e Isoelectoic Species : Tey ae te atoms, molecules o ios wic ave te same umbe of electos. Fo Eg. Cl A Electo 8 e 8 e Fo Eg. H O NH 3 e + 8 e e 0 e Fo Eg. 3 BF 3 SO e e 3 e Nuclea Isome : Nuclea isomes (isomeic uclei) ae te atoms wit te same atomic umbe ad same mass umbe but wit diffeet adioactive popeties. Example of uclea isomes is Uaium X (alf life.4 mi) ad Uaium Z (alf life 6.7 ous) Te easo fo uclea isomeism is te diffeet eegy states of te two isomeic uclei. Ote examples ae Z Z (T / 3.8 ) (T / 57 mi) B B (T / 4.4 ou) (T / 8 mi) QUESTIONS BASED ON NUCLEAR STRUCTURE If te mass of eutos is doubled & mass of electo is alved te fid out te atomic mass of 6 C ad te pecet by wic it is iceased. S t e p - 6 C e 6 p 6 6 amu 6 6 amu amu If te mass of eutos is doubled ad mass of e is alved te. amu p 6 amu 8 amu Imp. Note : mass of e is egligible, so it is ot cosideed i calculatio of atomic mass. S t e p - % Icemet Fial mass - Iitial mass 00 Iitial mass %

11 If mass of euto is doubled, mass of poto is alved ad mass of electo is doubled te fid out te cage i At. wt of 6 C. Remai same. Iceased by 5% 3. Iceased by 37.5% 4. Noe of tem S t e p - 6 C e 6 p 6 amu 6 If mass of euto is doubled, mass of poto is alved ad mass of electo is doubled,te ew atomic mass will be : amu p 3 amu 5amu S t e p - % Icemet Fial mass Iitial mass % Iitial mass THOMSON'S MODEL OF ATOM [904] Tomso was te fist to popose a detailed model of te atom. Tomso poposed tat a atom cosists of a uifom spee of positive cage i wic te electos ae peset at some places. Tis model of atom is kow as 'Plum-Puddig model'. DR AWBACKS : e - spee of +ve cage A impotat dawback of tis model is tat te mass of te atoms is cosideed to be evely spead ove tat atom. It is a static model. It does ot eflect te movemet of electo. RUTHERFORD's - SCATTERING EXPERIMENT -scatteig expeimet Ti gold foil ( cm) - Ray Most of paticles stike ee ZS scee Souce [Ra] of -ays [ He 4 ] + [doubly ioised He paticle] Slit system [lead plate] Cicula fluoescet scee Rute fod obseved tat : (i) (ii) Most of te -paticles (ealy 99.9%) wet staigt witout suffeig ay deflectio. A few of tem got deflected toug small agles.

12 (iii) A vey few -paticles (about oe i 0,000) did ot pass toug te foil at all but suffeed lage deflectios (moe ta 90 ) o eve come back i te diectio fom wic tey ave come i.e. a deflectio of 80. Followig coclusios wee daw fom te above obsevatios : () Sice most of te -paticle wet staigt toug te metal foil udeflected, it meas tat tee must be vey lage empty space witi te atom. () Sice few of te -paticles wee deflected fom tei oigial pat toug modeate agles; it was cocluded tat wole of te +ve cage is cocetated ad te space occupied by tis positive cage is vey small i te atom. Weeve -paticles come close to tis poit, tey suffe a foce of epulsio ad deviate fom tei pats. Te positively caged eavy mass wic occupies oly a small volume i a atom is called ucleus. It is supposed to be peset at te cete of te atom. (3) A vey few of te-paticles suffeed stog deflectios o eve etued o tei pat idicatig tat te ucleus is igid ad -paticles ecoil due to diect collisio wit te eavy positively caged mass. (4) Te elatio betwee umbe of deflected paticles ad deflectio agle is µ 4 si [ iceases µ deceases] wee µ deflected paticles deflectio agle As atomic umbe iceases, te umbe of potos iceases wic iceases te epulstio ad so deflectio agle iceases. APPLICATIONS OF RUTHERFORD MODEL O te basis of scatteig expeimets, Rutefod poposed te model of a atom, wic is kow as uclea atomic model. Accodig to tis model - (i) A atom cosists of a eavy positively caged ucleus wee all te potos ae peset. (ii) Te volume of te ucleus is vey small ad is oly a miute factio of te total volume of te atom. Nucleus as a adius of te ode of 0-3 cm ad te atom as a adius of te ode of 0-8 cm A N adius of te atom adius of te ucleus , A 0 5 N Tus adius (size) of te atom is 0 5 times te adius of te ucleus. Te adius of a ucleus is popotioal to te cube oot of te o. of ucleos witi it. R A /3 R R 0 A /3 cm Wee R (a costat) ad, A mass umbe (p + ) R adius of te ucleus. R A /3 cm

