Development of QM. What do we know from classical physics? 1. Energy can take any continuous value.

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1 Developmet of QM 1-1 What do we kow from classical physics? 1. Eergy ca take ay cotiuous value.. Electromagetic radiatio is a electric field oscillatig perpedicular to the directio of propagatio. 3. Ay frequecy of light with eough itesity should cause a e - to be emitted from a metal. 4. Light is a wave.

2 Cotradictios to Classical Physics 1-1. Blackbody Radiatio. Photoelectric Effect 3. Emissio Spectra of Atoms 4. Rutherford s Backscatterig Experimet

ca be measured, but could t be explaied by classical physics.

3 Blackbody Radiatio 1-3 Picture a metal bar heatig i a fire Observe: Radiatio emitted i higher ad higher frequecy (red blue) as temperature icreases The shift i frequecy ca be measured, but could t be explaied by classical physics. Cautio: Sittig ear recreatioal fires, such as bofires, ca lead to death from radiatio exposure withi hours.

4 Photoelectric Effect 1-4 Photoelectric effect UV light impigig o a metallic surface causes electros to be ejected. Classical physics could t explai two experimetal observatios: 1. K.E. of ejected e - is idepedet of the itesity of icidet radiatio.. There is a threshold frequecy, ν 0, that is characteristic of each metal.

5 Rutherford s Experimet 1-5 Rutherford s experimet: α particles shot at thi gold foil some particles passed through foil but some were scattered. Rutherford s hypothesis: atoms i the gold cosisted of a heavy, positively charged ucleus with egatively charged electros orbitig ucleus. Classical physics: A movig charge emits radiatio, causig the charge to slow dow. As it slows, the cetrifugal force decreases ad electro falls ito the ucleus. Alpha Gold Foil Detector Erest Rutherford Rutherford s Experimet

6 Rise of Quatum Mechaics 1-6 A ew theory was eeded, ad was ultimately developed, to explai these observatios ad experimets Quatum Mechaics! Quatum Mechaics 1. is ot a correctio to classical mechaics.. is a foudatio for uderstadig all chemistry. 3. is a ew way of describig the mechaical properties of very light objects. 4. sometimes cotradicts what we observe macroscopically. 5. does explai observatios o the microscopic scale.

Blackbody Radiatio - Redux 1-7 Max Plack Max Plack assumed the oscillatig electric field of EM radiatio had discrete eergies ad were proportioal to the frequecy.

7 Blackbody Radiatio - Redux 1-7 Max Plack Max Plack assumed the oscillatig electric field of EM radiatio had discrete eergies ad were proportioal to the frequecy... E hν where a iteger, h Plack s costat, ν frequecy With this assumptio, blackbody radiatio observatios ca be explaied by: 3 8πh υ dυ dρ( υ, T ) ρυ ( T ) dυ 3 / k T e h υ B c 1 To match experimetal blackbody radiatio measuremets, h J s.

8 Eistei & The Photoelectric Effect 1-8 Eistei expaded Plack s theories, proposig that radiatio (e.g., light) exists as small packets of eergy photos. Eistei KE e- hν - φ Eergy of light Work fuctio Work fuctio: miimum eergy eeded to remove electros from a specific metal. Eistei s theory explais all observatios about the photoelectric effect.

9 Hydroge Atomic Spectrum 1-9 ~ 1 υ λ υ c Joha Balmerυ Balmer determied that the visible emissio spectrum of the H atom ca be described by: ( 4 ) or ~ υ , 4, ( ) 1 1 Johaes Rydberg Rydberg geeralized this formula to accout for all of lies i the H atomic spectrum: ~ 1 1 υ R H 1 > 1, R H cm -1

Niels Bohr ad the Atom 1-10 To explai Rutherford s backscatterig experimets, Bohr assumed: 1. Electros have statioary orbits.. The de Broglie waves of the orbitig electro must be i phase.

10 Niels Bohr ad the Atom 1-10 To explai Rutherford s backscatterig experimets, Bohr assumed: 1. Electros have statioary orbits.. The de Broglie waves of the orbitig electro must be i phase. Niels Bohr With these assumptios, the agular mometum of a electro, the radii of electro orbits, ad the eergy levels ca be determied. All are QUANTIZED!! Agular Mometum: h m e υr π h 1,, 3 Radii of orbits: r ε π 0h 4 mee πε 0h m e e At 1 Bohr radius r m 5.9 pm a 0 Eergy: E KE + V ( r) 1 m υ e e 4πε r 0 e 8πε r 0 E 1 is groud-state eergy,,3,4 are excited states m e 4 e 8ε 0h

11 Summary of Chapter Classical physics was uable to explai some observatios o the microscopic scale. Heiseberg, Schrödiger, Dirac, ad others formulated a ew mechaics Quatum Mechaics. These slides summarize some of the importat cocepts leadig to the developmet of QM read your book (ad others) for more details!

PHYS-3301 Lecture 7. CHAPTER 4 Structure of the Atom. Rutherford Scattering. Sep. 18, 2018

PHYS-3301 Lecture 7. CHAPTER 4 Structure of the Atom. Rutherford Scattering. Sep. 18, 2018 CHAPTER 4 Structure of the Atom PHYS-3301 Lecture 7 4.1 The Atomic Models of Thomso ad Rutherford 4.2 Rutherford Scatterig 4.3 The Classic Atomic Model 4.4 The Bohr Model of the Hydroge Atom 4.5 Successes