MODERN PHYSICS. Contents. Theory Exercise Exercise Exercise Exercise Answer Key

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1 MODERN PHYSICS Cotets Topic Page No. Teory 0-03 Exercise Exercise Exercise Exercise Aswer Key 6-7 Syllabus Potoelectric effect ; Bor s teory of ydroge like atoms ; Caracteristic ad cotiuous X-rays, Moseley s law ; de Broglie wavelegt of matter waves. Name : Cotact No. ARRIDE LEARNING ONLINE E-LEARNING ACADEMY A-479 idra Viar, Kota Rajasta Cotact No

2 MODERN PHYSICS. CATHODE RAYS : (a) Geerated i a discarge tube i wic a ig vaccum is maitaied. (b) Tey are electros accelerated by ig potetial differece ( 0 to 5 Kilo Volt) (c) K.E. of C.R. particle accelerated by a p.d. V is ev = (d) Ca be deflected by Electric & magetic fields.. ELECTROMAGNETIC SPECTRUM : Ordered arragemet of te big family of electro magetic waves (EMW) eiter i ascedig order of frequecies or of wave legts Speed of E.M.W. i vacuum C = m/s = l 3. PLANK'S QUANTUM THEORY : A beam of EMW is a stream of discrete packets of eergy called PHOTONS, eac poto avig a frequecy ad eergy = E =. = plak 's costat = Js. P mv =. m 4. PHOTO ELECTRIC EFFECT : Te peomeo of te emissio of electros, we metals are exposed to ligt (of a certai miimum frequecy) is called poto electric effect. Results : (i) Ca be explaied oly o te basis of te quatum teory (cocept of poto). (ii) Electros are emitted if te icidet ligt as frequecy ³ 0 (tresold frequecy) emissio of electros is idepedet of itesity. Te wave legt correspodig to 0 is called tresold wave legt l 0. (iii) 0 is differet for differet metals. (iv) Number of electros emitted per secod depeds o te itesity of te icidet ligt. (v) EINSTEINS PHOTO ELECTRIC EQUATION : Poto eergy = K. E. of electro + work fuctio. = mv +f f = Work fuctio = eergy eeded by te electro i freeig itself from te atoms of te metal. f = 0 (vi) STOPPING POTENTIAL OR CUT OFF POTENTIAL : Te miimum value of te retardig potetial to prevet electro emissio is : ev cut off = (KE) max Note : Te umber of potos icidet o a surface per uit time is called poto flux. 5. WAVE NATURE OF MATTER : Beams of electros ad oter forms of matter exibit wave properties icludig iterferece ad diffractio wit a de Broglie wave legt give by l = p (wave legt of a praticle). A-479 Idra Viar, Kota Rajasta Page No. #

3 6. ATOMIC MODELS : (a) (b) THOMSON MODEL : (PLUM PUDDING MODEL) (i) Most of te mass ad all te positive carge of a atom is uiformly distributed over te full size of atom (0-0 m). (ii) Electros are studded i tis uiform distributio. (iii) Failed to explai te large agle scatterig a - particle scattered by ti foils of matter. RUTHERFORD MODEL : ( Nuclear Model) (i) Te most of te mass ad all te positive carge is cocetrated witi a size of 0-4 m iside te atom. Tis cocetratio is called te atomic ucleus. (ii) (iii) Te electro revolves aroud te ucleus uder electric iteractio betwee tem i circular orbits. A acceleratig carge radiates te ucleus spirallig iward ad fially fall ito te ucleus, wic does ot appe i a atom. Tis could ot be explaied by tis model. (c) BOHR ATOMIC MODEL : Bor adopted Ruterford model of te atom & added some arbitrary coditios. Tese coditios are kow as is postulates : (i) (ii) Te electro i a stable orbit does ot radiate eergy. i.e. mv kze = r r A stable orbit is tat i wic te agular mometum of te electro about ucleus is a itegral () multiple of. i.e. mvr = ; =,, 3,...( ¹ 0). p p (iii) Te electro ca absorb or radiate eergy oly if te electro jumps from a lower to a iger orbit or falls from a iger to a lower orbit. (iv) Te eergy emitted or absorbed is a ligt poto of frequecy ad of eergy. E =. FOR HYDROGEN ATOM : (Z = atomic umber = ) (i) L = agular mometum i te t orbit = p. (ii) r = radius of t circular orbit = (0.59 Aº) ; (Aº = 0-0 m) ; r a ev (iii) E Eergy of te electro i te t orbit = i.e. E a. Note : Total eergy of te electro i a atom is egative, idicatig tat it is boud. Bidig Eergy (BE) = - E = 3. 6 ev. (iv) E - E = Eergy emitted we a electro jumps from t orbit to t orbit ( > ). DE = (3.6 ev) é ê êë - ù ú úû. DE = ; = frequecy of spectral lie emitted. é = wave o. [ o. of waves i uit legt (m)] = R ê - l ëê ú Were R = Rydberg's costat, for ydroge = m -. (v) For ydroge like atom/species of atomic umber Z : r z = Bor radius Z = (0.59 Aº) Z ; E z = ( 3.6) R z = RZ Rydberg's costat for elemet of atomic o. Z. Note : If motio of te ucleus is also cosidered, te m is replaced by m. Were m = reduced mass of electro - ucleus system = mm/(m+m). I tis case E = ( 3.6 ev) Z. m m e ù ú û. Z ev A-479 Idra Viar, Kota Rajasta Page No. #

4 7. SPECTRAL SERIES : (i) Lyma Series : (Ladig orbit = ). é ù Ultraviolet regio = R ê - ú ; > êë úû (ii) Balmer Series : (Ladig orbit = ) é ù Visible regio = R ê - ú ; > ëê úû (iii) Pasca Series : (Ladig orbit = 3) é ù I te ear ifrared regio = R ê - ú ; > 3 ëê 3 úû (iv) Bracket Series : (Ladig orbit = 4) é ù I te mid ifrared regio = Rê - ú ; ëê 4 > 4 ûú (v) Pfud Series : (Ladig orbit = 5) é ù I far ifrared regio = R ê - ú ; > 5 êë 5 úû I all tese series = + is te a lie = + is te b lie = + 3 is te g lie... etc. were = Ladig orbit 8. EXCITATION POTENTIAL OF ATOM : Excitatio potetial for quatum jump from ¾ = E - E. electro carge 9. IONIZATION ENERGY : Te eergy required to remove a electro from a atom. Te eergy required to ioize ydroge atom is = 0 ( 3.6) = 3.6 ev. 0. IONIZATION POTENTIAL : Potetial differece troug wic a free electro is moved to gai ioizatio eergy =. X - RAYS : (i) Sort wavelegt (0. Aº to Aº) electromagetic radiatio. (ii) Are produced we a metal aode is bombarded by very ig eergy electros. (iii) Are ot affected by electric ad magetic field. (iv) Tey cause potoelectric emissio. Caracteristics equatio ev = m e = electro carge ; V = acceleratig potetial m = maximum frequecy of X - radiatio I -E electroic carge k a kb-caracteristic Spectrum Cotious Spectrum (v) Itesity of X - rays depeds o umber of electros ittig te target. (vi) Cut off wavelegt or miimum wavelegt, were V (i volts) is te p.d. applied to te tube l 400 V (vii) Cotiuous spectrum due to retardatio of electros. (viii) Caracteristic Spectrum due to trasitio of electro from iger to lower v = a (z - b) [ MOSELEY'S LAW ] b = for k a trasitio Note : (i) Bidig eergy = - [ Total Mecaical Eergy ] (ii) Velocity of electro i t orbit for ydroge (iii) For x - rays = R( z-b) (iv) c 37 æ ö ç - l ç è ø Series limit meas miimum wave legt of tat series. l m k b k a ; c = speed of ligt volt l A-479 Idra Viar, Kota Rajasta Page No. # 3