13 (iii) (iv) Tee is a empty space aoud te ucleus called exta uclea pat. I tis pat electos ae peset. Te o. of electos i a atom is always equal to o. of potos peset i te ucleus. As te uclea pat of atom is esposible fo te mass of te atom, te exta uclea pat is esposible fo its volume. Te volume of te atom is about 0 5 times te volume of te ucleus. vol. of te atom vol. of te ucleus F HG I K J e 3 A 8 F I N HG K J e0 j 3 Electos evolve oud te ucleus i closed obits wit ig speeds. Tis model was simila to te sola system, te ucleus epesetig te su ad evolvig electos as plaets. Dawbacks of Rute fod model : Nucleus () Tis teoy could ot explai te stability of a atom. Accodig to Ma xwell electo lose s it's eegy cot iuously i te fom of + electomagetic adiatios. As a esult of tis, te e - sould loss eegy at evey tu ad move close ad close to te ucleus followig a spial pat. Te ultimate esult will be tat it will fall ito e - te ucleus, teeby makig te atom ustable. () If te electos loss eegy cotiuously, te obseved spectum sould be cotiuous but te actual obseved spectum cosists of well defied lies of defiite fequecies (discotiuous). Hece, te loss of eegy by electo is ot cotiuous i a atom. Electomagetic waves (EM waves) o Radiat Eegy/Electomagetic adiatio : j Ex : It is te eegy tasmitted fom oe body to aote i te fom of waves ad tese waves tavel i te space wit te same speed as ligt ( m/s) ad tese waves ae kow as Electomagetic waves o adiat eegy. Te adiat Eegy do ot eed ay medium fo popogatio. Radio waves, mico waves, Ifa ed ays, visible ays, ultaviolet ays, x ays, gama ays ad cosmic ays. I Å Cosmic ay's ays x ays Ulta violet Visible Ifa ed Mico wave Radio waves V I B G Y O R Violet Idigo Blue Gee Yellow Oage Red (I A )

14 A wave is caacteized by followig six caactestics. Te uppe most poit of te wave is called cest ad te lowe most poit is called toug. Some of te tems employed i dealig wit te waves ae descibed below.. Wavelegt (Lambda) : It is defied as te distace betwee two eaest cest o eaest toug. It is measued i tems of a A (Agstom), pm (Picomete), m (aomete), cm(cet imete), m (mete). Fequecy () (u) Å 0 0 m, Pm 0 m, m 0 9 m, cm 0 m Fequecy of a wave is defied as te umbe of waves wic pass toug a poit i sec. It is measued i tems of Hetz (Hz ), sec, o cycle pe secod (cps) Hetz sec cps. 3. Time peiod (T) : Time take by a wave to pass toug oe poit. T sec. Cest a a Toug Cest Toug Diectio of popogatio 4. Velocity (c) Velocity of a wave is defied as distace coveed by a wave i sec. C C/ Sice C is costats / i.e. fequecy is ivesely popotioal to 5. Wave umbe ( ) ( u ba) It is te ecipocal of te wave legt tat is umbe of waves peset i cm m 00 cm 00 cm m (cm 00 m - ) It is measued i tems of cm, m etc, 6. Amplitude (a) Te amplitude of a wave is defied as te eigt of cust o dept of toug. C C QUESTIONS BASED ON EM WAVES Te vivid Bati statio of All Idia Radio boadcast o a fequecy of 368 Kilo Hetz. Calculate te wave legt of te Electomagetic waves emited by te tasmitte. As we kow velocity of ligt (C) C m/sec. Give (fequecy) 368 khz

15 Hz sec C m sec sec m Calculate i cm ad of yellow adiatios ave wavelegt of 5800 Å As we kow Å cm { Å 0 8 cm} cm 74.4 cm c cm sec cm sec - A paticula adiostatio boadcast at a fequecy of 0 Kilo Hetz aote adio statio boadcast at a fequecy of 98.7 mega Hetz. Wat ae te wave legt of adiatios fom eac statio. Statio I st C 3 0 m sec 0 0 sec Statio II d m C 3 0 m sec sec m How log would it take a adio wave of fequecy sec to tavel fom mas to te eat, a distace of km? Distace to be tavelled fom mas to eat km m Velocity of EM waves m/sec Time Dis ta ce Velocity m 3 0 m / sec sec. Wat will be te fequecy of poto of wavelegt 5 Å tavelig i vacuum? Velocity of ligt i vacuum m sec Wavelegt mete Fequecy Velocity 8 Wavelegt 3 0 mete / sec mete sec sec

16 PLANCK'S QUANTUM THEORY Accodig to plack's quatum teo y :. Te adiat eegy emitted o absobed by a body ot cotiuously but discotiuously i te fom of small discete packets of eegy ad tese packets ae called quatum.. I case of ligt, te smallest packet of eegy is called as 'poto' but i geeal case te smallest packet of eegy called as quatum. 3. Te eegy of eac quatum is diectly popotioal to fequecy of te adiatio i.e. E E o E c Popotioality costat o Plak's costat () kj sec. o J sec (eg 0 7 J) o eg sec. c 4. Total amout of eegy tasmitted fom oe body to aote will be some itegal multiple of eegy of a quatum. E Wee is a itege ad umbe of quatum c E c Calculate te eegy of a poto of sodium ligt of wave legt m i Joules m c m sec E o E c c { } Jules 3 0 m sec E m Joules Joules. Calculate te fequecy & eegy of a poto of wave legt 4000 Å (a) Calculatio of fequecy : 4000 Å m C m / sec m (b) Calculatio of eegy : sec sec E Joule sec Joule

17 Calculate te ad fequecy of a poto avig a eegy of electo volt ev J ev J E (a) Calculatio of wavelegt () : c E o (b) Calculatio of fequecy () : c Wic as a ige eegy? (a) (b) c E Js 3 0 m sec J m 3 0 m sec m sec sec A poto of violet ligt wit wave legt 4000 Å o (a) Violet ligt : A poto of ed ligt wit wave legt 7000 Å E violet c J sec 3 0 m sec m Joule (b) Red ligt : E ed c J sec 3 0 m sec m Joule So, E violet > E ed How may potos of ligts avig a wave legt of 5000 Å ae ecessay to povide Joule of eegy. E c E c 0 Joule m Joule sec 3 0 m sec potos

