Atomic Structure (J-Batch).pdf

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Avogadro constant Electron rest mass (0.000548 amu) NA me 6.02 × 1023 mol–1 9.10 × 10–31 kg 6.02 × 1023 mol–1 9.10 × 10–28 g Proton rest mass (1.00757 amu) mP 1.67 × 10–27 kg 1.67 × 10–24 g Neutron rest mass (1.00893 amu) mn 1.67 × 10–27 kg 1.67 × 10–24 g Planck constant h 6.62 × 10–34 J s 6.62 × 10–27 erg s Bohr’s velocity 6 Z 8 Z 2.188 ×10 × n m/sec. 2.188 ×10 × n cm/sec. Z2 Bohr’s energy –21.8×10–19 n2 J/atom –21.8 ×10–12erg/atom (–13.6 eV/atom) Bohr magneton (BM) e 9.27 × 10–24 J/T Energy Conversion Factorsa 1 erg = 10–7 J 1 cal = 4.184 J 1 eV = 1.602177 × 10–19 J = 1.602177 × 10–12 erg = 23.0605 kcal/mol Greek Alphabet Alpha   Beta   Gamma   Delta   Epsilon   Zeta   Eta   Theta   Iota   Kappa   Lambda   Mu   Nu   Xi   Omicron   Pi   Rho   Sigma   KEY CONCEPT STRUCTURE OF ATOM Rutherford's Model Bohr's Model Wave mechanical model EXTRA NUCLEAR PART (e− ) Electrons,protons & neutrons are the most important fundamental particles of atoms of all elements (Except hydrogen) Some uncommon Fundamental particles : 1. XA , A = Z + n 2. Reduced mass 1  1  1 = mM m = mass of e– ; M = Mass of nucleus  M m m  M h 3. Photon is considered massless bundle of energy. But to find its mass use m =  c 4. E = mc2 , E = h = hc/  = hc  5. Quantum efficiency or Quantum Yield = no. of molecules reacting no. of quanta absorbed 6. R = R (A)1/3 , R = 1.33 ×10–13 cm A = mass number 7. 1 m v2  K Ze .2e ; Tan   1 2   r 2 b number of a particles at  = K 1 sin 4  / 2 ; b = impact parameter 1 R  1 1   Z 8. Rydberg’s Equation  H   n n  1 2  9. Limiting spectral line (series limit) means n2 =  10. H line means we know n1 , n2 (longest  , shortest  , least E) [ H , H , H , H ] n(n 1) 11. No. of wavelengths observed in the spectrum = 2 when e– deexcites to ground state , n = no. of higher orbit 12. 1/2 mv2 = h – h0(w) (work function or B.E.) hc 0 = Threshhold frequency W = h = 0 1 13. Accelerating potential = eV = KE = 14.  = hc/E = 1240 ev. nm mv2 2 15. K 1 ; P.E. = 40 K q1 q2 r centrifugal force = mv2/r 16. mvr = n· h 2 = n . 17. En = E1 z2 n 2 2 2 me 4 = – n2 h2 z2 ; E =  22me4 h2 n 2 h 2 z 2e2 18. rn = Z x 42e2m 19. v =  n h 20. revolutions per sec = v/2r 21. Time for one revolution = 2r/v 22. Separation energy = En   En given  2, 3, 4,................. 23. No. of waves = n = no. of shells 24. I.E. = En= – Eground state of e- (K, L, M, N) 150 25.  = h/mv = h/p 26.  = Vinvolts Å 27. En  KE KE = 1/2 mv , E = h 28. x.p > h/4 2 29. 1/2 = a(z–b) b = screening constant 30. Nucleons 31. Isotopes, Isobars, Isotones (A – Z) 32. Isoelectronic 33. Isosters 34. Isodiaphers (A – 2Z) 35. paramagnetic h 36. Diamagnetic 37. S = 2 S(S  1) 38.  = B.M. n = number of unpaired e– ;

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Atomic Structure (J-Batch).pdf

• 2. Physical Constantsa Constant and Symbolb SI Value Gaussian Value Speed oflight invaccum c 2.99 ×108 m/s 2.99 × 1010 cm/s Proton &electron charge e 1.60 × 10–19 C 4.8 × 10–10 statC Permittivityofvaccum 0 8.85 × 10–12 C2/N-m2 Avogadro constant NA 6.02 × 1023 mol–1 6.02 × 1023 mol–1 Electronrest mass me 9.10 × 10–31 kg 9.10 × 10–28 g (0.000548 amu) Protonrest mass mP 1.67 × 10–27 kg 1.67 × 10–24 g (1.00757 amu) Neutronrest mass mn 1.67 × 10–27 kg 1.67 × 10–24 g (1.00893 amu) Planck constant h 6.62 × 10–34 J s 6.62 × 10–27 erg s Permeabilityofvaccums 0 4 × 10–7 NC–2 s2 Bohrradius a0 5.29 × 10–11 m 0.529 × 10–8 cm Bohr’s velocity 2.188 ×106 × n Z m/sec. 2.188 ×108 × n Z cm/sec. Bohr’s energy –21.8×10–19 2 2 n Z J/atom –21.8 ×10–12erg/atom (–13.6 eV/atom) Bohrmagneton (BM) e 9.27 × 10–24 J/T Gas constant R 8.3145 J/mol-K 8.3145 × 107 erg/mol-K Boltzmannconstant k 1.38 × 10–23 J/K 1.30 × 10–16 erg/K Gravitionalconstant G 6.67 × 10–11 m3/kg -s2 6.67 × 10–8 cm3/g-s2 Energy Conversion Factorsa 1 erg = 10–7 J 1 cal = 4.184 J 1 eV = 1.602177 × 10–19 J = 1.602177 × 10–12 erg = 23.0605 kcal/mol Greek Alphabet Alpha   Beta   Gamma   Delta   Epsilon   Zeta   Eta   Theta   Iota   Kappa   Lambda   Mu   Nu   Xi   Omicron   Pi   Rho   Sigma   Tau   Upsilon   Phi   Chi   Psi   Omega  
• 3. KEY CONCEPT STRUCTURE OF ATOM Rutherford's Model Bohr's Model Wave mechanicalmodel EXTRA NUCLEAR PART (e ) Electrons,protons & neutronsare the most important fundamentalparticles ofatomsofallelements (Except hydrogen) Some uncommonFundamentalparticles : 1. Z XA , A = Z + n 2. Reduced mass m 1 M 1 1    = mM m M  m = mass of e– ; M = Mass of nucleus 3. Photon is considered massless bundle of energy. But to find its mass use m = c h  4. E = mc2 , E = h = hc/  = hc  5. Quantum efficiency or QuantumYield = no of molecules reacting no of quanta absorbed . . 6. Rn = R1 (A)1/3 , R1 = 1.33 ×10–13 cm A = mass number 7. r e 2 . Z K v m 2 1 e 2    ; b 1 2 Tan   number of a particles at  = 2 / sin 1 K 4  ; b = impact parameter 8. Rydberg’s Equation 2 Z 2 2 n 1 2 1 n 1 H R 1               9. Limiting spectral line (series limit) means n2 =  10. H line means we know n1 , n2 (longest  , shortest  , least E) [ H , H , H , H ] 11. No. of wavelengths observed in the spectrum = 2 ) 1 n ( n  when e– deexcites to ground state , n = no. of higher orbit 12. 1/2 mv2 = h – h0 (w) (work function or B.E.) 0  = Threshhold frequency W = h0 = 0 hc  13. Accelerating potential = eV = KE = 1 2 mv2 14.  = hc/E = 1240 ev. nm 15. 0 4 1 K   ; P.E. = r q q K 2 1 centrifugal force = mv2 /r 16. mvr = n·  2 h =  . n 17. En = 2 z 2 n 1 E = – 2 2 4 2 2  me n h 2 z ; E1 = 2 h 4 me 2 2 
• 4. 18. rn = m 2 e 2 4 2 h x Z 2 n  19. v = h 2 e 2 n z   20. revolutions per sec = v/2r 21. Time for one revolution = 2r/v 22. Separation energy = E E n n given     2 3 4 , , ,................. 23. No. of waves = n = no. of shells 24. I.E. = En= – Eground state of e- (K, L, M, N) 25.  = h/mv = h/p 26. = volts in V 150 Å 27. En  KE KE = 1/2 mv2 , E = h 28. x.p > h/4 29. 1/2 = a(z–b) b = screening constant 30. Nucleons 31. Isotopes, Isobars, Isotones (A – Z) 32. Isoelectronic 33. Isosters 34. Isodiaphers (A – 2Z) 35. paramagnetic 36. Diamagnetic 37. S = ) 1 S ( S 2 h   38.  = ) 2 n ( n  B.M. n = number of unpaired e– ; 39. Radial Nodes ; Angular nodes ; Totalnodes (n – l – 1) l (n–1) 40. Total no. of e– in an energy level = 2n2 Total no. of e– in a sublevel = 2(2l+1) Maximum no. of e– in an orbital = 2 Total no. of orbitals in a sublevel = (2l+1) No. of subshells in main energyshell = n No. of orbitals in a main energy shell = n2 l = 0 1 2 3 4 s p d f g 41. ELEECTROMEGNETIC SPECTRUM  increases in meters. Distinction between the wave – particle nature of a photon and the particle–wave nature of sub- atomic particle. PHOTON SUB ATOMIC PARTICLE 1. Energy = h Energy = 1 2 m2 2. Wavelength =  c Wavelength = h m Note: We should never interchange any of the above and to write electronic conf. of Cation first write for neutral atom & then remove e– from outermost shell.