5 PART - I : OBJECTIVE QUESTIONS * Marked Questios are avig more ta oe correct optio. SECTION (A) : PHOTOELECTRIC EFFECT A-. If te frequecy of ligt i a potoelectric experimet is doubled te maximum kietic eergy of potoelectro (A) be doubled (B) be alved (C) become more ta double (D) become less ta double A-. We a cetimeter tick surface is illumiated wit ligt of wavelegt l, te stoppig potetial is V. We te same surface is illumiated by ligt of wavelegt l, te stoppig potetial is V/3. Te tresold wavelegt for te surface is (A) 4 l 3 (B) 4 l (C) 6 l (D) A-3.* If te wavelegt of ligt i a experimet o poto electric effect is doubled : (A) Te potoelectric emissio will ot take place. (B) Te potoemissio may or may ot take place. (C) Te stoppig potetial will icrease (D) Te stoppig potetial will decrease uder te coditio tat eergy of poto of doubled Wavelegt is more ta work fuctio of metal. 8 l 3 A-4. A-5. A-6. Potos of wavelegt 660 Å are icidet ormally o a perfectly reflectig scree. Calculate te umber of potos per secod fallig o te scree as total power of potos suc tat te exerted force is N : (A) (B) (C) (D) Noe of tese Let r ad b be respectively te umber of potos emitted by a red bulb ad a blue bulb of equal power i a give time. (A) r = b (B) r < b (C) r > b (D) data isufficiet 0 3 W of 5000 Å ligt is directed o a potoelectric cell. If te curret i te cell is 0.6 ma, te percetage of icidet potos wic produce potoelectros, is (A) 0.4% (B).04% (C) 0% (D) 0% A-7. Te stoppig potetial for te poto electros emitted from a metal surface of work fuctio.7 ev is 0.4 V. Idetify te eergy levels correspodig to te trasitios i ydroge atom wic will result i emissio of wavelegt equal to tat of icidet radiatio for te above potoelectric effect (A) = 3 to (B) = 3 to (C) = to (D) = 4 to A-8. Te frequecy ad te itesity of a beam of ligt fallig o te surface of potoelectric material are icreased by a factor of two. Treatig efficiecy of potoelectro geeratio as costat, tis will : (A) icrease te maximum eergy of te potoelectros, as well as potoelectric curret by a factor of two. (B) icrease te maximum kietic eergy of te poto electros ad would icrease te potoelectric curret by a factor of two. (C) icrease te maximum kietic eergy of te potoelectros by a factor of greater ta two ad will ave o effect o te magitude of potoelectric curret produced. (D) ot produce ay effect o te kietic eergy of te emitted electros but will icrease te potoelectric curret by a factor of two. A-479 Idra Viar, Kota Rajasta Page No. # 4

6 A-9. A-0. A poit source of ligt is used i a potoelectric effect. If te source is removed farter from te emittig metal, te stoppig potetial : (A) will icrease (B) will decrease (C) will remai costat (D) will eiter icrease or decrease. I a potoelectric experimet, te potetial differece V tat must be maitaied betwee te illumiated surface ad te collector so as just to prevet ay electro from reacig te collector is determied for differet frequecies f of te icidet illumiatio. Te grap obtaied is sow. Te maximum kietic eergy of te electros emitted at frequecy f is (A) f (B) V (f - f ) 0 (C) (f f 0 ) (D) ev (f f 0 ) A-. Cut off potetials for a metal i potoelectric effect for ligt of wavelegt l, l ad l 3 is foud to be V, V ad V 3 volts if V, V ad V 3 are i Aritmetic Progressio ad l, l ad l 3 will be: (A) Aritmetic Progressio (B) Geometric Progressio (C) Harmoic Progressio (D) Noe of tese A-. I a potoelectric experimet, electros are ejected from metals X ad Y by ligt of itesity I ad frequecy f. Te potetial differece V required to stop te electros is measured for various frequecies. If Y as a greater work fuctio ta X ; wic oe of te followig graps best illustrates te expected results? (A) (B) (C) (D) SECTION (B) : PHOTON EMISSION FROM A SOURCE,RADIATION PRESSURE AND DE-BROGLIE WAVES B-. B-. B-3. A poto of ligt eters a block of glass after travellig troug vacuum. Te eergy of te poto o eterig te glass block (A) icreases because its associated wavelegt decreases (B) Decreases because te speed of te radiatio decreases (C) Stays te same because te speed of te radiatio ad te associated wavelegt do ot cage (D) Stays te same because te frequecy of te radiatio does ot cage Te de Broglie wavelegt of a electro movig wit a velocity ms is equal to tat of a poto. Te ratio of te kietic eergy of te electro to tat of te eergy of poto is : (A) (B) 4 (C) (D) 4 A particle of mass M at rest decays ito two particles of masses m ad m, avig o zero velocities. Te ratio of te de Broglie wavelegts of te particles, l /l is : (A) m m (B) m m (C) : (D) m m B-4. B-5. I order to ave te same wavelegt for te electro (mass m e ) ad te eutro (mass m ) teir velocities sould be i te ratio (electro velocity / eutro velocity) : (A) m / m e (B) m m e (C) m e / m (D) oe A electro wit iitial kietic eergy of 00 ev is acceleratio troug a potetial differece of 50 V. Now te de-broglie wavelegt of electro becomes (A) Å (B). 5 Å (C) 3 Å (D).7 Å A-479 Idra Viar, Kota Rajasta Page No. # 5