18 Calculate te eegy associated wit te poto passig toug vacuum wit wavelegt 9900 Å. Fo vacuum, velocity of poto m/sec Joule sec mete E c J. sec 3 0 m sec m Joule BOHR'S ATOMIC MODEL Some Impo ta t fomulae : kq q Coulombic foce Cetifugal foce mv Agula mometum mv It is a quatum mecaical model. Tis model was based o quatum teoy of adiatio ad Classical law of pysics. Te impo tat postulates o wic Bo's Model is based ae te followig : st Postulate : Atoms as a ucleus wee all potos ad eutos ae peset. Te size of ucleus is vey small ad it is peset at te cete of te atom. d Postulate : Negatively caged electo ae evolvig aoud te ucleus i te same way as te plaets ae evolvig aoud te su. Te pat of electo is cicula. Te attactio foce (Coulombic o electostatic foce) betwee ucleus ad electo is equal to te cetifugal foce o electo. i.e. Attactio foce towads ucleus cetifugal foce away fom ucleus. 3 d Postulate : Electos ca evolve oly i tose obits wose agula mometum (mv) is itegal multiple of. i.e. mv Wole umbe Wee Plak's costat, Costat Agula mometum ca ave values suc as 5...but ca ot ave factioal values suc as.5,.,,.5..., 3, 4,

19 4 t Postulate : Te obits i wic electo ca evolve ae kow as statioay Obits because i tese obits eegy of electo is always costat. 5 t Postulate : Eac statioay obit is associated wit defiite amout of eegy teefoe tese obits ae also called as eegy levels ad ae umbeed as,, 3, 4, 5,... o K, L, M, N, O,... fom te ucleus outwads. 6 t Postulate Te emissio o absobtio of eegy i te fom of poto ca oly occu we electo jumps fom oe statioay state to aote & it is E E fial state E iitial state Eegy is absobed we electo jumps fom ie to oute obit ad is emitted we electo moves fom oute to ie obit. Sell 5 Sell 4 Sell 3 Sell Sell Nucleus Radii of vaious obits of ydoge atom : Coside, a electo of mass 'm' ad cage 'e' evolvig aoud a ucleus of cage Ze (wee, Z atomic umbe ad e is te cage of te poto) wit a tagetial velocity v. is te adius of te obit i wic electo is evolvig. By Coulomb's law, te electostatic foce of attactio betwee te movig electo ad ucleus is Coulombic KZe foce K 4 (wee is pemittivity of fee space) 0 K Nm C I C.G.S. uits, value of K dye cm (esu) mv Te cetifugal foce actig o te electo is Sice te electostatic foce balace te cetifugal foce, fo te stable electo obit. mv KZe...() Sell K Sell L Sell M Sell N Sell O (o) v KZe...() m Accodig to Bo's postulate of agula mometum quatizatio, we ave mv v m v adius m

20 v 4 m Equatig () ad (3)...(3) KZe m 4 m Solvig fo we get 4 mkze wee,, 3,..., Hece, oly cetai obits wose adii ae give by te above equatio ae available fo te electo. Te geate te value of, i.e., fate te eegy level fom te ucleus te geate is te adius. Te adius of te smallest obit ( ) fo ydoge atom (Z ) is me K m 0.59 Å 9 0 Radius of t obit fo a atom wit atomic umbe Z is simply witte as 0.59 Å Z CALCULATION OF ENERGY OF AN ELECTRON : Te total eegy (E) of te electo is te sum of kietic eegy ad potetial eegy. Kietic eegy of te electo ½ mv Potetial eegy columbic foce.d Total eegy / mv KZe Fom equatio () we kow tat mv KZe ½ mv KZe Substitutig tis i equatio (4) KZe.d...(4) KZe Total eegy (E) KZe KZe KZe Substitutig fo, gives us mz e 4 K E wee,, 3,... Tis expessio sows tat oly cetai eegies ae allowed to te electo. Sice tis eegy expessio cosist of so may fudametal costat, we ae givig you te followig simplified expessios. E.8 0 Z eg pe atom Z J pe atom 3.6 ( ev Kcal) ev.60 0 eg ( ev J) [E 33.6 Z Kcal/mole ( cal 4.8 J)] Z ev pe atom

21 Te eegies ae egative sice te eegy of te electo i te atom is less ta te eegy of a fee electo, i.e. te electo is at ifiite distace fom te ucleus wic is take as zeo. Te lowest eegy level of te atom coespods to, ad as te quatum umbe iceases, E becomes less egative. We, E 0, wic coespods to a ioized atom, i.e. te electo ad ucleus ae ifiitely sepaated. H H + + e (ioizatio) Calculatio of velocity : We kow tat mv ; v m By substitutig fo we ae gettig KZe v wee exceptig ad Z all ae costats v Z cm/sec. QUESTIONS BASED ON BOHR'S MODEL Calculate te adius of st, d,3 d,4 t Bo's Obit of ydoge. Radius of Bo's obit 0.59 Z (a) Radius of st obit : Å (b) Radius of d obit : 0.59 (c) Radius of 3 d obit : 0.59 (d) Radius of 4 t obit : Å Å Å Calculate te adius atio of 3 d & 5 t obit of He Z Å At. Numbe of He (5)

