HWsoln_27_28

HWsoln_27_28 - 2?.2 U5.ng Wicn‘s (lispluccnmnl law. a...

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Unformatted text preview: 2?.2 U5.ng Wicn‘s (lispluccnmnl law. a 0.289 8 X IIUI"2 m ~ K {a} Ania]: _+ H) Ix =2.898>< Itfi m ~ IOU nm a (12898 X I0‘2 I11 ~ K _m _l 1 H Am“ T— X [TI 2?.5 e . . -. —3_1 . J The energy el :1 phelen IS gur'en by E 2 E19“ 2 heth 1where h = 6.63 >< IU J '5; IS Plenek 5; eenslenl. m. (“awn—341.5)(3eexlean-=5) Leeuv ee E=+=—_j[—_m]= 2.49xl0'5eV x, 5.ee><|e- m l.e0><|(} J . ’e.e3>< IU'“ J4; '3.ee>< IUS mxs‘ a r {M £3ch )(4 .. ){ LUULL ]: 249W ,2, meme m Ihflx Ie J - “new we“ J4! '3.ee><1e3 m..--'.~;~ a I ,2, 5.ee><1e m _].eU><]U J 27.3 The energy entering the eye eneh seennrl is , _ V 33' , _ _ ~3 _ r :13: LA =(4.0>< In “ ‘W/ITT)|::(3J x10 3 m) J: 2.3x IU 15 v»- The energy el' :1 single phelen is - “mm X III“ 1.5! “3110x103 nix-'5‘ E=$=(_—H_Q'J= 3.98 >< IU'” J x, 300x IU 111 an llie nuniher nl' phelens entering the eye in gr 2 1.00 5; is; 3E rpm} (2.3x IU'” J_..-"s‘){1.ee a} 1 E E 3.93 :><](i'1ng J 27.14 The lerlnl energy-r nb5erberl b}! an eleelren i5 -J'9 1: E: re+KEm : 3.44 eV[% +%{9.] | x 10"“ kg)(4.2 >< IIE]5 [11/5 L. L . . er E=fi.3>< IU'” J The energy :1b5erberl by n 5qunre eenlirneler r51” 5nrl‘nee in UI‘IL‘ 5eee+nr| i5 5.15 = (19.: = (I~A]~r= (0.055 1R-’/|112:](|.UU:=<|0'4 "finer: 5}: 5.5 5:11:an 545 the number rrl' eleelrbns relen5ed per 5eeend i5 5.5 X I'D—6 J -12 E fiugx 10-19 J - 27.16 A plielen el' maximum energy and minimum iii-unrelenglh i5; preelueed 1when [he eleeli'ern gives; up all its; kinelie energy in n Hingle eellisiene er Am 2 fie/XE = fie/EV. a _ ‘ (hhSXHTMJrfl[Afl}xHfinflfl w _H in) V = Kym-m = X m a & maxmmJflflmmnflmfl T M [h] II V: 1(1) kV. ram-m = fi: I'L4 X10 m nmxm Qmmmev) iei A5; Seenzihmfie‘ x1 deerensen when [he pelenlinl LIilTereneee V. inerennes. min 27.28 The rle Breglie sit-'tts-‘elength (if n pnrtiele el' mass m. is A = My where the nitinientuni is given by TI p: yew: mzr/ l—(nfe) . Nnte that when the pnrtiele is net relutmstie, then y r: ], nnrl this relntivistie expression I'nr mernentuni reverts heek tn the elnssienl expression. in} Fer :1 pretrrn Inns-'ingr at speed it: 2.t)t)>< It]4 ni/s, 11¢: e 3an y =1 se "i ‘34 . 2,: h ——M’“‘X'U 15" )= |.98><]t)'”m :an _ [1 m ><: 10—” kg)(2fl{} x m“ nit-"'5; th‘t Fer :1 pretrrn them-insr at speed 11:" .tltlx It}? m/s 2,: h = h 1—{v/cf ympfl‘ mp“ ' (h.h3>< In“ 1.5;) _ (Ls? r>< Hr” kg}(2.ee x In? nix-s) 2.00 In? 2 |— = l.‘.~}8>~<|t)'J4 In 3.0UX It} mgs 27.31 in} The required eleelren nmmenlum is keV s m h ms X 10—34 J~s[ | keV _}:—: — I use s: 10'm J J :1 HM 10'“ m :1an the Intel energy is E = agile"? + E; keV~ s m 2 (41 >< I04 ] (3.00): 103 m/s.)2 +{5I1 L'er 2526 keV The kinelie energy is lhen KEzE—EgzfififikeV—Sllkevz . "same—34 J.s”s.0(:-><|03 ms’s‘ w - rm E=i=%w[%]= 1.2mm keV x, |.U><]() m Ihflxlfi J 27.34 The mnmenlum el' [he hlnek is p = my. and if the mean. is; known preeisely, [he uneerluinly in [he memenlum is fip 2 may. Frem [he uneerlninly prineiple, E h/flrrrw m if there is en uneer- lninly el' ex: (150 em = 5.0 X I'D—3 m in [he peeilien el' lhe pnrlielee the minimum uneerlninly in its; Spflfl'd in - :r' . n are Hr“ Jr: _, (emf). =%=—. 