7 SECTION (C) :BOHR S ATOMIC MODEL OF H-ATOM & H-LIKE SPECIES (PROPERTIES) C-.* Let A be te area eclosed by te t orbit i a ydroge atom. Te grap of l (A / A ) agaist I() (A) will pass troug te origi (B) will ave certai poits lyig o a straigt lie wit slope 4 (C) will be a mootoically icreasig oliear curve (D) will be a circle C-. Bor s atomic model : (A) assumes oly certai valuesof agular mometa to be possible for orbital electro of ydroge atom (B) explais lie spectra of elemets avig more taoe electgro i te outermost sell (C) assumes tat te electros ave wave properties (D) could ot explai ydroge spectra completely C-3. Te eergy gap betwee successive eergy levels i a ydroge atom : (A) decreases as icreases (B) decreases as decreases (C) icreases as icreases (D) eiter (A) or (B) C-4. C-5. A ydroge-like atoms as oe electro revolvig aroud a statioary ucleus. Te eergy required to excite te electro from te secod orbit to te tird orbit is 47. ev. Te atomic umber of te atom is : (A) 3 (B) 4 (C) 5 (D) 6 I te spectrum of ydroge atom, ratio of te logest wavelegt i Lyma series to te logest wavelegt i Balmer series is : (A) 5 7 (B) 93 (C) 4 9 (D) 3 C-6. Te electro i a ydroge atom makes a trasitio were ad are te pricipal quatum umbers of te two states. Assume te Bor model to be valid. Te time period of te electro i te iitial state is 8 times tat i te fial state. Te possible values of ad are (A) = 4, = (B) = 8, = (C) = 8, = (D) = 6, = 3 C-7.* C-8.* C-9. C-0. Te eergy, te magitude of liear mometum ad orbital radius of a electro i a ydroge atom correspodig to te quatum umber are E, P ad r, accordig to te Bor s teory of ydroge atom: (A) EPr is proportioal to / (B) P/E is proportioal to 0 (C) Er is ot costat for all orbits (D) Pr is proportioal to. A ydroge like atom of atomic umber Z is a excited state of quatum umber. It ca emit a maximum eergy poto of 04 ev. It makes a trasitio to quatum state, a poto of eergy 40.8 ev is emitted, te (A) Z = (B) Z = 4 (C) = (D) = I a ypotetical system a particle of mass m ad carge 3q is movig aroud a very eavy particle avig carge q. Assumig Bor s model to be true to tis system, te orbital velocity of mass m we it is earest to eavy particle is (A) 3q e 0 (B) 3q 4e 0 (C) 3q e 0 (D) 3q 4 I a ydroge atom, te bidig eergy of te electro i te t state is E, te te frquecy of revolutioof te electro i te t orbits is: (A) E / (B) E / (C) E / (D) E / e 0 A-479 Idra Viar, Kota Rajasta Page No. # 6

8 SECTION (D) :ELECTRONIC TRANSITION IN THE H/H-LIKE ATOM/SPECIES OF EFFECT OF MOTION OF NUCLEUS AND ATOMIC COLLISIONS D-. D-. Tree potos comig from emissio spectra of ydroge sample are picked up. Teir eergies are.ev, 0.eV ad.9ev. Tese potos must come from (A) a sigle atom (B) two atoms (C) tree atom (D) eiter two atoms or tree atoms I a ypotetical atom, if trasitio from = 4 to = 3 produces visible ligt te te possible trasitio to obtai ifrared radiatio is : (A) = 5 to = 3 (B) = 4 to = (C) = 3 to = (D) oe of tese D-3. Eergy levels A, B ad C of a certai atom correspod to icreasig values of eergy, i.e. E A < E B < E C. If l, l ad l 3 are te wavelegts of radiatios correspodig to trasitios C to B, B to A ad C to A respectively, wic of te followig relatios is correct? (A) l 3 = l + l (B) l 3 = ll l + l (C) l + l + l 3 = 0 (D) l 3 = l + l D-4. D-5. D-6.* D-7. A electro wit kietic eergy 0 ev is icidet o a ydroge atom i its groud state. Te collisio (A) must be elastic (B) may be partially elastic (C) must be completely ielastic (D) may be completely ielastic We a ydroge atom, iitially at rest emits, a poto resultig i trasitio = 5 =, its recoil speed is about : (A) 0 4 m/s (B) 0 m/s (C) 4. m/s (D) m/s A eutro collides ead o wit a statioary ydroge atom i groud state (A) If kietic eergy of te eutro is less ta 3.6eV, collisio must be elastic (B) if kietic eergy of te eutro is less ta 3.6eV, collisio may be ielastic. (C) ielastic collisio may takes place we iitial kietic eergy of eutro is greater ta 3.6eV. (D) perfectly ielastic collisio may take place. Te electro i a ydroge atom make a trasitio from a excited state to te groud state. Wic of te followig statemet is true? (A) Its kietic eergy icreases ad its potetial ad total eergies decrease (B) Its kietic eergy decreases, potetial eergy icreases ad its total eergy remais te same. (C) Its kietic ad toal eergies decrease ad its potetial eergy icreases. (D) its kietic potetial ad total eergies decreases. SECTION (E) : X-RAYS E-.* E-. E-3.* Cosider a metal used to produced some carateristic X-rays. Eergy of X-rays are give by E ad wavelegt as represeted by l. Te wic of te followig is true : (A) E(K a ) > E(K b ) > E(K g ) (B) E(M a ) > E(L a ) > E(K a ) (C) l(k a ) > l(k b ) > l(k g ) (D) l(m a ) > l(l a ) > l(k a ) Wic of te followig wavelegt will be abset from te X-ray spectrum if te X-ray tube is operated at 40,000 V? (A) 0. Å (B) 0.5 Å (C).0 Å (D).0 Å I a X-ray tube, te itesity of te emitted X-ray beam is icreased by (A) icreasig te filamet curret (B) decreasig te filamet curret (C) icreasig te target potetial (D) decreasig te target potetial A-479 Idra Viar, Kota Rajasta Page No. # 7

9 E-4. If a ig speed electro it a target : (A) eat is produced ad simultaeously cotiuous ad caracteristic X-rays are emitted (B) oly cotiuous X-ray are emitted (C) oly caracteristic X-rays are emitted ad cotious X-rays are ot emitted (D) oly eat is produced E-5. Te wavelegt of K a -lie from a elemet of atomic umber 4 is l. Te te wavelegt of K a -lie of a elemet of atomic umber is : (A) 4l (B) l/4 (C) 3.08l (D) 0.6 l E-6. Te K a X - ray emissio lie of tugste occurs at l = 0.0 m. Te eergy differece betwee K ad L levels i tis atom is about (A) 0.5 MeV (B). MeV (C) 59 kev (C) 36 ev E-7.* Regardig X ray spectrum wic of te followig statemet/s is/are true (A) Te caracteristic X ray spectrum is emitted due to excitatio of ier electros of atom (B) Wavelegt of caracteristic spectrum deped o te potetial differece across te tube. (C) Wavelegt of cotiuous spectrum is depedet o te potetial differece across tube (D) Noe of tese E-8. If te frequecies of K a, K b ad L a X-rays for a material K, a K b, L respectively, te a (A) K = a K b + L (B) a L = a K + a K b (C) K b = K + a L a (D) oe of tese PART - II : MISLLANEOUS QUESTIONS. COMPREHENSION TYPE I quatum mecaics, some quatities are discrete ad caot be cotiuous. Oe of tese quatities is te eergy. Eergy ca oly take certai values E, E, E 3, E 4..., wic are called eergy levels. Te eergy caot take ay values betwee E ad E, or E ad E 3 or E 3 ad E 4 etc. Certai trasitios from oe eergy level to aoter result i te emissio of a poto of radiatio, wereas oters ca oly take place if a poto is absorbed. Te eergy levels i a ewly discovered gas are expressed as: -Ez E = i wic E z is te groud state eergy. Take z = for simplicity, but do ot assume tat te gas is ydroge. A experimet is desiged to measure te eergy as a fuctios of te level. Te results obtaied are as follows : E (ev) Ez E =. Te ioizatio eergy of te gas must be : (A) 44 ev (B) 576 ev (C) 44 ev (D) +3.6 ev A-479 Idra Viar, Kota Rajasta Page No. # 8