22 Teefoe : 5 9 : 5 5 Calculate te adius atio of d obit of ydoge ad 3 d obit of Li + Atomic umbe of H Atomic umbe of Li 3 d obit adius of ydoge ( ) H d obit adius of Li + ( 3 )Li H 4 3 Li 3 3 H : 3 Li 4 : Te atio of te adius of two Bo's obit of Li + is :9. wat Would be tei omeclatue.. K & L. L & M 3. K & M 4. K & N x 0.59 x 3 y 9 y x y 9 x 3 K Sell M Sell y Calculate te adius of d excited state of Li +. d excited state, meas e is peset i 3 d sell so, Å.587 Å Calculate te adius atio of d excited state of H & st excited state of Li +. d excited state, meas e is peset i 3 d sell of ydoge st excited state, meas e exist i d sell of Li H Li d adius of excited state of ydoge st + adius of excited state of Li 3 H 7 4 Li

23 Calculate te eegy of Li + atom fo d excited state. Z E 3.6 Z 3 ad e exist i d excited state, meas e peset i 3 d sell i.e. 3 3 E ev/atom Calculate te atio of eegies of He + fo St & d excited state. (He + ) st Excited state : (He + ) d Excited state i.e. (He + ) d sell : (He + )3 d sell : 3.6 : : : 4 3 If te P.E. of a electo is 6.8 ev i ydoge atom te fid out K.E., E of obit wee electo exist & adius of obit.. P.E. K.E. 6.8 K.E. 6.8 K.E. K.E. 3.4 ev. E. KE. 3.4 ev 3. Obit d E 3.6 Z i.e Z Å 0.59 Å Å.6 Å Te ioizatio eegy fo te ydoge atom is 3.6 ev te calculate te equied eegy i ev to excite it fom te goud state to st excited state. Ioizatio eegy 3.6 ev

24 i.e. st eegy state 3.6 ev Eegy of st excited state i.e. d obit 3.4 ev so, E E ev If te total eegy of a electo is.5 ev i ydoge atom te fid out K.E, P.E, obit adius ad velocity of te electo i tat obit. Give E.5 ev (i) E KE K.E E { Z }.5 ev (ii) PE ev (iii) Obit 3 d E 3.6 Z (iv) Å ev v cm/sec cm / sec Calculate te velocity of a electo placed i te 3 d obit of te Li + io. Also calculate te umbe of evolutios pe secod tat it makes aoud te ucleus. Radius of d obit x () Z cm Velocity of electo i d obit, v.8 0 Z 8 8 cm/sec cm/sec No. of evolutios/sec 8 / v v.8 0 cm / sec cm ev/sec S P E C T R U M Electomaget ic spect um o EM spect um : Te aagemet obtaied by aagig vaious types of EM waves i odes of tei iceasig fequecy o deceasig wave legt is called as EM SPECTRUM

25 Spectum : low low E loge RW MW IR Visible Rays U.V X-ay Cosmic ig ig E Sote We a adiatio is passed toug a spectoscope (Pism) fo te dispesio of te adiatio, te patte (potogap) obtaied o te scee (potogapic plate) is called as spectum of te give adiatio Classificatio of Spectum () Emissio () Absoptio (a) Cotiuous (b) lie (c) bad (a) lie (b) bad ( ) Emissios spectum : We te adiatio emitted fom icadescece souce (eg. fom te cadle, su, tubeligt, bue, bulb, o by passig electic discage toug a gas at low pessue, by eatig some substace at ig temp) is passed diectly toug te pism ad te eceived o te scee te te obtaied spectum is called as emissio spectum. ( a ) Emissio cotiuous spectum o cotiuous spectum : We a aow beam of wite ligt is passed toug a pism, it is dispesed ito 7 colous fom violet to Red. Scee U V egio V Naow beam of wite ligt I B G Y Visible egio O R Ifaed egio ( b ) Emissio lie spectum : We a atomic gas is aised to icadescece souce o subjected to electical excitatio, it fist absobs eegy & te gives it out as adiatio. O examiig tese adiatio toug a spectoscope a spectum is obtaied wic ave well defied lies,eac coespodig to a defiite wave legt & tese lies ae sepaated fom eac ote by dak space. Tis type of Emissio spectum is called as Emissio lie spectum. Scee Icadescece souce Stopped afte a sot peiod Atomic gas } Slit system Lie Spectum

26 Special Note :. No two elemets will ave idetical lie spectum sice o two elemets ave idetical eegy level teefoe te lie spectum of te elemets ae descibed as fige pits diffeig fom eac ote like te fige pits of te uma beigs.. Sice lie spectum is obtaied by te emissio of eegy toug te atoms of te elemet teefoe lie spectum is also called as atomic spectum. ( c ) Emissio bad spectum : If molecula fom of te gas is used, it fist absobs eegy fo ot oly electo tasitio but fo otatioal, vibatioal ad taslatioal te emits adiatios. O examiig tese adiatios toug a spectoscope a spectum is obtaied o te scee, wic ae goup of closely packed lies called Bads, teefoe tis type of Emissio spectum is called as emissio bad spectum. Bads ae sepaated fom eac ote by dak space. Scee Icadescece souce Stopped afte a sot peiod Molecula gas Coloued Coloued Coloued Coloued } Bad Spectum Note : Sice bad spectum ae caused by molecules teefoe bad spectum ae also called as molecula spectum. ( ) Absoptio spectum We wite ligt is fist passed toug a solutio o vapous of cemical substace o gas ad te aalyzed by spectoscope, it is obseved tat some dak lies ae obtaied i otewise cotiuous spectum. Tis type of spectum is called as Absoptio spectum. Scee Coloued Icadescece souce Gas Coloued Coloued Coloued If wite ligt is passed toug atomic gas te te obtaied spectum is called as Absoptio lie spectum. If wite ligt is passed toug molecula gas te te obtaied spectum is called as Absoptio bad spectum. Hydoge lie spectum o Hydoge spectum : We a electic excitatio is applied o atomic ydoge gas at Low pessue,a bluis ligt is emitted. we a ay of tis ligt is passed toug a pism, a spectum of seveal isolated sap lie is obtaied.te wavelegt of vaious lies sow tat spectum lies lie i Visible, Ultaviolet ad Ifa ed egio. Tese lies ae gouped ito diffeet seies.

