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H133_quiz4_key - Name KE Physics H133(Spring 2011 Quiz#4...

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Unformatted text preview: Name: KE\/ Physics H133 (Spring, 2011): Quiz #4 Full credit 2 10 points Possibly useful relations: 2 h h 4 'U=/\f 14:77r w=27rf A2; Ezhf=hw= 3‘2 hc=1240eVenm (mcz)e— :0611MeV hc)2n2 , [€62 1 h? 157:5 41 EZ—<—4‘_'T' E =-— .~_= —13. 2 = :0. 53 L an‘l“ 2) n 8(TTLCA)L2 n,H 2a0,H n2 ( 6 eV)/n (10,}; mkeg 0 nm (hc)/(hw) 8m02L2 2(hc)a0 711271;} n12”; Aosci : —— /\ 014 : —-—4——— /\ T0 = z , _—_.— Ilv ni ‘ nf b hc(nf _ Tl?) hyd gen [C82 77,? _ n; (91 3 HUI) n12 .— 71?. 1. (2 pts.) (a) For a 1—dimensional box with infinitely high walls, the wavelength Agni? of a photon emitted during a transition from the 71:3 to the n=2 state is related to that of a photon emitted during a transition from n22 to 7121 by the following factor: i .. MT ,L >\ \5 0P1} ‘4‘ >:i>_5 3 ~ 03”“? L /\3_,2 2‘ . Ole . . ‘ /\2—+1 Tat-:33 $9,: .« box M f ~ 1 _ A C 4% U 3:7 l~~ LW 4 9. L " 3% SQLK (AN) C; {N493 “WAS 0.3"” “.1 \3 fl incmses 44% m (b) For a hydrogen atom, the wavelength A362 of a photon emitted during a transition from the 71:3 to the 7122 state is related to that of a photon emitted during a transition from 7122 to 77:1 by the following factor: m .m X373 ‘5 WE” mm“ l“ 3 a (— >“Jan”? C W ig‘ )\3—>2 : ‘ ' E‘Ll' ' ' ' )‘le \l! fififlfyq tomsfiw €9qu § :w « 3 —; Q? {“3608 lSMTS 5541\“304999 M 0, ”3"“ h (434.0: fl 3 '3 Show your work and check that your answer makes sense (e.g., should it be greater or less than one based on energy level spacings?). 2. (2 pts.) Explain qualitatively (e.g., in terms of quanton wavelengths) why the energy spacing in a harmonic oscillator increases with n more slowly than for a quanton in a box and decreases with n in a hydrogen-like atom. We 015900033 6% exam“; \94\/(\'S W 9 box TDMM 0 EQM‘wQ ltm ~ if“ . bs>4 wt‘t‘h \s W: 4 :mT‘ S3440 o4\\ 99°57qu ‘37:? r hormsmc 0244‘: Halo? 4‘ m 6&4T444 444M} 404414443 44‘444‘244444 $443444 943 N WT $4444 \W 644 4444444 QOQKDB We m 3‘ 0 \MC {4444544) ”Mm? Tut“ R34; R N Am); .4 ngm, 444 file Qwel ;4\ was N 443;“? 4444\W9 444a 4444:: 44495144 wT‘nC/f 444244434. 45?) Mm. Tm SQMHQB (ream 4'43 MCMSQ; . l 3. (2 pts.) For what range of energies is an electron bound in a hydrogen atom and for Vlr( what range of energies is it unbound? Explain. W E7 0 View E70 J\\ \Jst om \m (>th \jzomge “in Wall on C(11) ._- QQVQQ9 "‘0 \Q‘Pfifiks [0 CC? ELQ ah lumls on 291‘le <1)"6 I légv,mh1}%r“ 4. (2 pts.) Consider the lowest energy eigenstate for the Li++ ion (three protons, four neutrons with a single bound electron). (a) The electron’s orbit in that state will have the following approximate mean radius (fill in the value): JMJJJJJJJ _ JJJJ t; Wale 9“ ill“ I 3230 7‘1,Li —; ........... nm (5m 0)“ if)“ ANS (Ni) 3 N (wig; I Ni Warm 0&le \r\ LlofiQC # (\Eqfi Wot WV MKA 90(31):“ ill) 3 ON) ilk A ‘ Mlle J0 J5 \SKGGQJ) Si) q5L {DUN (j 2 JJ—JJJJV) JJJJJJ W JJJ J M Show your work and explain your results! 5. (2 pts.) In terms of 71., m, and u), what is the time dependence of the 3rd—lowest energy eigenvector in a harmonic oscillator and what is the time dependence of its probability density? (Just give the time— dependent part of the wave function.) Explain your answers. One point for each fixpart. F J’JJJJJJJ‘lJ) JJJ JJJ J 30 in 3“) lml (W 15 EMEJJJJ mink“) g fl)“ “$210) wimtw. ”(Ema 5 lllflx E)°< 61% TR (ml-Nkhéy §~N¥>le \3“ W93 (X 4(3)) hi)” )6: :5:th =i iii-9'9 J“); W “)“Jm AMQJQM My? ...
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