• 5. SHAPES OFATOMIC ORBITALS The spherical Polar Coordinates S pX py pz 2 z d 2 y 2 x d  dxy
• 6. dxz dyz 3 z f fxyz ) 2 y 2 x ( z f  ) 2 z 2 y ( x f  ) 2 x 2 z ( y f  3 x f 3 y f
• 8. BOHR’S MODEL Q.21 Calculate energyofelectron which is moving in the orbit that has its rad. sixteen times the rad. offirst Bohr orbit for H–atom. Q.22 The electronenergyinhydrogenatomisgivenby . ergs n 10 7 . 21 E 2 12 n     Calculate theenergyrequired to remove an e  completelyfromn =2 orbit . What is the largest wavelength in cmoflight that can be used to cause this transition. Q.23 Calculate the wavelengthin angstromofphotonthat isemitted whenan e in Bohr orbit n=2returns to the orbit n=1. The ionization potentialofthe ground state ofhydrogenatomis 2.17×1011 erg/atom. Q.24 Theradiusofthe fourthorbit ofhydrogenatomis0.85 nm. Calculatethevelocityofelectroninthis orbit. Q.25 The velocity ofe ina certain Bohr orbit ofthe hydrogenatombears the ratio 1:275 to the velocityof light. What is thequantumno. "n" ofthe orbit and the wave no. ofthe radiationemittedfor the transition fromthe quatumstate (n+1) to the ground state. Q.26 Electrons ofenergy12.09 eVcan excitehydrogenatoms. To whichorbit is the electroninthe hydrogen atomraised and what are the wavelengthsofthe radiations emitted asit drops back to the ground state. Q.27 A doubly ionised lithiumatomis hydrogen like with atomic number z = 3. Find the wavelength of the radiationrequired to excite the electron in Li2+ fromthe first to the third Bohr orbit. Q.28 Estimate the differencein energybetweenIand II Bohr Orbit fora hydrogen atom.At what minimumat no. a transition from n=2 to n=1 energy level would result in the emission of Xrays with = 3.0 × 108 m? Which hydrogenlike species does this at no correspond to. Q.29 Find out the no. ofwaves made bya Bohr electron inone complete revolution inits 3rd orbit. Q.30 Iodine molecule dissociates into atoms after absorbing light of4500A0. Ifone quantumofradiation is absorbed byeachmolecule, calculate the K.E. ofiodine atoms (Bond energy of I2 = 240 KJ/mol) Q.31 Calculate thewavelength ofradiation emitted, producing a line inLyman series, when anelectronfalls fromfourthstationarystate inhydrogenatom. Q.32 Calculate the wave no. for theshortest wavelengthtransitioninthe Balmer series ofatomic hydrogen. GENERAL Q.33 What is de-Broglie wavelengthofa He-atomin a container at roomtemperature.(Use Uavg) Q.34 Throughwhat potentialdifference must anelectronpass to have a wavelengthof500 Å. Q.35 A proton is accelerated to one- tenth of the velocity of light. If its velocity can be measured witha precision + 1%. What must be its uncertainityin position. Q.36 To what effectivepotentiala protonbeambe subjectedto give its protons a wavelengthof 1 ×1010 m. Q.37 Calculate magnitude of angular momentum ofan e– that occupies 1s, 2s , 2p , 3d , 3p. Q.38 Calculate thenumber ofexchange pairsofelectrons present inconfiguration ofCu according toAufbau Principle considering 3d & 4s orbitals. Q.39 He atomcanbe excited to 1s1 2p1 by = 58.44nm. Iflowest excited state for He lies 4857cm–1 below the above. Calculatethe energyfor the lower excitation state. Q.40 Wave functions ofelectrons inatoms &molecules are called________. Q.41 The outermost electronicconf. ofCr is___________.