27 6 7 Q P 5 O 4 I.R. egio Backet Fa I.R. egio Humpey I. R. egio Pfud N 3 Ifa Red egio o Pasce seies M Visible egio o Balme seies Ulta violet egio o Lyma seies L K S e i e s Discoveed by egios Numbe of lies lyma lyma U.V. egio,3,4... / Balme Balme Visible egio 3,4,5... / Pasce Pasce Ifa ed (I.R.) 4,5,6... / 3 3 Backet Backet I.R. egio 5,6,7... / 4 4 Pfud Pfud I.R. egio 6,7,8... / 5 5 Humpey Humpey fa I.R. egio 7,8,9... / 6 6 QUESTIONS BASED ON SPECTRUM I a ydoge spectum if electo moves fom 7 to obit by tasitio i multi steps te fid out te total umbe of lies i te spectum. Lyma ( ) 7 6 Balme ( ) 7 5 Pasce ( 3) Backet ( 4) Pfud ( 5) 7 5 Humpey ( 6) 7 6 Total Total umbe of lies ca be calculated as follows : Total umbe of lies I a ydoge spectum if electo moves fom 6 t to d by tasitio i multi steps te fid out te umbe of lies i spectum Total umbe of lie Total umbe of lies

28 I a ydoge spectum if electo moves fom 6 t to 3 d obit by tasitio i multi steps te fid out te followig steps : (a) Total umbe of lies i spectum (b) Total umbe of lies i U.V. egio (c) Total umbe of lies i visible egio (d) Total umbe of lies i IR egio (a) Calculatio of total umbe of lies : (b) (c) (d) Calculatio of umbe lies peset i U.V. egio. e moves fom 6 t to 3 d obit i multisteps. Fo U.V. egio, e sould be comes ito st sell. So te umbe of lies i U.V. egio zeo. Calculatio of total umbe of lies i visible egio. Fo visible egio, e sould be comes ito d sell, so te umbe of lies i visible egio zeo. Calculatio of total umbe of lies i I.R. egio. I I.R. egio, Pasce, Backet ad Pfud seies ae peset. Numbe of lies i Pasce seies Numbe of lies i Backet seies Numbe of lies i Pfud seies So total umbe of lies I Balme seies of H atom/spectum, wic electoic tasitios epesets 3 d lie? I Balme seies 3 d to d lie 4 t to d lie 5 t to d 3 lie Ifiite to d Last lie o limitig lie So, As is 5 t to d lie 3 d lie I H atom if e moves, fom t obit to st obit by tasitio i multi steps, if tee ae total umbe of lies i spectum ae 0 te fid out te value of. Total umbe of lies So, ( 5) + 4 ( 5) 0 ( + 4) ( 5) 0 5 Calculate te wavelegt of st lie of Balme seies i Hydoge spectum. Fo fist lie of Balme seies, 3

29 R() 4 9 R R R Å 5 R Å Calculate te fequecy of te last lie of te lyma seies i ydoge spectum. Fo last lie of Lyma seies, RZ R R cm C C C R m sec cm cm sec cm sec Calculate wavelegt of 3 d lie of Backet seies i ydoge spectum. Fo 3 d lie of Backet seies 4, 7 RZ 4 7 R R 6 49 R R 784 Teefoe, R Å 33

30 Wat will be te sotest ad logest wavelegt of absoptio lies of ydoge gas cotaiig atoms i goud state? Give Z, R RZ Fo sotest wavelegt E sould be maximum fo tat, cm cm cm Fo lagest wavelegt E sould be miimum so, cm 5 Å A seies of lies i te spectum of atomic ydoge lies at wavelegts , 48.7, 434.7, 40.9 m. Wat is te wavelegt of ext lie i tis seies. Te give seies of lies ae i te visible egio ad tus appeas to be Balme seies Teefoe, ad? fo ext lie If cm ad may be calculated fo te last lie R Tus ext lie will be obtaied duig te jump of electo fom 7 t to d sell, i.e. R cm 397. m Te wave umbe of St lie of Balme seies of ydoge spectum is 500 cm. Te wave umbe of St lie of Balme seies of Li + spectum will be? Wave umbe of st lie of Balme seies of ydoge spectum. RZ o Z R R fo H, Z 500 cm Wave umbe of st lie of Balme seies of Li + io is. Z R {Z 3 fo Li + } cm

31 Calculate te atio of maximum of Lyma & Balme seies? E Maximum of Lyma seies lie of Lyma seies Maximum of Balme seies st lie of Balme seies st Lyma Balme L B R R 3 R 4 R R 4 5 R 36 B L 7 5 L B A cetai electoic tasitio fom a excited state to goud state of te Hydoge atom i oe o moe steps gives ise of 5 lies i te ulta violet egio of te spectum.how may lies does tis tasitio poduce i te ifa ed egio of te spectum? 5 7 (Lyma Seies) ulta violet egio : 5 Lies i.e. e is comig fom 6 t to st Obit 5 6 Ifaed egio lie (i) Pasce seies (6 3) 3 (ii) Backet (6 4) (iii) Pfud (6 5) Total Numbe of li e s ae 6 Limitatio of te Bo's model :. Bo's teoy does ot explai te spectum of multi electo atom.. Wy te Agula mometum of te evolvig electo is equal to, as ot bee explaied by Bo's teoy. 3. Bo iteelate quatum teoy of adiatio ad classical law of pysics wit out ay teoitical explaatio.tis was te biggest dawback of tis model. 4. Bo's teoy does ot explai te fie stuctue of te spectal lies. Fie stuctue of te spectal lie is obtaied we spectum is viewed by spectoscope of moe esolutio powe. 5. Bo teoy does ot explai te spilitig of spectal lies i te pesece of magetic field (Zemma's effect) o electic field (Stak's effect)