10 . Wic of te followig sapes is most likely to represet te grap of E versus /? (A) (B) (C) (D) 3. A trasitio from te = state to te = 3 state results : (A) i emissio of a poto of eergy 44 ev (B) i emissio of a poto of eergy 80 ev (C) i emissio of a ultraviolet poto (D) oly accomplised if a poto is absorbed COMPREHENSION # : Assumig tat ature sould exercise symmetry, price Louis victor de broglie, i 93, ypotesised tat matter ad a dual (wave-particle) ature like radiatio. Duality of radiatio was already establised. Matter was earlier supposed to ave oly te particle beaviour. de Broglie s idea of matter also as wave did ot fid a experimetal evidece at tat time but it was soo establised from te expreimets performed by davisso ad germer ad Tomso tat electros could be diffracted. Tese experimets verified de broglie s idea tat matter ad also a wave caracter. de Broglie furter cocluded tat wavelegt of matter wave associated wit a movig object could be expressed as l = p Were P is te liear mometum of te object. Idea of duality of matter as some very improtat ad immediate applicatios. It could explai quatisatio of agular mometum ad eergy i te bor model of te atom. I fact, bor s model as may sortcomigs. It was ot immediately clear wy sould agular mometum or eergy be quatised so tat oly discrete values of tese quatities are allowed. de Brogile s cocept, as applied to te motio of electro i a atom, treated electro as matter waves bet ito a circle aroud te ucleus. It was suggested tat allowed bor s orbits arise if te electro matter waves iterfere costructively ad tat it will result i a statioary wave tat fits ito te circular orbit as sow i Fig. Also it could be sow tat quatisatio of agular mometum (mr = /p) was te a atural cosequece of suc a visualisatio of waves fittig i te orbits. Aswer te followig questios. 4. For a allowed orbit, radius will be a itergal multiple of l l (A) l (B) (C) p (D) l p 5. Eergy of te particle ca be expressed as (a = pr ; r = radius of orbit) m (A) 4 a a (B) 8m (C) 8ma m (D) 4a 6. Miimum eergy tat will be require to excite te particle from te groud state to a iger state will be 3m (A) 4 a 3 a (B) 8m 3 (C) 8ma 3m (D) 4a A-479 Idra Viar, Kota Rajasta Page No. # 9

11 . MATCH THE COLUMN 7. Usig Bor s model, matc te followig. (Were te letters ad Z ave usual meaig) (A) Due to revolvig electro, te magetic field produced (P) 5 at its cetre is proportioal to (B) Magetic momet of revolvig electro is proportioal to (Q) (C) De-Broglie wave legt of revolvig electro is proportioal to (R) Z 3 (D) Areal velocity of revolvig electro about ucleus is (S) idepedet of Z proportioal to 8. I te sow experimetal setup to study potoelectric effect, two coductig electrodes are eclosed i a evacuated glass-tube as sow. A parallel beam of moocromatic radiatio, falls o potosesitive electrode. Assume tat for eac potos icidet, a potoelectro is ejected if its eergy is greater ta work fuctio of electrode. Matc te statemets i colum I wit correspodig graps i colum II. Colum-I Colum-II (A) Potocurret versus itesity (p) of radiatio is represeted by (B) Maximum kietic eergy of ejected potoelectros versus frequecy for electrodes of differet work fuctio is represeted by (frequecy remai same) (C) Poto curret versus applied voltage for differet itesity of radiatio is represeted by (frequecy remai same) (q) (r) (D) Poto curret versus applied voltage at costat itesity of radiatio for electrodes of differet work fuctio. (frequecy remai same) (s) 3. True or False 9. (i) If a electro moves to a large orbit its total eergy decreases. (ii) Te wavelegts of ard X-rays are larger ta tose of soft X-rays. (iii) Some Frequecies of te Balmer lies of te ydroge atom lie i te ultraviolet regio. (iv) Caracteristic X-rays deped o te ature of te target from wic tey are emitted. (v) Catode rays are streams of particles travellig towards te catode. (vi) Caracteristic X-rays are emitted we te bombardig electros kock out electros from te ier sells of te target atoms ad te outer electros fall ito tese vacacies. A-479 Idra Viar, Kota Rajasta Page No. # 0

12 4. FILL IN THE BLANKS 0. (i) Te eergy of a poto of... X-ray from a Coolidge tube comes from a atomic trasitio i te target (ii) Te potocurret i a experimet o potoelectric effect icreases if te itesity of te source is... (iii) Te wavelegt of te caracteristic X - ray K a lie emitted by a ydroge like elemet is 0.3 A o. Te wavelegt of te K b lie emitted by te elemet will be. (iv) I a x-ray tube, electros accelerated troug a potetial differece of 5000 V strike a copper target. Te speed of te emitted x-rays iside te tube is m/s. (v) I te Bor model of te ydroge atom, te ratio of te kietic eergy to te total eergy of te electro i a quatum state is. PART - I : MIXED OBJECTIVE * Marked Questios are avig more ta oe correct optio. SINGLE CORRECT ANSWER TYPE. If l mi is miimum wavelegt produced i X-ray tube ad l ka is te wavelegt of k a lie. As te operatig tube voltage is icreased. (A) (l k l mi ) icreases (C) l ka icreases (B) (l k l mi ) decreases (D) l ka decreases. A atom cosists of tree eergy levels give by a groud state wit eergy E 0 = 0, te first excited state wit eergy E = K ad te secod excited state wit eergy E = K were K > 0. Te atom is iitially i te groud state. Ligt from a laser wic emits potos wit eergy.5k is sied o te atom. Wic of te followig is/are correct? (A) Te potos are absorbed, puttig oe atom i a state E ad oe atom i a state E. (B) A poto will always be absorbed, but alf te time te atom will go ito te state wit eergy K ad te oter alf ito te state wit eergy K. I tis way, eergy will be coserved o te average. (C) Te atom absorbs a poto, goes ito te first excited state wit eergy K ad emits a poto wit eergy 0.5 K to coserve eergy. (D) Te atom does ot absorb ay poto ad stays i te groud state. C 3. Te work fuctio of a certai metal is l. We a moocromatic ligt of wavelegt l < l 0 is 0 icidet suc tat te plate gais a total power P. If te efficiecy of potoelectric emissio is % ad all te emitted potoelectros are captured by a ollow coductig spere of radius R already carged to potetial V, te eglectig ay iteractio betwee plate ad te spere, expressio of potetial of te spere at time t is : (A) V + 00 lpe t 4pe 0 RC (B) V lpet 400pe 0 RC (C) V lpe t (D) 4pe 0 RC 4. I a Coolidge tube experimet, te miimum wavelegt of te cotiuous X-ray spectrum is equal to 66.3 pm, te (A) electros accelerate troug a potetial differece of.75 kv i te Coolidge tube (B) electros accelerate troug a potetial differece of 8.7 kv i te Coolidge tube (C) de-broglie wavelegt of te electros reacig te aticatode is of te order of 0mm. (D) de-broglie wavelegt of te electros reacig te aticatode is 0.0Å. A-479 Idra Viar, Kota Rajasta Page No. #