• 9. EXERCISE-II Q.1 X-rays emitted froma copper target anda molybdenumtarget arefound to containaline ofwavelength 22.85nmattributedto theK lineofanimpurityelement. TheK linesofcopper (Z=29)andmolybdenum ( Z = 42) have wavelength 15.42 nmand 7.12 nm respectively. Using Moseley’s law, 1/2 = a (Z – b) calculate the atomic number oftheimpurityelement. Q.2 1.8 g hydrogenatoms are excited to radiations. The studyofspectraindicates that 27% ofthe atomsare in 3rd energy level and 15% of atoms in 2nd energy level and the rest in ground state. If I.P. of H is 21.7 × 1012 erg. Calculate  (i) No. ofatoms present in III &II energylevel. (ii) Totalenergyevolved when allthe atoms returnto ground state. Q.3 One mole He+ ions areexcited. Spectralanalysis showed existence of50% ions in 3rd orbit, 25%in 2nd and rest inground state. Calculate totalenergyevolved when allthe ions return to the ground state. Q.4 The energyofan excited H-atomis–3.4 eV. Calculate angular momentumofe–. Q.5 The vapoursofHg absorb someelectrons accelerated byapotentialdiff. of4.5 volt as a result ofwhich light is emitted. Ifthe fullenergyofsingle incident e is supposed to be converted into light emitted by single Hg atom, find the wave no. ofthe light. Q.6 The hydrogen atomintheground state is excitedbymeans ofmonochromatic radiation ofwavelength xA0. The resulting spectrum consists of 15 different lines . Calculate the value ofx. Q.7 The eyes of certain member of the reptile familypass a single visualsignalto the brainwhenthevisual receptors are struck byphotons ofwavelength 850 nm. Ifa totalenergyof3.15 10 14 J is required to tripthe signal, what is the minimumnumber ofphotons that must strikethe receptor. Q.8 Iftheaverage life time ofanexcited state ofH atomis oforder 10–8 sec, estimate how manyorbits ane– makes whenit is in the state n = 2 and before it suffers a transition to n =1 state. Q.9 Calculate the frequencyofe– inthe first Bohr orbit in a H-atom. Q.10 A single electron orbits around a stationary nucleus o f charge +Ze where Z is a constant from the nucleus and e is the magnitude ofthe electric charge. The hydrogen like species required 47.2 eV to excite the electronfromthe second Bohrorbit to the third Bohr orbit. Find (i) the value ofZ and give the hydrogenlike species formed. (ii) the kinetic energyand potentialenergyofthe electron inthefirst Bohr orbit. Q.11 Astationary He+ ion emitted a photon corresponding to a first line of the Lyman series. The photon liberatedaphotonelectronfrom astationaryHatomingroundstate.What isthevelocityofphotoelectron. Q.12 To what series does the spectral lines of atomic hydrogen belong if its wave number is equal to the differencebetweenthewave numbersofthe followingtwo linesofthe Balmerseries486.1and 410.2nm. What is the wavelengthofthis.
• 11. Q.24 Find the wavelength ofthe first line of He+ ion spectralseries whose intervalbetween extreme line is            1 4 2 1 cm 10 7451 . 2 1 1 Q.25 The ionisation energyofa H-like Bohr atomis 4 Rydbergs (i) What isthewavelengthofradiationemittedwhenthee– jumpsfromthefirstexcitedstateto thegroundstate. (ii) What is the radius offirst Bohr orbit for this atom. [ 1 Rydberg = 2.18 × 10–18 J] DE-BROGLIE Q.26 What is de Broglie wavelength associated with an e– accelerated through P.D. = 100 KV. Q.27 Calculatethede-broglie wavelengthassociated withmotionofearth(mass6 × 1024 Kg)orbiting around the sun at a speed of 3 × 106 m/s. HEISENBERG Q.28 A base ballofmass 200 g is moving withvelocity30 × 102 cm/s. Ifwe canlocate the base ballwith an error equalinmagnitude to the  ofthe light used (5000 Å), how willthe uncertaintyinmomentumbe compared withthe totalmomentumofbase ball. Q.29 An electron has a speed of 40 m/s, accurate up to 99.99%. What is the uncertainity in locating its position.
