h133_1094_4_key

h133_1094_4_key - H133 1094 Session 4 lKEH Write your name...

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Unformatted text preview: H133: 1094 Session 4 lKEH \ Write your name and answers on this sheet and hand it in at the end. After the indicated time, move on to the next activity, even if you are not finished! 1. Quanton in a Box [12 min.] Start up the PhET applet "Quantum Bound States". (Start->Programs->PhET, choose " Quantum Phenomena" from the left menu, and click on the Quantum Bound States icon). This applet shows energy levels and the corresponding wavefunctions and probability densities for the energy eigenvectors of different potentials. The "square well" potential that comes up initially is a finite-depth version of the "quanton in a box" potential. a. What force would a Newtonian (i.e., classical) particle feel at each x position? Note that the " wavefunctions don't go to zero at the "walls" of the well; could this happen classically? Explain. IR“ 53‘ 9 m (Farm/a to CPLLl-Lg’l— l" in ”l" will out ’ro'l‘tu‘ lit d‘l' kms’ilwm 'LU'O five :1 3‘43er 0 ‘ fight? if K )6 :l *5 (Jose: 5 nee \iem 'pot ‘ moi mm mam org min. t. “EH-l :- b. For wtliaténergie’so would a quantorige "unbouhd'z" (Le, 11:? confined to i]? well)? 0‘ OWICPQ . $0.“ N'mfijoh "Slmulffiimi‘ \‘l‘ W“) lee unbgumi Spar me.) E7 “3”» c. Roughly predict the energy of the n=2 state (second-lowest energy) by estimating its wavelength from the simulation and using this to find the momentum and then the kinetic energy. (To show the wave function, click on the 2nd level, switch the Display to "Wave Function", and press "Pause" to stop time.) Compare to the value given by the simulation. N ‘ ‘5'; m ‘ in wo‘vfihncfifix 1‘: cues anm 2:) 9: WA oc (MW 2: “Pg“ “l : mow E a. 5:: 1 L293 ._., mos ‘ égi“;&5;vim assess» s Mira/136 w; empty _ ‘30“ PhD—mic; BtEmigmaV '1.»— ......M _\ URS-u‘i‘fx‘lm Nflxtu“ .31 \ d. PredICt (and explain) what will happen to the energy levels if you make the box 3 alloider. [Hint Does the wave function penetrate the walls more or less?] Check your prediction by selecting "Configure Potential" and reducing the "Height". Try a new explanation if you were wrong the first time. 93-5 CELL lots/.2 t5; mafia; Bellamy“ } fit wow Waiter) penal—muss m1 3so ll“ ”l3 \ontytcx 90 90 \5 smile ans “has; E“ guts clown. We; W3 with “its Simula im, e. Do two-minute problem Q8T.3. [See qupition (QSth) for reference] >\’-' Christel} Wiggl— winwlacfi a? 3—54.) 3a loweazslr to l+333, heist—oi) 50 ‘fimglra 3M :5 Ea / EL 60 li,% E ln CUM.) teller-ll E " wit ya ’ 2. l-tarmonic Oscillator [12 minutes] Chan go the Potential Well using the pulldown menu on the upper right to Harmonic Oscillator. This has the potential energy k*x2f2, which is the same as a spring. a. For what energies would a q anton be "unbound" 0.6., not confined to the harmonic oscillator)? “h envoys an. \aotm . b. Vibrational levels of olecules are described by a harmonic oscillator potential. Do problem (288.4. M0031"; waytlmfi) ‘ {items smolhdr (“r-0t ‘33 “:le 91L .z ,a “3%ve rm ,.- "r" “Mi. XM“ )x “tells ‘3 asst) am ' 9f «0}?2Vt c. Time dependence 1. Based on Rule 6, what is the time dependence of the probability density for the state with E2? (Find the time dependence of the wave functiori psi2(x,t) for a state composed only of eigenvector IE2> and th n calculate the probability density.) Does this agree with the simulation? may .. 