13 5. A electro is i a excited state i ydroge-like atom. It as a total eergy of 3.4 ev. If te kietic eergy of te electro is E ad its de-broglie wavelegt is l, te (A) E = 6.8 ev, l = m (B) E = 3.4 ev, l = m (C) E = 3.4 ev, l = m (D) E = 6.8 ev, l = m 6. If radiatio allow wavelegts from ultraviolet to ifrared is passed troug ydroge gas at room temperature, absorptio lies will be observed i te : (A) Lyma series (B) Balmer series (C) bot (A) ad (B) (D) eiter (A) or (B) 7. I te ydroge atom, if te referece level of potetial eergy is assumed to be zero at te groud state level. Coose te icorrect statemet. (A) Te total eergy of te sell icreases wit icrease i te value of (B) Te total eergy of te sell decrease wit icrease i te value of. (C) Te differece i total eergy of ay two sells remais te same. (D) Te total eergy at te groud state becomes 3.6 ev. 8. A electro i ydroge atom first jumps from secod excited state to first excited state ad te, from first excited state to groud state. Let te ratio of wavelegt, mometum ad eergy of potos i te two cases be x, y ad z, te select te wrog aswer/(s) : (A) z = /x (B) x = 9/4 (C) y = 5/7 (D) z = 5/7 MULTIPLE CORRECT ANSWER(S) TYPE 9. Select te correct alterative(s): We potos of eergy 4.5 ev strike te surface of a metal A, te ejected poto electros ave maximum kietic eergy T A ev ad de Broglie wave legt l A. Te maximum kietic eergy of poto electros liberated from aoter metal B by potos of eergy 4.70 ev is T B = (T A.50) ev. If te de- Brogleie wave legt of tese poto electros is l B = l A, te: (A) te work fuctio of A is.5 ev (B) te work fuctio of B is 4.0 ev (C) T A =.00 ev (D) T B =.75 ev 0. Potoelectric effect supports particle ature of ligt because (A) tere is a miimum frequecy below wic o potoelectros are emitted (B) te maximum kietic eergy of potoelectros depeds oly o te frequecy of ligt ad is idepedet of itesity. (C) eve we te metal surface is illumiated wit very small itesity te potoelectros (if ³ t ) leave te surface immediately (D) electric carge of te potoelectros is quatized. Te potetial differece applied to a X-ray tube is icreased. As a result,i te emitted radiatio. (A) te itesity icreases (B) te miimum wavelegt icreases (C) te itesity remais ucaged (D) te miimum wavelegt decreases. A ydroge-like atoms as groud state bidig eergy.4 ev. Te : (A) its atomic umber is 3 (B) a electro of 90 ev ca excite it to a iger state (C) a 80 ev electro caot excite it to a iger state (D) a electro of 8. ev ad a poto of 9.8 ev are emitted we a 00 ev electro iteracts wit it 3. X-rays (A) cause ioisatio of air we tey pass troug it (B) ca be deflected by electric ad magetic fields (C) ca be used to detect flaws i metal castigs (D) travel wit te speed of ligt A-479 Idra Viar, Kota Rajasta Page No. #

14 4. Te K sell ioisatio eergies for cobalt, copper ad molybdeum are 7.8, 9.0 ad 0. KeV respectively. If a X-ray tube operates at 5 kv wit ay of te above metals as targets, te : (A) caracteristic X-rays of K series will be emitted oly from cobalt (B) caracteristic X-rays of K series will be emitted oly from copper ad cobalt (C) caracteristic X-rays of K series will be emitted from cobalt, copper ad molybdeum. (D) te sortest wavelegt of cotiuous X-rays emitted is te same for te tree metals. 5. Accordig to Eistei s teory of relativity, mass ca be coverted ito eergy ad vice-versa. Te ligtest elemetary particle, take to be te electro, as a mass equivalet to 0.5 MeV of eergy, we ca te say tat : (A) te miimum amout of eergy available troug coversio of mass ito eergy is.0 MeV. (B) te least eergy of a g-ray poto ta ca be coverted ito mass is.0 MeV. (C) te miimum eergy released by coversio of mass ito eegy is 0.5 MeV. (D) Noe of tese 6. Two electros are movig wit te same speed v. Oe electro eters a regio of uiform electric field wile te oter eters a regio of uiform magetic field, te after sometime if te de Broglie wavelegts of te two are l ad l, te wic are possible: (A) l = l (B) l > l (C) l < l (D) Data isufficiet 7. A beam of ultraviolet ligt of all wavelegts passes troug ydroge gas at room temperature, i te x-directio. Assume tat all potos emitted due to electro trasitio iside te gas emerge i te y-directio. Let A ad B deote te ligts emergig from te gas i te x ad y directios respectively. (A) Some of te icidet wavelegts will be abset i A. (B) Oly tose wavelegts will be preset i B wic are abset i A. (C) B may cotai some visible ligt. (D) B may cotai some ifrared ligt. 8. A eutro collides ead-o wit a statioary ydroge atom i groud state. Wic of te followig statemets are correct (Assume tat te ydroge atom ad eutro as same mass) : (A) If kietic eergy of te eutro is less ta 0.4 ev collisio must be elastic. (B) If kietic eergy of te eutro is less ta 0.4 ev collisio may be ielastic. (C) Ielastic collisio may be take place oly we iitial kietic eergy of eutro is greater ta 0.4 ev. (D) Perfectly ielastic collisio ca ot take place. 9. A free ydroge atom i groud state is at rest. A eutro of kietic eergy K collides wit te ydroge atom. After collisio ydroge atom emits two potos i successio oe of wic as eergy.55 ev. (Assume tat te ydroge atom ad eutro as same mass) (A) miimum value of K is 5.5 ev. (B) miimum value of K is.75 ev (C) te oter poto as eergy 0. ev (D) te upper eergy level is of excitatio eergy.75 ev. PART - II : SUBJECTIVE QUESTIONS. A ligt beam of wavelegt 400 m is icidet o a metal plate of work fuctio. ev. A particular electro absorbs a poto ad makes some collisios before comig out of te metal. Assumig tat 0% of te istataeous eergy is lost to te metal i eac collisio.fid te miimum umber of collisios te electro ca suffer before it becomes uable to come out of metal. (use c = 400 ev Å). Cosider Bor's teory for ydroge atom. Te magitude of agular mometum, orbit radius ad frequecy of te electro i t eergy state i a ydroge atom are l, r & f respectively. Fid out te value of ' x ', if (frl) is directly proportioal to x. 3. A sample of ydroge atom gas cotais 00 atoms. All te atoms are excited to te same t excited 4800 state. Te total eergy released by all te atoms is Rc (were Rc = 3.6 ev), as tey come to 49 te groud state troug various types of trasitios ad maximum total umber of potos tat ca be emitted by tis sample are 00m. Fid ad m A-479 Idra Viar, Kota Rajasta Page No. # 3