• 12. EXERCISE-III Q.1 The ratio ofthe energyofa photonof2000 Å wavelength radiation to that of4000 Åradiation is (A) 1 / 4 (B) 4 (C) 1 / 2 (D) 2 Q.2 The maximumenergyis present inanyelectron at (A) Nucleus (B) Ground state (C) First excited state (D) Infinite distancefromthe nucleus Q.3 Which electronic levelwould allow the hydrogenatomto absorb a photon but not to emit a photon (A) 3s (B) 2p (C) 2s (D) 1s Q.4 The third line in Balmer series corresponds to an electronic transition between which Bohr’s orbitsin hydrogen (A) 5  3 (B) 5  2 (C) 4  3 (D) 4  2 Q.5 Correct set offour quantumnumbers for valence electron ofrubidium( Z = 37) is (A) 5, 0, 0, + 2 1 (B) 5, 1, 0, + 2 1 (C) 5, 1, 1, + 2 1 (D) 6, 0, 0, + 2 1 Q.6 The correct set ofquantumnumbers for the unpaired electronofchlorine atomis n l m n l m (A) 2 1 0 (B) 2 1 1 (C) 3 1 1 (D) 3 0 0 Q.7 The orbitaldiagraminwhichtheAufbau’s principle is violated is 2s 2px 2py 2pz 2s 2px 2py 2pz (A)    (B)     (C)     (D)     Q.8 The totalnumberofneutrons indipositive zinc ions with mass number 70 is (A) 34 (B) 40 (C) 36 (D) 38 Q.9 Principalquantumnumberofanatomrepresents (A) Sizeofthe orbital (B) Spinangular momentum (C) Orbitalangular momentum (D) Space orientationofthe orbital Q.10 Whichofthe following sets ofquantumnumbers represent animpossible arrangement n l m ms n l m ms (A) 3 2 –2 2 1 (B) 4 0 0 2 1 (C) 3 2 –3 2 1 (D) 5 3 0 2 1 Q.11 The orbitalangularmomentumofanelectronin2s orbitalis: (A)  1 2 2 .   (B) Zero (C)  2 (D) 2 2 .   Q.12 The explanationfor the presence ofthree unpaired electrons inthe nitrogenatomcanbe given by (A) Pauli’sexclusionprinciple (B) Hund’s rule (C)Aufbau’s principle (D)Uncertaintyprinciple
• 13. Q.13 The maximumnumber ofelectrons that can be accommodated in the Mth shellis (A) 2 (B) 8 (C) 18 (D) 32 Q.14 Whichquantumnumberwilldetermine the shape ofthe subshell (A) Principalquantumnumber (B)Azimuthalquantumnumber (C) Magneticquantumnumber (D) Spinquantumnumber Q.15 The electronic configuration ofan element is 1s2 2s2 2p6 3s2 3p6 3d5 4s1. This represents its (A) Excited state (B) Ground state (C) Cationic form (D) None Q.16 Whichofthe following has maximumnumber ofunpaired electron(atomic numberofFe 26) (A) Fe (B) Fe (II) (C) Fe (III) (D) Fe (IV) Q.17 Whichquantumnumber is not relatedwithSchrodinger equation (A) Principal (B)Azimuthal (C) Magnetic (D) Spin Q.18 According to Bohr’satomic theory, whichofthe following is/are correct: (I) Kinetic energyofelectron 2 2 n Z (II) The product ofvelocityofelectronand principle quantumnumber ‘n’Z2 (III) Frequencyofrevolutionofelectron in an orbit  3 2 n Z (IV) Coulombic force ofattractiononthe electron 4 3 n Z (A) I, III, IV (B) I, IV (C) II (D) I Q.19 If0 isthe thresholdwavelengthforphotoelectric emission, wavelengthoflight falling onthe surfaceof metal, and m, mass ofelectron, thende Broglie wavelengthofemitted electron is (A) 2 1 0 0 ) ( mc 2 ) ( h             (B) 2 1 0 0 mc 2 ) ( h             (C) 2 1 0 0 mc 2 ) ( h             (D) 2 1 0 mc 2 h        Q.20 It is knownthat atomcontain protons, neutrons and electrons. Ifthe mass ofneutron isassumed tohalf ofits originalvalue where as that ofproton is assumed to be twice ofits originalvalue then theatomic mass of C 14 6 willbe (A) same (B) 25% more (C) 14.28 % more (D) 28.5% less Q.21 Give the correct order ofinitialsT(true) or F (false) forfollowing statements. (I) Ifanion has 2 electrons in K shell, 8 electrons in L shelland 6 electrons inM shell, then number ofS electrons present in that element is 6. (II) The maximumnumber ofelectrons ina subshellis givenby2n2. (III) Ifelectronhas magnetic number –1, then it cannot be present ins-orbital. (IV) Onlyone radialnode is present in 3p orbital. (A) TTFF (B) FFTF (C) TFTT (D) FFTF Q.22 Predict the magnetic moment for S2–, Co3+ [At. no. of S = 16, Co = 27] Q.23 The criticalwavelengthfor producing the photoelectric effect in tungsten is 2600Å. What wavelength would be necessaryto produce photoelectrons fromtungston having twice the kinetic energyofthese produced at 2200Å ?
