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 orbits that fit e λ allowed Agular mometum, eergy, radius quatized L Today: Quatum model of light istei s photo model 2 Today Z 13.6eV 2 r 2 Z 0.0529m 1, 2, 3... Phys. 102, Lecture 25, Slide 2
Atomic uits At atomic scales, Joules, meters, kg, etc. are ot coveiet uits lectro Volt eergy gaied by charge +1e whe accelerated by 1 Volt: U qv 1e = 1.610 19 C, so 1 ev = 1.610 19 J Plack costat: h = 6.626 10 34 J s Speed of light: c = 3 10 8 m/s hc 25 210 J m 1240 ev m lectro mass: m = 9.1 10 31 kg mc 2 13 8.210 J 511, 000 ev Phys. 102, Lecture 24, Slide 3
Photoelectric effect Light shiig o a metal ca eject electros out of atoms (UV) Light Photoelectro Maximum kietic eergy of electro K W Light must provide eough eergy to overcome Coulomb attractio of electro to uclei: W 0 ( Work fuctio ) e light ergy of M wave 0 Work fuctio of metal Phys. 102, Lecture 25, Slide 4
Classical model vs. experimet Classical predictio K W 1. Icreasig itesity should icrease light, K e 2. Chagig f (or λ) of light should chage othig e light 0 I uc light light + + + xperimetal result 1. Icreasig itesity results i more e, at same K e 2. Decreasig f (or icreasig λ) decreases K e, ad below critical value f 0, e emissio stops DMO Phys. 102, Lecture 25, Slide 5
Photo Model of Light istei proposed that light comes i discrete packets called photos, with eergy: Photo eergy photo hf Frequecy of M wave f c λ Plack s costat 34 h 6.62610 Js x: eergy of a sigle gree photo (λ = 530 m, i vacuum) photo hc λ 1240eV m 530 m 2.3eV hc 1240eV m ergy i a beam of gree light (ex: laser poiter) light Nphotophoto CheckPoit 2.1: Higher/lower λ = lower/higher Phys. 102, Lecture 25, Slide 6
ACT: CheckPoit 2.2 A red ad blue light emittig diode (LDs) both output 2.5 mw of light power. Which oe emits more photos/secod? A. Red B. Blue C. The same Phys. 102, Lecture 25, Slide 7
Photoelectric effect explaied Quatum model 1. Icreasig itesity results i more photos of the same eergy 2. Decreasig f (or icreasig λ) decreases photo eergy xperimetal result 1. More e emitted at same K e 2. Lower K e ad if hf photo < hf 0 = W 0 e emissio stops K hf W e 0 K e W 0 Phys. 102, Lecture 25, Slide 8
ACT: Photoelectric effect You make a burglar alarm usig ifrared laser light (λ = 1000 m) & the photoelectric effect. If the beam hits a metal detector, a curret is geerated; if blocked the curret stops ad the alarm is triggered. Metal 1 W 0 = 1 ev Metal 2 W 0 = 1.5 ev Metal 3 W 0 = 2 ev You have a choice of 3metals. Which will work? A. 1 ad 2 B. 2 ad 3 C. 1 oly D. 3 oly Phys. 102, Lecture 25, Slide 9
Atomic spectra lectros i atom are i discrete eergy levels = 4 = 3 2 Z 13.6eV 2 r e ca jump from oe level to aother by absorbig or emittig a photo Absorptio (e jumps up i eergy) hf i f = 2 Absorptio missio missio (e jumps dow i eergy) hf i f = 1 Oly certai f (or λ) are emitted or absorbed > spectral lies ergy levels are differet for elemets, so spectra are differet ergy is coserved hf DMO Phys. 102, Lecture 25, Slide 10
Calculatio: H spectral lies Calculate the wavelegth of light emitted by hydroge electros as they trasitio from the = 3 to = 2 levels = 4 = 3 = 2 missio: hf i f hc 2 1 1 Z 13.6eV λ 2 2 f i 1 Z 1 1 λ 2 7 1 1.097 10 m 2 2 f i 7 λ 6.5610 m Usig hc 1240eV m = 1 Phys. 102, Lecture 25, Slide 11
Solar spectrum Spectrum from celestial bodies ca be used to idetify its compositio Hydroge Solar spectrum Su radiates over large rage of λ because it is hot (5800K). Black spectral lies appear because elemets iside su absorb light at those λ. Phys. 102, Lecture 25, Slide 12
ACT: CheckPoit 3.1 lectro A falls from eergy level = 2 to = 1. lectro B falls from eergy level = 3 to eergy level = 1. Which photo has a loger wavelegth? A. Photo A B. Photo B C. Both the same = 4 = 3 = 2 = 1 Phys. 102, Lecture 25, Slide 13
ACT: CheckPoit 3.2 The electros i a large group of hydroge atoms are excited to the = 3 level. How may spectral lies will be produced? A. 1 B. 2 C. 3 D. 4. 5 = 4 = 3 = 2 = 1 Phys. 102, Lecture 25, Slide 14
Fluorescece Molecules, like atoms, have discrete eergy levels. Usually may more, ad orgaized i bads Decay is o radiative, usually goes ito vibratioal/rotatioal eergy of molecule Absorptio missio emissio emissio Groud state DMO λ λ absorptio absorptio Fluorescet molecules that emit visible light absorb shorter λ (ex: UV) Phys. 102, Lecture 25, Slide 15
Youg s double slit revisited Light itesity is reduced util oe photo passes at a time Iterferece patter = probability d si θ mλ Wait! Is light a wave or a particle? Both! What if we measure which slit the photo passes through? Iterferece disappears! Phys. 102, Lecture 25, Slide 16
ACT: Photos & electros A free photo ad a electro have the same eergy of 1 ev. Therefore they must have the same wavelegth. A. True B. False Phys. 102, Lecture 25, Slide 17
Summary of today s lecture Quatum model of light Light comes i discrete packets of eergy Light itesity is related to umber of photos, ot photo eergy Spectral lies Trasitios betwee eergy levels Wave particle duality Waves behave like particles (photos) Particles behave like waves (electros) photo hf hf hc λ Phys. 102, Lecture 25, Slide 18