Shedding light on atomic energy levels (segment of Hydrogen spectrum)

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3.0 ev.85 ev.55 ev.69 ev Fri. 8.4-.7 More Eergy Quatizatio RE 8.b Mo. Tues. Wed. Lab Fri. 9.-., (.8) Mometum ad Eergy i Multiparticle Systems 9.

1 3.0 ev.85 ev.55 ev.69 ev Fri More Eergy Quatizatio RE 8.b Mo. Tues. Wed. Lab Fri. 9.-., (.8) Mometum ad Eergy i Multiparticle Systems 9.3 Rotatioal Eergy Quiz 8 Review Exam (Ch 5-8) Exam (Ch 5-8) RE 9.a HW8: Ch 8 Pr s, 3, 7(a-c) RE 9.b Practice Exam (brig to class) Sheddig light o atomic eergy levels (segmet of Hydroge spectrum)

2 Where we ve bee: Eergy o the macroscopic scale Eergy o the atomic scale Where we re goig: Eergy o the electroic scale + 0 electro m v e e electro& ucleus 4 o eq r uc hydroge 4 o e r Mathematically like solar system, but much too small ad delicate to directly see orbital radii ad speeds eed aother way to deduce

3 Hydroge Eergy Levels etc. 3.6eV ev ev -.5 ev = = 5 = 4 = 3 Excited States 3.6eV ev = 4 o e r 3.6eV -3.6 ev = Groud State

4 Hydroge Eergy Levels: Excitatio 3.6eV ev ev -.5 ev = = 5 = 4 = 3 Excited States ev = -3.6 ev = Groud State

5 Hydroge Excitatio: st i groud state 3.6eV ev ev -.5 ev = = 5 = 4 = 3 Excited States ev = -3.6 ev Marks the occupied state = Groud State

6 Hydroge Excitatio: d Adsorbs eergy from Collisio 3.6eV ev ev -.5 ev excites to d state = = 5 = 4 = 3 Excited States ev = -3.6 ev = Groud State

7 Hydroge Excitatio: 3 rd Looses Eergy by photo emissio, 3.6eV ev ev -.5 ev de-excites to groud state = = 5 = 4 = 3 Excited States ev = Photo Emissio E E E ph ph ph E H 3.6eV 0.eV 3.6eV -3.6 ev = Groud State

8 Example Atoms i Gas-Discharge Tube 06_Adsorb_emit.py.

9 Frak-Hertz Experimet Moitorig electro beam s loss of eergy to the atoms Hydroge Gas Discharge Tube e Eergy of Hydroge s = to trasitio 0.eV Electro s kietic eergy High acceleratig voltage Medium acceleratig voltage Low acceleratig voltage Distace alog tube Differet exitig kietic eergies are reflected i differet curret readigs

10 Here are the quatized eergy levels (+) for a atomic or molecular object, ad the object is i the "groud state" (marked by a dot). A electro with kietic eergy 6 ev is fired at the object ad excites the object to the 5 ev eergy state. What is the remaiig kietic eergy of this electro? a) 9 ev b) 6 ev c) 4 ev d) 3 ev e) ev - ev - ev -5 ev -9 ev

11 Absorptio Spectrum 06_spectrum.py.

12 A collectio of some atoms objects is kept very cold, so that all the objects are i the groud state. Light cosistig of photos with a rage of eergies from to 7.5 ev passes through this collectio of objects. What photo eergies will be depleted from the light beam ( dark lies )? a) ev, 5 ev, 9 ev b) 3 ev, 4 ev c) 0.5 ev, 3 ev, 4 ev d) 4 ev, 7 ev e) 3 ev, 4 ev, 7 ev - ev - ev -5 ev -9 ev

above some threshold frequecy, f, electros are freed, curret Threshold frequecy relates to metal plate s ioizatio eergy (work