• 14. Q.24 Theshortest wavelengthofHe atominBalmerseriesis x, thenlongest wavelengthinthe Paschene series ofLi+2 is (A) 5 x 36 (B) 7 x 16 (C) 5 x 9 (D) 9 x 5 Q.25 Anelectronina hydrogenatominits ground state absorbs energyequalto the ionisationenergyofLi+2. The wavelengthoftheemitted electronis: (A) 3.32 ×10–10 m (B) 1.17 Å (C) 2.32 × 10–9 nm (D) 3.33 pm Q.26 In compound FeCl2 the orbitalangular momentumoflast electronin its cation &magnetic moment (in Bohr Magneton) ofthis compound are (A) 35 , ) 6 (  (B) 24 , ) 6 (  (C) 0, 35 (D) noneofthese Q.27 An electron, aprotonand an alpha particle have kinetic energies of16E, 4E and E respectively. What is the qualitativeorder oftheir de Broglie wavelengths? (A) e > p =  (B) p =  > e (C) p > e >  (D)  < e » p Q.28 Question: Is the specie paramagnetic? STAT-1: The atomic number ofspecie is 29. STAT-2: The charge on the specie is + 1. (A) Statements(1) alone is sufficient but statement (2) isnot sufficient. (B) Statement (2) alone is sufficient but statement (1) isnot sufficient. (C) Bothstatement together are sufficient but neither statement aloneis sufficient. (D) Statement (1) &(2) togetherare not sufficient. Q.29 Question :Are the rays in discharge tube cathode rays? STAT1 : Rays are deflected towards – ve electrode kept externally. STAT2 : Rays are produced at low pressure and high voltage. (A) Statements(1) alone is sufficient but statement (2) isnot sufficient. (B) Statement (2) alone is sufficient but statement (1) isnot sufficient. (C) Bothstatement together are sufficient but neither statement aloneis sufficient. (D)Anyoneofthemis sufficient. Q.30 Given H for the process Li(g)  Li+3(g) + 3e– is 19800 kJ/mole &IE1 for Liis 520 thenIE2 & IE1 ofLi+ arerespectively(approx, value) (A) 11775, 7505 (B) 19280, 520 (C) 11775, 19280 (D) Datainsufficient Q.31 The ratio ofdifferencein wavelengths of1st and 2nd lines ofLymanseries inH–like atomto difference in wavelength for 2nd and 3rd lines ofsame series is: (A) 2.5 : 1 (B) 3.5 : 1 (C) 4.5 : 1 (D) 5.5 : 1 Q.32 Whichofthefollowing statement isINCORRECT. (A) m e ratio forcanalrays is maximumfor hydrogenion. (B) m e ratio for cathode rays us independent ofthe gas taken. (C) The nature ofcanalrays is dependent onthe electrode material. (D) The m e ratio for electron is expressed as V B 2 E 2 2 , whenthe cathode rays go undeflected under the influence ofelectric field E, magneticfield B and V is potentialdifference applied across electrodes.
• 15. Q.33 The quantumnumbers offour electrons(e1 to e4) are given below n l m s n l m s e1 3 0 0 +1/2 e2 4 0 1 1/2 e3 3 2 2 –1/2 e4 3 1 –1 1/2 The correct orderofdecreasing energyofthese electrons is: (A) e4 > e3 > e2 > e1 (B) e2 > e3 > e4 > e1 (C) e3 > e2 > e4 > e1(D) none Q.34 Ifradius ofsecond stationaryorbit (inBohr's atom) is R. Thenradius ofthirdorbit willbe (A) R/3 (B) 9R (C) R/9 (D) 2.25R Q.35 An electronin a hydrogen atomin its ground state absorbs 1.5 times as much energyas the minimum required for it to escape fromthe atom. What is the velocityofthe emitted electron? (Given mass of e– = 9.1 ×10–28 gm) PROBLEM ON DE-BROGLIE, HEISENBERG & SCHRODINGER EQUATIONS Q.36 An electroncan undergo diffraction bycrystals . Throughwhat potentialshould a beamofelectron be accelerated so that its wavelength become equalto 1.54Aº . Q.37 The first use ofquantumtheoryto explain the structure ofatomwas madeby: (A) Heisenburg (B) Bohr (C) Planck (D) Einstein Q.38 The wavelength associated with a golfweighing 200g and moving at aspeed of5m/h isofthe order (A) 10–10m (B) 10–20m (C) 10–30m (D) 10–40m Q.39 Ifthe nitrogenatomhad electronic configuration1s7, it would have energylower that ofnormalground state configuration 1s2 2s2 2p3 , because the electrons would be closer to the nucleus. Yet 1s7 is not observed because it violates :– (A) Heisenberguncertainityprinciple (B) Hunds rule (C) Pauli’sexclusionprinciple (D) Bohr postulateofstationaryorbits Q.40 WavelengthofhighenergytransitionofH-atomsis 91.2 nm. Calculate thecorresponding wavelengthof He atoms. Q.41(i) The wave functionof2s electronis given by 2s =                            o a r 2 e a r 2 a 1 2 4 1 o 2 / 3 o It has a node at r = r0, find relation between r0 and a0. (ii) Find wavelengthfor100 g particle moving withvelocity100 ms–1. Q.42 The electron inthe first excited state ofH-atomabsorbs a proton and is further excited. the Debroglie wavelengthofthe electroninthisexcited state is 1340pm. Calculate the wavelengthofphotonabsorbed bytheatomand also longest wavelengthradiationemitted whenthis electronde-excited to ground state. Q.43 The uncertainityprinciplemaybe stated mathematically p.x   4 h where p representsthe uncertainityinthe momentumofa particleandxrepresntsthe uncertainityin itsposition. Ifanelectronistravelingat 200m/swithin1m/suncertainity, whatisthetheoreticaluncertainity inits positioninm(micrometer)?