15 4. Cosider a system i wic te electros do ot ave spi ad a spi quatum umber does ot exist. How may electros ca tere be i te state wit pricipal quatum umber = 3? 5. A ydroge atom emits radiatio of wavelegt 0.5 m. Wat are te values of te two levels ivolved? 6. A beam of 5.0 m wavelegt X-rays is icidet o a gas of uexcited ydroge atoms. It expels te atomic potoelectros from te ydroge atoms.teir speed is x m/s te fid value of x. 7. Hydroge atom i its groud state is excited by meas of moocromatic radiatio of wavelegt 975Å. How may differet lies are possible i te resultig spectrum? You may assume te ioizatio eergy for ydroge atom as 3.6 ev. 8. To stop te flow of potoelectros produced by electromagetic radiatio icidet o a certai metal, a egative potetial of 300 volts is required. If te potoelectric tresold of te metal is 500Å, Te frequecy of te icidet radiatio is = 7.45 x 0 4x cycles/s te fid value of x. 9. A moocromatic beam of ligt ( l = 4900 A ) icidet ormally upo a surface produces a pressure of 5 x 0 7 N/m o it. Assumig tat 5% of te ligt icidet is reflected ad te rest absorbed. Te umber of potos fallig per secod o a uit area of ti surface is.93 x 0 4.te fid value of. 0. A gas of ydroge like atoms ca absorb radiatios of 68 ev. Cosequetly, te atoms emit radiatios of oly tree differet wavelegts. All te wavelegts are equal or greater ta tat of te absorbed poto. (A) Determie te iitial state of te gas atoms. (B) Idetify te gas atoms.. Te magetic field at a poit associated wit a ligt wave is B = 0 6 Tesla si [( s )t] si [( s )t]. If tis ligt falls o a metal surface avig a work fuctio of.0 ev, wat will be te maximum kietic eergy of te potoelectros?. Oe milliwatt of ligt of wavelegt l = 4560 Å is icidet o a cesium metal surface. Calculate te electro curret liberated. Assume a quatum efficiecy of = 0.5 %. [work fuctio for cesium =.89 ev] Take c = 400 ev-å. 3. A sodium lamp of power 0 W is emittig potos of wavelegt 590 m. Assumig tat 60% of te cosumed eergy is coverted ito ligt, fid te umber of potos emitted per secod by te lamp. 4. Poto electros are liberated by ultraviolet ligt of wavelegt 3000 Å from a metallic surface for wic te potoelectric tresold wavelegt is 4000 Å. Calculate te de Broglie wavelegt of electros emitted wit maximum kietic eergy. 5. Fid te temperature at wic te average kietic eergy of te molecules of ydroge equals te bidig eergy of its electro i groud state, assumig average kietic eergy of ydroge gas molecule = 6. A moocromatic ligt source of frequecy illumiates a metallic surface ad ejects potoelectros. Te potoelectros avig maximum eergy are just able to ioize te ydroge atoms i groud state. We te wole experimet is repeated wit a icidet radiatio of frequecy æ ö ç è 6 ø 3 kt 5 te potoelectros so emitted are able to excite te ydroge atom beam wic te emits a radiatio of wavelegt of 5 Å. Fid te frequecy. 7. Cosider a gas of ydroge like ios i a excited state A. It emits potos avig wavelegt equal to te wavelegt of te first lie of te lyma series togeter wit potos of five oter wavelegts. Idetify te gas ad fid te pricipal quatum umber of te state A.. A-479 Idra Viar, Kota Rajasta Page No. # 4

16 8. From te coditio of te foregoig problem, fid ow muc (i %) te eergy of te emitted poto differs from te eergy of te correspodig trasitio i a ydroge atom. 9. At wat miimum kietic eergy must a ydroge atom move for it's ielastic eado collisio wit aoter statioary ydroge atom so tat oe of tem emits a poto? Bot atoms are supposed to be i te groud state prior to te collisio. 0. O icreasig te operatig voltage i a x-ray tube by.5 times, te sortest wavelegt decreases by 6 pm. Fid te origial value of operatig voltage.. A X-ray tube operates at 0 kv. Suppose te electro coverts 70% of its eergy ito a poto at eac collisio. Fid te lowest tree wavelegt emitted from te tube. Neglect te eergy imparted to te atom wit wic te electro collides.. Fid te wavelegt of te K a lie i copper (Z = 9 ), if te wave legt of te K a lie i iro (Z = 6) is kow to be equal to 93 pm. (Take b = ) PART-I IIT-JEE (PREVIOUS YEARS PROBLEMS) * Marked Questios are avig more ta oe correct optio.. (a) Electros wit eergy 80keV are icidet o te tugste target of a X-ray tube. K sell electros of tugste ave -7.5keV eergy. X-rays emitted by te tube cotai oly (A) a cotiuous X-ray spectrum (Bremsstralug) wit a miimum wavelegt of ~ 0.55Å. (B) a cotiuous X-ray spectrum (Bremsstralug) wit all wavelegts. (C) te caracteristic X-ray spectrum of tugste. (D) a cotiuous X-ray spectrum (Bremsstralug) wit a miimum wavelegt of ~ 0.55Å ad te caracteristic X-ray spectrum of tugste. [ JEE '000, Screeig + /35 ] (b) Imagie a atom made up of a proto ad a ypotetical particle of double te mass of te electro but avig te same carge as te electro. Apply te Bor atom model ad cosider all possible trasitios of tis ypotetical particle to te first excited level. Te logest wavelegt poto tat will be emitted as wavelegt l (give i terms of te Rydberg costat R for te ydroge atom) equal to (A) 9/(5R) (B) 36/(5R) (C) 8/(5R) (D) 4/R. (a) A ydroge - like atom of atomic umber Z is i a excited state of quatum umber. It ca emit a maximum eergy poto of 04 ev. If it makes a trasitio to quatum state, a poto of eergy 40.8 ev is emitted. Fid,, Z ad te groud state eergy (i ev) for tis atom. Also, calculate te miimum eergy (i ev) tat ca be emitted by tis atom durig de-excitatio. Groud state eergy of ydroge atom is ev. [JEE '000, Mais 6+4/00] (b) We a beam of 0.6 ev potos of itesity.0 W/m falls o a platium surface of area m ad work fuctio 5.6 ev, 0.53% of te icidet potos eject potoelectros. Fid te umber of potoelectros emitted per secod ad teir miimum ad maximum eergies (i ev). Take ev = J. 3. A ydroge - like gas (described by te Bor model) is observed to emit six wavelegt, origiatig from all possible trasitios betwee a group of levels. Tese levels ave eergies betwee a group of levels. Tese levels ave eergies betwee ev ad ev (icludig bot tese values): (a) Fid te atomic umber of te atom. [ JEE '00, Mais, 4 + /60 ] (b) Calculate te smallest wavelegt emitted i tese trasitios. [ Take c = 40 ev - m, groud state eergy of ydroge atom = ev ] A-479 Idra Viar, Kota Rajasta Page No. # 5

17 4. Te attractive potetial betwee electro ad ucleus is give by v = v 0 l r, v 0 ad r 0 are costats r 0 ad ' r ' is te radius. Te radius ' r ' of te t Bor's orbit depeds upo pricipal quatum umber ' ' as: [ JEE '003, Scr. 3/84 ] (A) r µ (B) r µ (C) r µ (D) r µ 5. If Bor's teory is applicable to 00 Fm 57, te radius of tis atom i Bor's uit is :[ JEE '003, Scr. 3/84 ] (A) 4 (B) /4 (C) 00 (D) I a potoelectric effect experimet, potos of eergy 5 ev are icidet o te potocatode of work fuctio 3 ev. For poto itesity I A = 0 5 m s, saturatio curret of 4.0 m A is obtaied. Sketc te variatio of potocurret i p agaist te aode voltage V a i te figure below for poto itesity I A (curve A) ad I B = 0 5 m s (curve B) (i JEE grap was to be draw i te aswer seet itself.) [JEE '003, Mais /60] 7. Caracteristic X-rays of frequecy Hz are emitted from a metal due to trasitio from L-to K-sell. Fid te atomic umber of te metal usig Moseley s law. Take Rydberg costat R =. 0 7 m. [JEE '003, Mais /60] 8. Te grap is sowig te potocurret wit te applied voltage of a potoelectric effect experimet. Te (A) A & B will ave same itesity ad B & C ave same frequecy (B) B & C ave same itesity ad A & B ave same frequecy (C) A & B will ave same frequecy ad B & C ave same itesity (D) A & C will ave same itesity ad B & C ave same frequecy [JEE '004, Scr.; 3/84] 9. A proto ad poto bot ave same eergy of E = 00 K ev. Te debroglie wavelegt of proto ad poto be l ad l te l /l is proportioal to - [JEE '004, Scr. 3/84] (A) E / (B) E / (C) E (D) E 0. Te potos from Balmer series i ydroge spectrum avig wavelegt betwee 450 m to 700 m are icidet o a metal surface of work fuctio ev. Fid te maximum kietic eergy of oe poto electro. [JEE 004 Mais, 4/60]. Te wavelegt of K a X-ray of a elemet avig atomic umber z = is l. Te wavelegt of K a X-ray of aoter elemet of atomic umber z is 4l. Te z is - [JEE '005, Scr, 3/84] (A) (B) 44 (C) 6 (D) 4. A poto of 0. ev eergy collides wit a ydroge atom i groud state ielastically. After few microsecods oe more poto of eergy 5 ev collides wit te same ydroge atom. Te wat ca be detected by a suitable detector. (A) oe poto of 0. ev ad a electro of eergy.4 ev (B) potos of eergy 0. ev (C) potos of eergy 3.4 ev (D) poto of 3.4 ev ad oe electro of.4 ev [JEE (Scr.) 005, 3/84] A-479 Idra Viar, Kota Rajasta Page No. # 6