2.1x III} 3' m/s - m. 4mn(&x)m 4n{_{}.3{}kg}{5.flxlfl' m) 27.36 (a) With uncertainty in: in pesitien. the minimum uncertainty in the speed is flip it 2:: J~a _ - _ $3.: I E —=+= 0.230 m '5': '1 m. 4PTIH{_.-ir) 4::(21I) kgll | .00 In} th) II" we knew Fuxxy‘a initial pnaitinn ancl yeleeity exactly; hi5 Iinal pnaitinn al'ter an elapaetl time I weuld he giyen by X}: 2 xi; + vii. Since we have uncertainty in heth the initial peei- tien antl the speed. the uncertainty in the tinal [mailien i5; ax j, = ml: +(fleI )r = I .00 m +(e.250 m/a)(5.tltl a): 23.8 [a] With the eleelrieel l'eree supplying the eenlripelzll eeeelerfllien. nevi/r; = kfel /r,f, 13kg: /ml,rfl . 1where 2;? 2 film] 2 n2{(].()52 9 nm}. gwmg efl Thus‘ M2 (meme? N.nfi..-’t::2‘)(|.6ex10—19 (7)2 6 pl: E = fi=mxle m/s {9.||><l()' kg)(e.e-529><le m) (h) ICEl 2%mfzrfzg(9.l l>< le'“ kg)(2.]9>< Ie6 [11/5]; ._. L. =2.]8><]U"3 {i}: 1.60%: IIUI'“;J J Ir '—.J .: “8.99mi? N~.n?..-"e2‘ “moxie”? CE n {ensegxm m) 2—4.35 X I'EII'l8 J: —2?.2 eV 23.13 The unurgy ahgm‘hcd by lhc alum is 23.17 {a} The energy emitted by [he elem is; AEzE4—E2 =—13.e eV[4]3 — :3 ]= 2.55 w The wan-'elenglh el' lhe phelen predueetl is lhen he he (6.6.axltm'“1.5)(3eex103 Inf-"5) E, at" (2.55 uv)(1.ne><1er19 J,-"eV:} = 4.88 x10"? [11 = x || || | eenrfnued an ear gmge {hi Since. nmmcnlum must he cunsurvcuL lhu: phnlnn and lhu: alum gun in uppnsilu directions with equal magnitude mmncnlzi. Thus. p = Himmfl = Fit/i. ur h fi.h3>< 10'“ 1.5 “2—:ejé: 0.314 m 5; mate-m f” 23.23 r=— m fi=_ :13 FE ' r?an ao_0.0529nm z z z 2 mykve {10 Fur HCJ" Z: 2 and r: 0.052 9 nun/2 = 0.026 5 nm . {h} Fur Lipfl Z: 3 and r: 0.052 9 nun/3 = I000]?r 6 nm . 0:} Fur Barf”. Z: 4 and r: 0.052 9 nun/4 = 0.013 2 nm . 28.31 in] For Eluulrnn #l nml nlm I‘nr Eluclrnn #2. n = 3 illI'LI F = |.T|n: nllnrr qunnllnn numhcrr; I'nr each of lln: EU nllnwml slnlcs‘ urn Iischl in lln: lnhlus hulnw. Elcclmn #I Elcclmn #2 H Elnclmn #I Elnclmn #2 H Then: an.) 3H nllnwml slnlcs ‘ since Eluulrnn #I cnn Inn-1: any nl"ll1ru:.: pussihlc x-‘nlucra nl~ ml, I‘nr hnlh spin up and Hpil'l LIUWIL [Ululing six pnwihlc HlillL‘S. Fur catch nl‘ llmsc Slillflfi. Elm:— lrnn #2 can In: in cillnn' nl' lhc rcnmining Iiw slums. 23.33 to} Zireoniuni. with 40 eleetrons. has 4 eleetrons outside a elosetl krypton eore. The krypton eore. with 36 eleetrons. has all states up through the 4p suhshell Iilleel. Normally. one would expeet the next 4 eleetrons to go into the 4d suhshell. However. on eseeption to the rule oeeurs at this point. untl the is suhshell Iills [with 2 electrons) hel'ore the 4d suhshell sturts tilling. The two remainingr eleetrons in rireoniuni are in on ineotnplete 4d subshell. Thus. n = 4. and If: 2 for eneh ol' these eleetrons. th) For eleetrons in the 4d suhshell. with i: 2. the possible values ol‘ mt. are my 2 t}. i |. i2 ontl those for MS are ms 2 i I/2 . tel We have 40 eleetrons. so the eleetron eonligurution is: I32 233 2;? 333 3;? 3d” 433 4106 46?? so = [Krl4d2 sf ...
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This note was uploaded on 09/13/2009 for the course PHY 102 taught by Professor Luo during the Spring '08 term at SUNY Buffalo.

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HWsoln_27_28 - 2?.2 U5.ng Wicn‘s (lispluccnmnl law. a...

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