• 16. Q.44 Fromthefollowing observations predict thetype oforbital: Observation1: x y plane acts as a nodal plane Observation2: The angular functionofthe orbitalintersect the three axisat originonly. Observation3: R2(r) / v/s r curve is obtained for the orbitalis (A) 5pz (B) 6dxy (C) 6 dx2–y2 (D) 6 dyz Q.45 Question : Is the orbital ofhydrogenatom3px? STAT 1: The radialfunction ofthe orbitalis R(r) = 2 / 2 / 3 0 e ) 4 ( a 6 9 1      ,= 2 r STAT 2: The orbitalhas 1 radial node &0 angular node. (A) Statement (1)alone is sufficient. (B) Statement (2)alone is sufficient (C) Bothtogether is sufficient. (D) Neitheris sufficient Q.46 What isuncertainityinlocationofaphotonofwavelength5000Åifwavelengthis knownto anaccuracy of 1 pm? (A) 7.96 × 10–14 m (B) 0.02 m (C) 3.9 ×10–8 m (D) none
• 17. EXERCISE-IV Q.1 With what velocityshould an particle traveltowards the nucleus of a Cu atom so as to arrive at a distance 1013 m. Q.2 Acompound of Vanadium has magnetic moment of 1.73 BM work out electronic configuration of VanadiumIoninthe compound. Q.3 The energyofanelectron inthe first Bohr orbit ofHatomis13.6 eV. The possible energyvalue(s) of the excited state(s) for electrons inBohr orbits ofhydrogenis/are : (A)  3.4 eV (B)  4.2 eV (C)  6.8 eV (D) + 6.8 eV Q.4 The electrons, identified by n & l ; (i) n = 4 , l = 1 (ii) n = 4 , l = 0 (iii) n = 3 , l = 2 (iv) n = 3 , l = 1 canbe placed in orderofincreasing energy, fromthe lowest to highest as : (A) (iv) < (ii) < (iii) < (i) (B) (ii) < (iv) < (i) (C) (i) < (iii) < (ii) < (iv) (D) (iii) < (i) < (iv) < (ii) Q.5 Gaseous state electronicconfigurationofnitrogen atomcanbe represented as: (A)  (B)  C) D) Q.6 The electronic configuration ofan element is 1s2 2s2 2p6 3s2 3p6 3d5 4s1. This represents its: (A) excited state (B) ground state (C) cationic form (D) none Q.7 The number ofnodalplanes in a px orbitalis: (A) one (B)two (C) three (D)zero Q.8 Calculate the energyrequired to excite one litre ofhydrogengas at 1 atmp and 298Kto the first excited state ofatomic hydrogen. The energyfor the dissociation ofH – H is 436 KJ mol–1. Q.9 The quantumnumbers +1/2 and –1/2 for theelectronspin represent: (A) rotation ofthe electronin clockwise and anticlockwise direction respectively. (B) rotationofthe electronin anticlockwise andclockwise direction respectively. (C) magnetic moment ofthe electronpointing upand downrespectively. (D) two quantummechanicalspin states whichhaveno classicalanalogue. Q.10 Rutherfords experiment , which established the nuclear modelofatom, used a beamof:– (A)  - particles, which impinged ona metalfoiland get absorbed. (B)  - rays, which impinged ona metalfoiland ejected electron. (C) Heliumatoms, which impinged on a metalfoiland got scattered. (D) Heliumnuclie, whichimpinged ona metalfoilandgot scattered. Q.11 The spin magnetic moment ofcobalt ofthe compund Hg[Co(SCN)4] is [Given: Co+2] (A) 3 (B) 8 (C) 15 (D) 24 Q.12 The radiusofwhichofthefollowing orbit is same as that ofthefirst Bohr’s orbit ofhydrogen atom? (A) He+ (n = 2) (B) Li2+ (n = 2) (C) Li2+ (n = 3) (D) Be3+ (n = 2) Q.13 Giveninhydrogenic atomrn, Vn, E, Kn stand forradius, potentialenergy, totalenergyand kinetic energy in nth orbit. Find the value ofU,v,x,y.