32 SOMMERFELD EXTENSION OF THE BOHR'S MODEL Accodig to sommefeld electo evolve aoud te ucleus i te Elliptical Obits. Cicula obit is a special case of elliptical obit we te legt of majo axis becomes equal to te legt of mio axis te te sape of obit will be cicula. v Mio axis e Focus Focus Majo axis. Radial compoet : If electos evolve i elliptical obit te its agula mometum sows two compoets J wee adial quatum umbe. [ ( )...0] Sell umbe. Azimutal Compoets: J Azimutal quatum umbe [,, 3, 4...] Sell umbe So total Agula mometum J Let 4 + Te costat Vaiable J J + J + + wee picipal quatum umbe Te legt of majo axis idicates by + i.e. ad legt of mio axis idicates by Te pat of electo K If 4 te,, 3, 4 Vaiable Vaiable Legt of majo axis Legt of mio axis K 4, 4, 4 3, Elliptical pat cicula pat

33 If 5 te,, 3, 4, 5 K 5, 5, 5 3, 5 4, Elliptical pat Cicula pat If Te Elliptical pat ( ) ( ) 0 Ciculas pat I t obit : Numbe of elliptical pat ( ) Numbe of cicula pat I evey atom, st obit is always cicula. THE DUAL NATURE OF MATTER (THE WAVE NATURE OF ELECTRON). I 94. a Fec pysicist, Louis De Boglie suggested tat if te atue of ligt is bot tat of a paticle ad of a wave, te tis dual beavio sould be tue fo te matte also.. Accodig to De Boglie, te wavelegt of a electo is ivesely popotioal to its mometum p. o p mv Hee Plack's costat p p mometum of electo Mometum (p) Mass (m) Velocity (c) mv m(k.e.) Fom te de-boglie equatio it follows tat wavelegt of a paticle decease wit icease i velocity of te paticle. Moeove, ligte paticles would ave loge wavelegt ta eavie paticles, povided velocity is equal. If a caged paticle Q is acceleated toug potetial diffeece V fom est te de-boglie wavelegt is mqv de-boglie cocept is moe sigificat fo micoscopic o sub-micoscopic paticles wose wavelegt ca be measued. Te cicumfeece of te t obit is equal to times te wavelegt of te electo. Wavelegt of electo is always calculated usig De-boglie calculatio. Two paticles X ad Y ae i motio. If te wavelegt associated wit paticle X is m, calculate te wavelegt associated wit paticle Y if its mometum is alf of X. Accodig to de Boglie equatio x p ad y p x y p x y p y But p y ½ p x (give) x x / p x ½ y p x B A m m

34 Calculate te de Boglie wavelegt of a ball of mass 0. kg movig wit a speed of 30 ms mv m Tis is appaet tat tis wavelegt is too small fo odiay obsevatio. Altoug te de Boglie equatio is applicable to all mateial objects but it as sigificace oly i case of micoscopic paticles. Sice, we come acoss macoscopic objects i ou eveyday life, de Boglie elatiosip as o sigificace i eveyday life. HEISENBERG UNCERTAINTY PRINCIPLE Bo's teoy cosides a electo as a mateial paticle. Its positio ad mometum ca be detemied wit accuacy. But, we a electo is cosideed i te fom of wave as suggested by de-boglie, it is ot possible to ascetai simultaeously te exact positio ad velocity of te electo moe pecisely at a give istat sice te wave is extedig tougout a egio of space. I 97, Wee Heisebeg peseted a piciple kow as Heisebeg ucetaity piciple wic states as : "It is impossible to measue simultaeously te exact positio ad exact mometum of a body as small as a electo." Te ucetaity of measuemet of positio, x, ad te ucetaity of mometum p o mv, ae elated by Heisebeg's elatiosip as : ( p mv, p mv) x. p > 4 wee is Plack's costat. x v ucetaity poduct o x. mv > 4 o x. v 4 m Fo a electo of mass m ( g), te poduct of ucetaity is quite lage. x. v > > m We x 0, v ad vice-vesa eg sec pe gam appoximately I te case of bigge paticles (avig cosideable mass), te value of ucetaity poduct is egligible. If te positio is kow quite accuately, i.e., x is vey small, v becomes lage ad vice-vesa. I tems of ucetaity i eegy E, ad ucetaity i time t, tis piciple is witte as, E. t 4 Heisebeg eplaced te cocept of defiite obits by te cocept of pobability. Wy electo caot exist iside te ucleus accodig to Heisebeg's ucetaity piciple? Diamete of te atomic ucleus is of te ode of 0 5 m Te maximum ucetaity i te positio of electo is 0 5 m. Mass of electo kg. x. p 4 x (m.v) /4

35 v 4 x.m v ms Tis value is muc ige ta te velocity of ligt ad ece ot possible. DE BROGLIE RELATIONSHIP & HEISENBERG'S UNCERTAINTY PRINCIPLE Te mass of a paticle is mg ad its velocity is cm pe secod. Wat sould be te wavelegt of tis paticle if eg secod. () cm () cm (3) cm (4) cm Give tat m mg 0 3 g c cm/sec eg sec. mc cm cm Wic of te followig sould be te wavelegt of a electo if its mass is kg ad its velocity is /0 of tat of ligt ad te value of is joule secod? () mete () mete (3).46 0 mete (4) mete Give tat m kg c of velocity of ligt 0 o c mete/secod i.e mete/secod joule secod mc o mete o.46 0 mete Wat sould be te mometum (i gam cm pe secod) of a paticle if its De Boglie wavelegt is Å ad te value of is eg secod? () () (3) (4) Give tat Å 0 8 cm eg secod o p gam cm/sec.

