ATOMIC STRUCTURE EXERCISE # 1

Transcription

1 ATOMIC STRUCTURE EXERCISE #. A N A N 5 A N (5 ) 5 A 5 N. R R A /. (6) / cm 5. (6) / cm fm 5 m 5 fm. C 8. d m m A 6.75 m.59 A Fo atom E.6 E ().6.6 e E (e + ).6.6 e E (Li + ).6 E (Be + ).6 As B 6. E 78. kcal/mol.6 e.6 e E.6 kcal/mol fo atom m/sec. 9. (A) Eegy of goud state () e +.6 e 5. e (B) P.E. of Ist obit of -atom ( P.E.)T.E..6e 7.e (C) Eegy of II excited state(ii ) e () () (D) I.E. E.8 9 J J. E 5.6 (5).5 e. Li + & e + bot ave same o. of electo so spectum patte will be simila.li + e +. mq 5. x.p put value p. 5 kg ms 6. Obital agula mometum () ( ). fo 8. M 5 s, s p 6, s p 6 d 5, s M + s, s p 6, s p 6 d, s 9. + s, s p 6, s p 6 d (upaied () de ) 6 Fe+ s s p 6 s p 6 d 6 (upaied de ) 8 Ni+ s s p 6 s p 6 d 7 (upaied de ) (Li ) / / () / / 8. Let state () () (Li + ). d 7 9 Cu+ s s p 6 s p 6 d 9 (upaied de ) state () () Total spi () K e s L 8e s p M e s p 6 d N e s fo d e,. Cl s s p 6 s p 6 Fo last e, l, m ±

2 5. (A) v.8 6 v o v v (B) f o f v / f / (C) / [T ] F m v ( / ) F F / 7. Cage i agula mometum ( ) () ( ) is a itege value (( ) ) so as (B,C) So as (A,B,D) ATOMIC STRUCTURE EXERCISE #..6z E as move away fom te ucleus te eegy iceases, ece eegy is maximum at ifiite distace fom te ucleus. ( ). We electo jump ige level to lowe level, it emit te poto lowe level to ige level, It absob poto. ece 's' oly absob poto because it is lowest eegy level. 's'. R I balme seies, electo jumps ige eegy level to d eegy level. ece tid lie fom we electo jump fift eegy level to eegy level. 5 (, d 5 ). 7 Rb s s p 6 s p 6 d s p 6 5s m s 5 +/ 5. Aufbau's piciple : electo fills i obital iceasig ode of eegy level A 7 7. >,m to + s ½ Te value of cm is wog, m,,, +, + 8. ud's ule 9. C s s p 6 s p 6 d 5 s ; M + s s p 6 s p 6 d 5 s i.e. it epeset bot goud state ad catioic fom.. Fe + s s p 6 s p 6 d 5. Scodige equatio gives oly, l ad m quatum umbe, spi quatum umbe is ot elated to scodige equatio., l m. + m + m K.E. m e [ ] mc e e mc [ ] mk.e. m mass of euto ; m p mass of poto m m p atomic mass (m + m p ) [m ~ m p ] (8 + 6) m p atomic mass ( + ) 6 m p % icease 6.8 %

3 5. R fo sotest wave legt, R z x R R fo logest wave legt of paca seies, R z R 6. (IE) (IE) z Li 6 x J/atom ME R x A 7. Fe + s s p 6 s p 6 d 6 8. upaied electo () Magatic momet () ( ) BM (6) obital agula mometum () ( ) () 6 e ME M e 6 E p ; p ME M E M E ; ece e p 9. Cu + s s p 6 s p 6 d all te electo ae paied ; ece it is paamagatic (). Li (g) Li + + e 5 Li + (g) Li + + e a KJ/mol. Li + (g) Li + + e b KJ/mol. b b (IE ) (IE) (IE) z 9 Li (IE ) 87 KJ/mol Li 5 + a (IE ) a 76 KJ/mol Li Li p. R R ( ) ( ) st lie of lyme seies, d lie of lyme seies, d lie of lyme seies,. Te aode ay/caal ay idepedet to te electode mateial.. Eegy ode decide fom ( + ) ule ;( + ) is miimum eegy is miimum ; if ( + ) value is equal, lowe te value of '' lowe te eegy.. 5. (( + ) ; ( + ) ; ( + ), '' ) / 9 e > e > e > e ;.5 R mv. 5.8 mete 6. Acc to paulis a obital accomdate maximum two electo, ece paulis exclusio piciple voilates. ( ) 7. Fo d yz, xy ad xz ae odal pale ode ( ) 6 9. x y + y 8 O 8 + y 9 y 9 x x ece x Na Na peset i d peiod No of euto mole of Na.6. Mole of euto... E ev m.8 + K.E. K.E e K.E E e v v.8 6 m/s