18 3. Te potetial eergy of a mass m is give by te followig relatio U = E 0 for 0 x = 0 for x > If l ad l are te de-broglie wavelegts of te mass i te regio 0 x ad for x > respectively ad te total eergy be E 0, te fid te value of l? [JEE (Mais) 005, /60] l 4. Te grap betwee /l ad stoppig potetial (V) of tree metals avig work fuctios f,f ad f 3 i a experimet of poto electric effect is plotted as sow i te figure. Wic of te followig statemet(s) is/ are correct? [Here l is te wavelegt of te icidet ray]. [JEE 006, 5/84] (A) Ratio of work fuctios f : f : f 3 = : : 4. (B) Ratio of work fuctios f : f : f 3 = 4 : :. (C) taq is directly proportioal to c/e, were is Plack s costat ad c is te speed of ligt. (D) Te violet colour ligt ca eject potoelectros from metals ad If te wavelegt of te t lie of Lyma series is equal to te de-broglie wavelegt of electro i iitial orbit of a ydroge like elemet (z = ). Fid te value of. [JEE 006, 5/84] 6. Te largest wavelegt i te ultraviolet regio of te ydroge spectrum is m. Te smallest wavelegt i te ifrared regio of te ydroge spectrum (to te earest iteger) is [JEE 007, 3/8] (A) 80 m (B) 83 m (C) 88 m (D) 648 m 7. STATEMENT- [JEE 007, 3/8] If te acceleratig potetial i a X-ray tube is icreased, te wavelegts of te caracteristic X-rays do ot cage. STATEMENT- We a electro beam strikes te target i a X-ray tube, part of te kietic eergy is coverted ito X-ray eergy. (A) Statemet- is True, Statemet- is True; Statemet- is a correct explaatio for Statemet- (B) Statemet- is True, Statemet- is True; Statemet- is NOT a correct explaatio for Statemet- (C) Statemet- is True, Statemet- is False (D) Statemet- is False, Statemet- is True. 8. Electros wit de-broglie wavelegt l fall o te target i a X-ray tube. Te cut-off wavelegt of te emitted X-rays is : [JEE 007, 3/8] (A) l 0 = mcl (B) l0 = mc m c l (C) l 0 = 3 (D) l 0 = l 9. Wic oe of te followig statemets is WRONG i te cotext of X-rays geerated from a X-ray tube? [JEE 008, 4/63 ] (A) Wavelegt of caracteristic X-rays decreases we te atomic umber of te target icreases (B) Cut-off wavelegt of te cotiuous X-rays depeds o te atomic umber of te target (C) Itesity of te caracteristic X-rays depeds o te electrical power give to te X-ray tube (D) Cut-off wavelegt of te cotiuous X-rays depeds o te eergy of te electros i te X-ray tube A-479 Idra Viar, Kota Rajasta Page No. # 7

19 Paragrap : I a mixture of H He + gas (He + is sigly ioized He atom), H atoms ad He + ios are excited to teir respective first excited states. Subsequetly, H atoms trasfer teir total excitatio eergy to He + ios (by collisios). Assume tat te Bor model of atom is exactly valid. [IIT-JEE 008, /63] 0. Te quatum umber of te state fially populated i He + ios is : (A) (B) 3 (C) 4 (D) 5. Te wavelegt of ligt emitted i te visible regio by He + ios after collisios wit H atoms is (A) m (B) m (C) m (D) m. Te ratio of te kietic eergy of te = electro for te H atom to tat of He + io is : (A) 4 (B) (C) (D) Paragrap for Questio Nos. 3 to 5 [IIT-JEE 009, 3 4/60, ] We a particle is restricted to move alog x-axis betwee x = 0 ad x = a, were a is of aometer dimesio, its eergy ca take oly certai specific values. Te allowed eergies of te particle movig i suc a restricted regio, correspod to te formatio of stadig waves wit odes at its eds x = 0 ad x = a. Te wavelegt of tis stadig wave is related to te liear mometum p of te particle accordig to p te de-broglie relatio. Te eergy of te particle of mass m is related to its liear mometum as E =. m Tus, te eergy of te particle ca be deoted by a quatum umber takig values,,3,..., ( =, called te groud state) correspodig to te umber of loops i te stadig wave. Use te model described above to aswer te followig tree questios for a particle movig i te lie x = 0 to x = a. Take = J s ad e = C. 3. Te allowed eergy for te particle for a particular value of is proportioal to : (A) a (B) a 3/ (C) a (D) a 4. If te mass of te particle is m = kg ad a = 6.6 m, te eergy of te particle i its groud state is closest to : (A) 0.8 mev (B) 8 mev (C) 80 mev (D) 800 mev 5. Te speed of te particle, tat ca take discrete values, is proportioal to : (A) 3/ (B) (C) / (D) 6. Potoelectric effect experimets are performed usig tree differet metal plates p, q ad r avig work fuctios f p =.0 ev, f q =.5 ev ad f r = 3.0 ev respectively. A ligt beam cotaiig wavelegts of 550 m, 450 m ad 350 m wit equal itesities illumiates eac of te plates. Te correct I-V grap for te experimet is [Take c = 40 ev m] [JEE 009, 3/60, ] (A) (B) (C) (D) 7. A a-particle ad a proto are accelerated from rest by a potetial differece of 00V. After tis, teir l p de-broglie wavelegt are l a ad l p respectively. Te ratio, to te earest iteger, is : [JEE 00, 3/63] l a A-479 Idra Viar, Kota Rajasta Page No. # 8