36 Wat sould be te mass of te sodium poto if its wavelegt is 5894Å, te velocity of ligt is mete/secod ad te value of is kg m /sec.? () () (3) (4) m m c c ( 5894Å m) 34 m o o kg Wat sould be te ucetaity i te velocity of a electo if te ucetaity i its positio is m, te mass of electo is kg ad te value of is joule/secod? () () (3) (4).36 0 Ucetaity i positio (x) m m 5 0 m Mass of electo (m) kg. v 4m x m/sec. o v v m/sec. Wat sould be te ucetaity i velocity of a paticle of kg mass if ucetaity i positio is Å ad te value of is Joule sec.? () () (3) (4) Give tat x Å 0 0 m m kg Joule sec. v 4 m x o v m/sec m/sec m/sec. Wat sould be te ucetaity i positio if ucetaity i mometum is 0 g cm/sec. ad value of is Joule sec.? () m () m (3) m (4 ) m Give tat p 0 g cm/sec. 0 7 kg m/sec Joule sec.

37 x p 4 x 4 p o x m A ball weigs 5 g moves wit a velocity of cm/sec te fid out te De Boglie associated wit it. mv eg sec cm / sec cm cm Wic of te followig as least De Boglie if tey ave same velocity.. e. p 3. CO 4. SO mv mass of SO is geate ta te mass of e, p, CO costat v Same least will be SO m If ucetaity i positio of a e is same as te x of He atom. If p of e is te fid p i He atom. x p 4 Sice x is same fo bot. teefoe p will be same by e pe 4 x Pe P x(he) PHe He 4 P e P He P He Calculate te ucetaity i te positio of a paticle we te ucetaity i mometum is (a) 0 3 g cm sec (b) Zeo. Give p 0 3 g cm sec eg sec. 3.4 Accodig to ucetaity piciple

38 So, x. p 4 x. 4 p cm (b) We te value of p 0, te value of x will be ifiity. Te ucetaity i positio ad velocity of a paticle ae 0 0 m ad ms espectively. Calculate te mass of te paticle ( Joule Sec.) Accodig to Heisebeg's ucetaity piciple, x.m v o 4 m 4 x. v kg Calculate te ucetaity i velocity of a cicket ball of mass 50 g if te ucetaity i its positio is of te ode of Å ( kg m s ). x. m v 4 v 4x.m ms QUANTUM NUMBERS : Te set of fou iteges equied to defie a electo completely i a atom ae called quatum umbes.te fist tee ave bee deived fom Scodige wave equatio. (i) Piciple quatum umbe () : It descibes te size of te electo wave ad te total eegy of te electo. It as itegal values,,3,4..., etc, ad is deoted by K,L,M,N...,etc. Te maximum umbe of electos wic ca be peset i a picipal eegy sell is equal to. No eegy sell i te atoms of kow elemets possesses moe ta 3 electos. (ii) Azimutal quatum umbe () : It descibes te sape of electo cloud ad te umbe of subsells i a sell. It ca ave values fom 0 to ( ), i.e., 0 (s-subsell), (p-subsell), (iii) Magetic quatum umbe (m) : (d-subsell), 3 (f-subsell). It descibes te oietatios of te subsells. It ca ave values fom to + icludig zeo, i.e., total ( + ) values. Eac value coespods to a obital. s-subsell as oe obital, p-subsell tee obitals (p x, p y ad p z ), d-subsell five obitals (d xy, d yz, d zx, d x y, d z ) ad f-subsell as seve obitals. Te total umbe of obitals peset i a mai eegy level is ' '.

39 (iv) Spi quatum umbe (s) : It descibes te spi of te electo. It as values +/ ad /. (+) sigifies clockwise spiig ad ( ) sigifies aticlockwise spiig. RULES FOR FILLING OF ORBITALS. Aufbau Piciple : Aufbau is a Gema wod ad its meaig 'Buildig up' Aufbau piciple gives a sequece i wic vaious subsell ae filled up depedig o te elative ode of te Eegies of vaious subsell. Piciple : Te subsell wit miimum eegy is filled up fist ad we tis subsell obtaied maximum quota of electos te te ext subsell of ige eegy stats fillig. Te sequece i wic vaious subsell ae filled is te followig. s s 3s 4s 5s 6s 7s Statig poit p 3p 4p 5p 6p 7p 3d 4d 5d 6d 4f 5f. ( + ) ule : s, s, p 6, 3s, 3p 6, 4s, 3d 0, 4p 6, 5s, 4d 0, 5p 6, 6s, 4f 4, 5d 0, 6p 6, 7s, 5f 4, 6d 0, 7p 6 Accodig to it te sequece i wic vaious subsell ae filled up ca also be detemied wit te elp of ( + ) value fo a give subsell. PRINCIPLE OF ( + ) RULE : Te subsell wit lowest( + ) value is filled up fist, we two o moe subsell ave same (+) value te te subsell wit lowest value of is filled up fist. Sub Sell + s 0 s 0 p 3 () 3s () 3p 3 4 () 4s () 3d 3 5 () 4p 4 5 () 5s (3) 4d 4 6 () 5p 5 6 () 6s (3)