4 . Fequecy v z/ T / z Fequecy z T T z. Radial ode () ( ) Agula ode () s, 5p x, 6 dxy avig adial ode. agula ode i all 's' obital i zeo. / 8 / ('s' ). s-obital is speical ece it is o-diectioal. (s-). B.E. I.E. (I.E.) ay atom (I.E.) z..6 z z 9 z E E e 5. x p x.p (p) (v) 8m v m v m 5. () it is a solutio of scodige wave equatio. 6. [acc to de-boglie teoy] 7. m y.5 m x, v y.75 v x mv x, m xv y x m yv y y.5m x.75 v y 5. A x 8. Obital agula mometum () ( ) s p d f 8. m ( +) m 5. M + s s p 6 s p 6 d 5. Acc to ( + ) ule, afte p, ( +) s always filled. 5. Ni + s s p 6 s p 6 d 8 magatic momet () ( ) () T z T T / l,,,,, s, p, d, f, g 8. Fom ( + ) ule, same as Q. 9. Te value of to ( ) Numbe of electo fo give value of (+) ece () ( ). v mv m m. Acc to scodige model e beave as wave oly. (e ). Te maximum pobability of fidig a electo is decibe te obital, wic is deote by. ( ). m e mv m v c c m v v v e m m c 5. E E v, E v E E v E E v, E v v + v v v v v v v v 5 5. E C E B E B E A E C E A add equatio () ad () E C E A put i equatio ()...(i)...(ii)...(iii)

5 5 6. E E E z (fo atom) (fo e + atom) 5 7. Fist Excitatio potetial () E E + 6 e 5 8., ; 5 ; 6 5 ; ( )( ) , total umbe of stectum lie ae (5 ) lyme Balme Pasce bactt lie i visible eigo. ATOMIC STRUCTURE EXERCISE # Compeesi o #. C s s p 6 s p 6 d 5 s M + s s p 6 s p 6 d 5 s Fe + s s p 6 s p 6 d 6 Co + s s p 6 s p 6 d 5. ( ).7 ( + ) + + ( + ) ( ) Numbe of upaied electo + [A] s s. Fe + [A] d 5 Ti + [A] d Co + [A] d 6 all ae avig upaied electo ece paamagetic & coloued.. Fe [A] d 6 s ud's ad Pauli's piciple is voileted. ( ) ATOMIC STRUCTURE. Distace to be tavelled fom mas to eat 8 7 km () 8 m elocity 8 8 Time D/ m/sec 8.66 sec.. ( a ) I.P. E E E ( 5.6) 5.6 l.v. ( b ) E [ ( 5.)] 5. l.v. E (m).9m Spi quatum umbe (m s ),, tat is oe obital accomodate maximum e ((m s ),, e ) Numbe of elemet i ay peiod p (fo eve peiod o.) umbe of elemet 6. fo g - sub-sell 5,,,, {g - subsell} umbe of electo ( + ) 9 8 umbe of obital ( + ) 9 ay obital ca ave moe two electo EXERCISE # [A] ( c ) E.8 ( 5.6) l.v..5 (.m).88 7 m ( d ) (i) E 5.6 ( 6) (ii) E 5.6 ( ) J e E.77 9 e

6 . J () J [6.6 5 ] E L m R.9 7 m m.? [fist lie] [secod lie] R 9 Å R...(i) R...(ii) R R R (i) (ii) 86 Å 9...(i)... (ii) ( ).7 m... (iii) we will solve te tee equatio ad we will get R.96 7 m 9. E kj/mole J/mole. IE 85.. Radius 6(R) T.E..6 l.v..85 l.v..6 9 J..7 E eg 7 Joule.7 E.7 J.E egs (b) (m) cm.7 5 cm. E I.E..7 eg/atom (m ).7 7 J m m Å m Å () ~ 5.,, E.6 ( ) kj / mole 99.5 kj/mol e

7 6. ( i ) E.6.6 []. x v t ( i i ). R 8. e x x 7..8 mole (.8 Na) atoms 7% IIId eegy level.8 Na.7 5% IId eegy level.8 Na.5 E E E.8 N A.7 IE N A.5 IE 9.68 atom 8. Numbe of atom i d obit.5 N A Numbe of atom i d obit.5 N A Total eegy evolve.5 N A (E E )+.5N A (E E ) 9. Agula mometum. e e (m) o.5 () m m 9 m.6 m.6 6 m ( ) 5 6 Å R 6 5 x Å x 8 sec oud m so, o. of evolutios ( ) / E of Ist Bo obit o.6 (i m) (m) 9 Å. 7 9 R 65 z E (. + 7).6 E E.8 8 g / atom E (E E ) m.89 6 m/sec.89 8 cm/sec