8:" ”t in) 60 \HnJ-tilsilanyfimminstantiate: 063mg) d. Time dependence H. Now use "Superposition State" to make a state with equal parts E0 and E2 (so c0 and c2 should be equal). Choose "Normalize" and then "Apply". Measure the period of the probability densit usin the clock in the lower left. Bonus: How is the result rrfilated to the energies E0 and E2? \‘ fit if f \ 9W5) ”Hoot-D"- QWE: \E‘JCH‘ +13%) Q a. M stilt Mun i 3. Models of the Hydrogen Atomllti minutes] 6“ T553: (My ‘ 1565?; Start up the PhET applet "Models of the Hydrogen Atom". This applet simulates an experiment in which you shoot photons of many different wavelengths ("White") or a single wavelength ("Monochromatic") at a box with hydrogen gas. With the switch on "Experiment", you can see what actually happens outside the box. With the switch on "Prediction", you can compare various models ranging from more classical to more quantum mechanical to see what they predict. 3. Turn on the electron gun and ”Show Spectrometer". Take a look first at "Experiment", then switch to "Prediction". Try each of the models. Note that some are in clear contradiction to the experiment (e.g., the Billiard Ball model predicts many photons bouncing backwards). For the last three, “Short- electron energy diagram ". b. For the "Classical Solar System" model, there is quickly a "kaboom". What is happening and why? (filing the icon (again tpureplriy it.) How is th's axvoided i uantu mechanical models? ' \ $1;th new raw. ln'Qs 50m 8 mm 3 30°31 mart] g * m) 59mm mitt “it ct‘rief‘i’lctl grim WEB-El? pggofiggaéfg’oj qféi‘fgfi cw?) awn (JED c. How doeskae deBroglie model cdmpare i0 btligeBo model. (E. g., 51ml arities and differences.) QR: \"uM Maxims cream turbid“ mmsam cm (331 ‘mm . Cm, \‘p \ No Sn 9&ng C\V’L,Un\.m . as a porTxrlt <2: lie. mg"; mm as ex M»: onset) in at Q h. a) d. Which of the models will (approximately) reproduce the known hydrogen spectrum? .30)? \&%®§u 3 mod gdwr‘bgtfwago, 4. Discharge Lamps [12 minutes] Start up the PhET applet "Neon Lights and Other Discharge Lamps". This simulates the type of light we saw in class. You can show ”One Atom" of gas or "Multiple Atoms". Start with "One Atom". a. Switch from "Single" Electron Production to "Continuous" and click on the Spectrometer. What is the source of energy to move an atom from e ground stat to excited state? The est-h, e are tel “is, ex A between .- awe once: \sWQéQECW—A a; cdhe‘tencfmi'b TR (Ki—6mg. b. The Spectrometer shows only one wavelength of light. Why? What do you need to change to get more wavelengths? (Try it!) What if the energy of collision is less than the n=2 level (marked with a circled number ”17% is Mu) QRWM [LNG/H- MTM“ 5“) mite $4. (kt—3 LEW) 3 50 0m) awflimnt 0*) {C} {:9‘5?‘ Eugene. W {peg—E'm acts) ‘0») \nC‘i‘ChSh fit \I’Mcmy 46 05d more we»: v9 ‘5 ,fl \st ha ”he re“; “Mi {Maggi shrines PM «HM, c. Switch to "Multiple Atoms" and click on the Spectrometer again. Identify the wavelength of the red line and show that the Bohr model qqttantitatively predicts it. [Hint see Q8X.S on pg. £56.] Looks \\\Ce 685 mo 00. $.99? newéiet‘ ‘ _ ‘ 333*: it «misses {mamas (mm regressed a): thine / d. Hi Take a look at other atoms besides hy ogen. Why do they have more visible lines in Eh spectra? than, lMRT) \errls stem/h chug manuals Sb Tereifiw; use in its verb ...
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