40 3. Pauli' s Exclusio piciple : I 95 Pauli stated tat o two electo i a atom ca ave same values of all fou quatum umbes. A obital ca accomodates maximum electos wit opposite spi. 4. Hud' s Maximum Multiplicity Rule : (Multiplicity : May of te same kid) Accodig to Hud's ule electos ae distibuted amog te obitals of subsell i suc a way as to give maximum umbe of upaied electo wit paallel spi. i.e. i a subsell paiig of electo will ot stat util ad uless all te obitals of tat subsell will get oe electo eac wit same spi. SPIN MULTIPLICITY It is give by S + wee S is te total spi. (a) (b) Fo (a), S 0 Spi multiplicity S (siglet) Fo (b), S Spi multiplicity S (tiplet) Fid out te agula mometum of a electo i (a) 4s obital (b) 3p obital (c) 4 t obital (a) 0 fo 4s obital, ece obital agula mometum 0 Agula mometum i a obital (b) fo 3p obital Agula mometum i 4 t obit Agula mometum (c) 4 Give below ae te sets of quatum umbes fo give obitals. Name tese obitals. (i) 4,, m 0 (ii) 3,, m ± (iii) 4, 0, m 0 (iv) 3,, m ± (i) 4dz (ii) 3p x o 3p y (iii) 4s (iv) 3d x y o 3d xy ELECTRONIC CONFIGUR ATION OF ELEMENTS Based o te ules, we ca easily detemie te electoic cofiguatios of most elemet. We just eed to kow te atomic umbe of a elemet, te ode i wic obitals ae to be filled ad te maximum umbe of electos i a sell, sub-sell o obital. Te cofigutio so obtaied ca be epeseted i two ways. As a illustatio, let us coside fluoie (Z 9) : F(Z 9) s, s, p x, p y, p z o s s p x p y p z Impotace of kowig te exact electoic cofiguatio of a elemet lies i te fact tat te cemical popeties of a elemet ae depedet o te beaviou ad elative aagemet of its electos.

41 Electoic cofiguatios of eavie elemets (beyod Z 56) deviate a little fom te ode metioed peviously. Tese ae listed below : L at a i des La (Z 57) : [Xe]6s 5d (ot 4f ) Ce (Z 58) : [Xe]6s 5d 4f P (Z 59) : [Xe]6s 5d 4f Actiides Ac (Z 89) : [R]7s 6d (ot 5f ) T (Z 90) : [R]7s 6d 5f Pa (Z 9) : [R]7s 6d 5f Beyod Z 03 Z 04 : [R]5f 4 6d 7s EXCEPTIONAL CONFIGUR ATIONS Z 05 : [R]5f 4 6d 3 7s Z 06 : [R]5f 4 6d 4 7s Z : [R]5f 4 6d 0 7s Stability of Half Filled ad Completely Filled Obitals Cu as 9 electos. its expected electoic cofiguatio is s,s, p 6, 3s, 3p 6, 4s, 3d 9. But a sift of oe electo fom lowe eegy 4s obital to ige eegy 3d obital will make te distibutio of electo symmetical ad ece will impat moe stability. Tus te electoic cofiguatio of Cu is s, s, p 6, 3s, p 6, 4s, d 0 Fully filled ad alf filled obital ae moe stable. We kow tat fully filled ad alf filled obital ae moe stable. Ca you wite te electoic cofiguatio of C(Z 4)? C (Z 4) s, s, p 6, 3s, 3p 6, 4s, 3d 5. Sice alf filled obital is moe stable, oe 4s electo is sifted to 3d obital. A compoud of vaadium as a magetic momet of.73 BM wok out te electoic cofiguatio of te vaadium i te compoud. Magetic momet Wee is umbe of upaied electos.73 o (.73) +, Vaadium atom must ave te upaied electo ad tus its cofiguatio is : 3 V4+ : s s p 6 3s 3p 6 3d WAVE MECHANICAL MODEL OF ATOM Sco di ge wave equat io : Geeal wave equatio y A si t wee, y displacemet A amplitude t time Nodes

42 Developed by scodige, tis model is based o te paticle ad wave atue of electo is kow as WAVE MECHANICAL MODEL of atom. Te motio of electo aoud ucleus is oud motio ad may be cosideed to be aalogous to te STANDING WAVES, te waves wic ae geeated by pluckig te stetced stig. Te amplitude of te stadig wave is idepedet of time ad is a fuctio of te distace fom oe fixed ed. Te deived eq. by scodige is Scodige wave equatio 8 m (E V ) 0 x y z wee Amplitude of e wave (o wave fuctio) m mass of e E Total eegy V Potetial eegy o 8 m (E V ) 0 wee Laplacia opeato x y z 8 m + (E V) 0 8 m V E H E H 8 m V Hemiltoio opeato SCHRODINGER EQUATION IN CARTESIAN COORDINATE : Z cos y sisi x sicos Te scodi ge equat io ca be wit te i tems of ca te sia coodiates (x, y, z) o i tems of speical pola coodiates (,, ). Howeve fo most calculatios it is simple to solve te wave equatio i pola coodiates. We Scodige wave equatio i pola coodiates is solved fo ydoge atom te solutio obtaied ca be factoized ito sepaate pats, oe beig te fuctio of ad ote te fuctio of ad. (, ) R() f (, ) R() Radial fuctio f (, ) Agula fuctio x cos si cos z si R si si y