8 6. 7. ( a ) ( / ) N Å 8 p.86 Å ( b ) E.7 IE 6 ( c ) IE.7 6 e max E IE k E IE B.E kj/mole w v e/atom v v v E e E 97.9 kj/mol E 5.67 e. + E + E w + E w + E w w w w [ ] w w 6.6 ( 5. 5 ) w w w E E E w w E E...(i)...(ii) w 8.9 kj/mol w E. e (m) 6 m.6 Å. (KE) max stoppig potetial () stoppig potetial.6 5. U avg. 8 kj m U avg U avg m Å volt x m v 6.66 x.67 7 kg x x.5 m e Cu [A]. s, d 9 o o. of ex cage pai ( ) 5 6 Total excages E of ligt absobed i oe poto ( E) absobed Let potos ae absobed, teefoe, ( ) Total eegy absobed() absobed Now, E of ligt e-emitted out i oe poto emitted (E)

9 Let potos ae e-emitted te, ( ) o Eegy coveted ito K.E J % of eegy used i kietic eegy Total eegy e-emitted out emitted % As give E absobed 7 absobed. + B.. B 7 E e-emitted out emitted 7 emitted 7 58 absobed 5.57 v B v B BE 9 kj / mole Å e/mole v o (m).. mole Na No. of potos (m) m.9 7 m 5. Eegy equied to beak bod 6. Eegy give to I molecule J Also eegy used fo beakig up of I molecule J Eegy used i impatig kietic eegy to two I atoms [.7.98] 9 J K.E./iodie atom [(.7.98)/] J Å.88 pm m 5. cm/sec 5 Å m 5 P m m g 5 m 5. v m/sec v. x J/molecule J Eegy of poto used fo tis pupose J Eegy left afte dissociatio of bod ( ) m.x.x 5.7 x.7 9..

10 ATOMIC STRUCTURE. Give tat m cm. 9 m. 7 cm ad v v v R R v R...(i) Fo lie I of Balme seies R 9678 o Fo lie II of Balme seies ; R 9678 o Tus give electoic tasitio occus fom 6 t to t sell. Also by eq. (i) (6 t t ) v cm. E ext kj/mol D.E kj/mol P RT.8. T.E kJ. E(ev) (m) Eegy of st poto.8 e 8.5 Eegy of st poto.79 e. E e (E 5. e) EXERCISE # [B]. Sice we obtai 6 emissio lies, it meas electo comes fom t obit eegy emitted is equal to, less ta ad moe ta.7 e. So it ca be li tis : (6 t.7 e ) E E.7 e, E E <.7 e, E E >.7 e (a), (E E ) atom (E E ) (b) IP.6.6 (.9). e (c) Maximum eegy emittede E (E E ).75 (.9).5e Miimum eegy emittede E (E E ).66 (.9).7e 5. E 7.e(7 +.) E E 7e E.e( ) 7 e.89 E. 9.6 e E E 7. e E 7. + E. e E Å E c J.75e So electo will excite to t eegy level ad we comeback umbe of emissio lie will be 6. miimum eegy emitted E E.66 e (t 6 ) 5 E m 88 Å 7. (a) ke q J (b) At distace d 5 m let K.E. is x J ad PE k qq d PE. J By eegy cosevatio : 6. x +. x.6 J, ke PE (.6 ) d d.8 m 9 9

11 8. pe du, sice F d Å m.9 Fo stable atom F mv ke mv so mv, PE mv...()...() E (ii).59.(a). m, E (ev). W 5 e A.65A.65 m e ke E W 75 e 75 volt T.E () (b) 5 A A. A Fom bo's postulate mv puttig tis i equatio () m m m puttig tis i equatio () T.E. E m m 6 6 m 6 m k e m k e 6 9.(a) (E E ) 68 e (E E ) z 6 (b) (ke) E e (c) Eegy equied E 89.6 e.5 m E IP R.8 8 J J E E.8 8 J E E E J c m (c) sice p dp d d dp (. ) d m. Sice electo is i some exited state of e + so it's eegy.6 e so eegy eed to exitatio is also <.6 e & oly fo ydoge E E <.6 e. So. Now fo e + tis eegy is equal to te eegy gap of d ad 6t obit so iitial state is ad fial state is 6. e +.6 e <.6 e E E <.6 e e + d 6t 6. mv R 8R 9.65