13 Quatitatively Relatig Light s Eergy ad Frequecy The Photo-electric Effect Ioizig metal plate Shie moo-chromatic (sigle color) light o metal ith low frequecy light, o matter how bright, o electros are freed, o curret measured ur up frequecy; at ad above some threshold frequecy, f, electros are freed, curret Threshold frequecy relates to metal plate s ioizatio eergy (work fuctio) by E = hf Deduce: light falls like rai with packets of eergy related to its frequecy E = hf h = Js = evs

14 Example: He-Ne laser. Gas discharge tube filled with He ad Ne. They have a rich emissio spectrum but the tube s legth, like the strig of a piao is right to help light resoate at just oe frequecy, Hz, a rich red. How much eergy does oe red photo of from the He-Ne have? This is a 0.95mW = J/s laser; that s the rate at which the beam of photos carry away eergy. How may photos are emitted per secod?

15 q Simple Harmoic Oscillator Eergy spectrum & Structure Eergy 3 s m ax. eq eq eq s m ax. k Imagie a charged particle ridig a mass o a sprig E system = E light = hf s (stretch) ssmax. kssmax. kssmax.3 eq f kss ks m Radiates light with the same frequecy as its ow oscillatio hf E light Mass-o-sprig must loose this much eergy Still oscillatig at same f agai radiates light of frequecy f. Etc. eq

16 q Simple Harmoic Oscillator Eergy spectrum & Structure Imagie a charged particle ridig a mass o a sprig f ks m We ve deduced Eergy s m ax. s (stretch) eq eq kss k s s max. E mi Takes real Quatum Mechaics to ail dow E mi : hf Emi eq hf where =,,3, eq k s s max. eq

0 kg mass o our 3 N/m sprig, iitially displaced 0.

17 Example: Macro-scopic mass o sprig We certaily do t otice that a mass o a sprig has oly specific allowed eergies, it seems to be able to oscillate with ay eergy / amplitude (util it breaks). Give a 0.0 kg mass o our 3 N/m sprig, iitially displaced 0.m, how much eergy has it got, ad how big is the step to the ext eergy level lower? How about a H molecule, what s the eergy step size for its vibratios? Roughly 0-7 kg mass protos ad 00 N/m sprig costat.

18 Two atoms joied by a chemical bod ca be modeled as two masses coected by a sprig. I oe such molecule, it takes 0.05 ev to raise the molecule from its vibratioal groud state to the first excited vibratioal eergy state. How much eergy is required to raise the molecule from its first excited state to the secod excited vibratioal state? ) 0.05 ev ) 0.05 ev 3) 0.05 ev 4) 0.0 ev 5) 0.0 ev

19 Molecule A: atoms of mass M A Molecule B: atoms of mass 4*M A Stiffess of iteratomic bod is approximately the same for both. Which molecule has vibratioal eergy levels spaced closer together? ) A ) B 3) the spacig is the same Suppose the atoms i diatomic molecules C ad D had approximately the same masses, but Stiffess of bod i C is 3 times as large as stiffess of bod i D. Which molecule has vibratioal eergy levels spaced closer together? ) C ) D 3) the spacig is the same

20 Pb: k s ~ 5 N/m Al: k s ~ 6 N/m Which vibratioal eergy level diagram represets Pb, ad which is Al? ) A is Pb ad B is Al ) A is Al ad B is Pb 3) A is both Pb ad Al 4) B is both Pb ad Al

21 Stiffer / stroger bods, bigger steps betwee eergy levels Type of State Eergy Scale Hadroic (quark composites) 0 8 ev Nuclear (ucleo composites) 0 6 ev Electroic (atoms & molecules) ev Vibratioal (molecules) 0 - ev Rotatioal (molecules) 0-4 ev

Phys 102 Lecture 25 The quantum mechanical model of light

Phys 102 Lecture 25 The quantum mechanical model of light Phys 102 Lecture 25 The quatum mechaical model of light 1 Recall last time Problems with classical physics Stability of atoms Atomic spectra Photoelectric effect Quatum model of the atom Bohr model oly