20 Paragrap for questios 8 to 30 Te key feature of Bor s teory of spectrum of ydroge atom is te quatizatio of agular mometum we a electro is revolvig aroud a proto. We will extet tis to a geeral rotatioal motio to fid quatized rotatioal eergy of a diatomic molecule assumig it to be rigid. Te rule to be applied is Bor s quatizatio coditio. [JEE 00, 3 3/63, ] 8. A diatomic molecule as momet of iertia I. By Bor s quatizatio coditio its rotatioal eergy i te t level ( = 0 is ot allowed) is : (A) æ ç è 8p I ö ø (B) æ ö ç è 8p I ø æ (C) ö ç æ è 8p I ø (D) ö ç è 8p I ø 9. It is foud tat te excitatio frequecy from groud to te first excited state of rotatio for te CO molecule is close to 4 0 p (Take = p 0 34 J s ) Hz. Te te momet of iertia of CO molecule about its cetre of mass is close to (A) kg m (B) kg m (C) kg m (D) kg m 30. I a CO molecule, te distace betwee C (mass = a.m.u.) ad O (mass = 6 a.m.u.), were a.m.u. = kg, is close to : 3 (A) m (B) m (C) m (D) m 3. Te wavelegt of te first spectral lie i te Balmer series of ydroge atom is 656 Å. Te wavelegt of te secod spectral lie i te Balmer series of sigly-ioized elium atom is : [IIT-JEE 0; 4/60 coducted by IIT Kapur] (A) 5 Å (B) 640 Å (C) 430 Å (D) 4687 Å 3. A silver spere of radius cm ad work fuctio 4.7 ev is suspeded from a isulatig tread i freespace. It is uder cotiuous illumiatio of 00 m wavelegt ligt. As potoelectros are emitted, te spere -gets carged ad acquires a potetial. Te maximum umber of potoelectros emitted from te spere is A 0 Z (were < A < 0). Te value of Z is : [IIT-JEE 0; 4/60 coducted by IIT Kapur] 33. A proto is fired from very far away towards a ucleus wit carge Q = 0 e, were e is te electroic carge. It makes a closest approac of 0 fm to te ucleus. Te de Broglie wavelegt (i uits of fm) of te proto at its start is (take te proto mass, m p = (5/3) 0 7 kg; /e = J.s/C; 4pe = 9 09 m/ F; fm = 0 5 m) [JEE 0 (3, )/36] [coducted by IIT Deli] 34. A particle of mass m is projected from te groud wit a iitial speed u 0 at a agle a wit te orizotal. At te igest poit of its trajectory, it makes a completely ielastic collisio wit aoter idetical particle, wic was trow vertically upward from te groud wit te same iitial speed u 0. Te agle tat te composite system makes wit te orizotal immediately after te collisio is : [IIT-JEE (Advaced) P- 03] 0 (A) 4 p (B) 4 p + a (C) p a (D) p A-479 Idra Viar, Kota Rajasta Page No. # 9

21 35. Te work fuctio of Silver ad Sodium are 4.6 ad.3 ev, respectively. Te ratio of te slope of te stoppig potetial versus frequecy plot for Silver to tat of Sodium is : [IIT-JEE (Advaced) P- 03] 36. Te radius of te orbit of a electro i a Hydroge-like atom is 4.5 a 0, were a 0 is te Bor radius. Its orbital 3 agular mometum is. It is give tat is Plack costat ad R is Rydberg costat. Te possible p wavelegt(s), we te atom de-excites, is (are) [IIT-JEE (Advaced) P- 03] (A) 9 3R (B) 9 6R (C) 9 5R (D) 4 3R PART-II AIEEE (PREVIOUS YEARS PROBLEMS) * Marked Questios are avig more ta oe correct optio.. If 3.6 ev eergy is required to lioize te ydroge atom, te te eergy required to remove a electro from = is : [AIEEE 00 4/300] () 0. ev () 0 ev (3) 3.4 ev (4) 6.8 ev. Sodium ad copper ave work fuctios.3 ev ad 4.5 ev respectively. Te te ratio of tresold wavelegts is earest to : [AIEEE 00 4/300] () : () 4 : (3) : (4) : 4 3. Formatio of covalet bods i compouds exibits : [AIEEE 00 4/300] () wave ature of electro () particle ature of electro (3) bot wave ad particle ature of electro (4) oe of tese 4. Two idetical, potocatodes receive ligt of frequecies f ad f. If te velocities of te potoelectros (of mass m) comig out are respectively v ad v, te : [AIEEE 003 4/300] () v - v = (f - f) () m v - v é = ê ë m + (f f) ú û ù / (3) v - v = (f + f) (4) v m - v é = ê ë m - (f f) 5. Wic of te followig atoms as te lowest ioizatio potetial? [AIEEE 003 4/300] 4 33 () 7 N () 55 Cs 40 6 (3) 8 Ar (4) 8 O 6. Te wavelegt ivolved i te spectrum of deuterium ( D) are sligtly differet from tat of ydroge spectrum, because : [AIEEE 003 4/300] () size of te two uclei are differet () uclear forces are differet i te two cases (3) masses of te two uclei are differet (4) attractio betwee te electro ad te ucleus is differet i te two cases 7. If te bidig eergy of te electro i a ydroge atom is 3.6 ev, te eergy required to remove te electro from te first excited state of Li + is : [AIEEE 003 4/300] () 30.6 ev () 3.6 ev (3) 3.6 ev (4).4 ev ú û ù / A-479 Idra Viar, Kota Rajasta Page No. # 0

22 8. I Bor series of lies of ydroge spectrum, te tird lie from te red ed correspods to wic oe of te followig iter-orbit jumps of te electro for Bor orbits is a atom of ydroge? [AIEEE 003 4/300] () 3 () 5 (3) 4 (4) 5 9. Te de Broglie wavelegt of a teis ball of mass 60 g movig wit a velocity of 0 metres per secod is approximately - (Plack's costat, = Js) [AIEEE 003 4/300] () 0 33 metre () 0 3 metre (3) 0 6 metre (4) 0 5 metre 0. Te orbital agular mometum for a electro revolvig i a orbit is give by l (l + ). Tis mometum p for a s-electro will be give by - [AIEEE 003 4/300] () +. p () zero (3) p (4). p. A radiatio of eergy E falls ormally o a perfectig reflectig surface. Te mometum trasferred to te surface is: [AIEEE 004 4/300] () E/c () E/c (3) Ec (4) E/c. Accordig to Eistei s potoelectric equatio, te plot of te kietic eergy of te emitted potoelectros from a metal Vs te frequecy, of te icidet radiatio gives a straigt lie wose slope : () depeds o te ature of te metal used [AIEEE 004 4/300] () depeds o te itesity of te radiatio (3) depeds bot o te itesity of te radiatio ad te metal used (4) is te same for all metals ad idepedet of te itesity of te radiatio 3. Te work fuctio of a substace is 4.0 ev. Te logest wavelegt of ligt tat ca cause potoelectro emissio from tis substace is approximately : [AIEEE 004 4/300] () 540 m () 400 m (3) 30 m (4) 0 m 4. A potocell is illumiated by a small brigt source placed m away. We te same source of ligt is placed m away, te umber of electros emitted by potocatode would : [AIEEE 005 4/300] () decrease by a factor of 4 () icrease by a factor of 4 (3) decrease by a factor of (4) icrease by a factor of 5. Te diagram sows te eergy levels for a electro i a certai atom. Wic trasitio sow represets te emissio of a poto wit te most eergy? [AIEEE 005 4/300] = 4 = 3 = = I II III IV () III () IV (3) I (4) II 6. If te kietic eergy of a free electro doubles, its de-broglie wavelegt cages by te factor : () () (3) (4) [AIEEE 005 4/300] A-479 Idra Viar, Kota Rajasta Page No. #