• 18. (A) U = n n K V (P) 1 (B) n r 1  Ex (Q) –2 (C) rn  Zy (R) –1 (Z =Atomic number) (D) v= (Angularmomentumofelectron (S) 0 in itslowest energy)
• 19. ANSWER KEY EXERCISE -I LIGHT Q.1 6563 Å ; 1216 Å ; 1026 Å Q.2 6 Q.3 0.527 Q.4 6235 Å Q.5 4863 Å Q.6 1.096 × 107 m–1 Q.7 3 × 1021 Q.8 photons Q.9 n1 =1, n2=2 Q.10 1.827 × 105 J/mol PLANCK’S QUANTUM THEORY Q.11 4.9 × 10–7 m Q.12 28 photons Q.13 1403 KJ/mol Q.14 4.5 ×1014 s–1 Q.15 497 KJ/mol Q.16 319.2 KJ/mol Q.17 6.57 ×10–34 Js Q.18 8.68 % Q.19 0.62 Å Q.20 3.06 V BOHR’S MODEL Q.21 – 1.36 × 10–19 Joules Q.22 5.425×10–12 ergs, 3.7×10–5 cm Q.23 1220 Å Q.24 5.44 × 105 m/s Q.25 2 ; 9.75 × 104 cm–1 Q.26 3 , 6563 Å , 1215 Å , 1026 Å Q.27 113.74 Å Q.28 10.2 eV , z = 2 Q.29 3 Q.30 2.186 × 10–20 Joules Q.31 9.7 × 10–8 m Q.32 27419.25 cm–1 GENERAL Q.33 0.79 Å Q.34 6.03×10–4 volt Q.35 1.05×10–13 m Q.36 0.0826 volts Q.37 0 ; 0 ;  2 h 2 ;  2 h 6 ;  2 h 2 Q.38 25 Q.39 3.3 × 10–18 J Q.40 orbitals Q.41 3s2 3p6 3d5 4s1 EXERCISE-II Q.1 24 Q.2 292.68×1021 atoms, 162.60×1021 atoms, 832.50 KJ Q.3 331.13×104 J Q.4 h/ Q.5 3.63 ×106 m–1 Q.6 938 Å Q.7 1.35×105 Q.8 8×106 Q.9 6530×1012Hz Q.10 5 ; 340 ev , – 680 eV Q.11 3.09 × 108 cm/sec Q.12 Brackett ; 2.63 ×10–4 cm Q.13 rn = e 2 2 2 2 m 208 e 3 K 4 h n    n = 25 ; 55.2 pm Q.14 9.15 ×1019 Hz , yes, 58.5×10–15 J Q.15 1022 Q.16 47.26% Q.17 six , 18800 Å Q.18 6.4×10–13 J, 2.1×10–13J, 3.4×10–14m Q.19 E = 6 4 2 3 6 6 e K m 384 h n  Q.20 6 ; 489.6 eV , 25.28 Å Q.21 910 Å ;U.V. Q.22 973.5 Å Q.23 +1/2 , +1/2 , +1/2 , +3/2 and 2,2,2,4 Q.24 4689 Å Q.25 303.89 Å , 2.645 × 10–9 cm DE-BROGLIE Q.26 3.88 pm Q.27 3.68 × 10–65 m HEISENBERG Q.28 1.75 × 10–29 Q.29 0.0144 m
• 20. EXERCISE-III Q.1 D Q.2 D Q.3 D Q.4 B Q.5 A Q.6 C Q.7 B Q.8 B Q.9 A Q.10 C Q.11 B Q.12 B Q.13 C Q.14 B Q.15 B Q.16 C Q.17 D Q.18 A Q.19 A Q.20 C Q.21 C Q.22 zero, 4.9 B.M. Q.23  = 1900Å Q.24 B Q.25 B Q.26 B Q.27 A Q.28 C Q.29 A Q.30 A Q.31 B Q.32 C Q.33 C Q.34 D Q.35 1.54 × 106m/s PROBLEM ON DE-BROGLIE, HEISENBERG & SCHRODINGER EQUATIONS Q.36 63.12 volts Q.37 B Q.38 C Q.39 C Q.40 22.8 nm Q.41 (i) r0 = 2a0, (ii) 6.626 × 10–35 m Q.42 4860 Å, 18788 Å Q.43  2.9 ×2 × 10–5 m  58 m Q.44 D Q.45 B Q.46 B EXERCISE-IV Q.1 6.3 × 106 m/s Q.2 [Ar] 3d1 Q.3 A Q.4 A Q.5 A,D Q.6 B,C Q.7 A Q.8 97.819 KJ Q.9 D Q.10 D Q.11 C Q.12 D Q.13 (A) Q, (B) P, (C) R, (D) S
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