* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download cp351c04
Survey
Document related concepts
Renormalization wikipedia , lookup
Matter wave wikipedia , lookup
James Franck wikipedia , lookup
Elementary particle wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Astronomical spectroscopy wikipedia , lookup
Mössbauer spectroscopy wikipedia , lookup
Tight binding wikipedia , lookup
Wave–particle duality wikipedia , lookup
Geiger–Marsden experiment wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Atomic orbital wikipedia , lookup
Electron configuration wikipedia , lookup
Transcript
Chapter 4: Atomic Structure The Nuclear Atom The Atom as the smallest division of an element quantization of electric charge oil drop experiments q = ne e/m => mass of electrons neutral atoms as “natural” state “Plum Pudding” model - - - - BUT..... cphys351 c4:1 Rutherford scattering (alpha particles from heavy nuclei) = test of “plum pudding” model a alpha particles emitted in some radioactive decays speeds ~ 2E7 m/s q = +2e, m ~ 8000 x me (a is a He4 nucleus) light flash alpha source thin foil lead collimator cphys351 c4:2 Expected (from plum pudding): small scattering angles, no back scattering - - - - Results: some larger scattering angles, including some back scattering The Nuclear Atom: small heavy nucleus (99.8% of atom’s mass) with positive electric charge ~ 1/100,000 radius of atom electron “cloud” => electrons orbit nucleus cphys351 c4:3 Rutherford Scattering (theoretical results): N( ) ntZ2 e 4 Ni (8 0 ) 2 r 2 KE 2 sin 4 ( /2) N( ) fraction of incident particles scattered at Ni n number of atoms per volume in foil Z Atomic number (number of protons in nucleus) r distance from foil to screen KE initial KE of alpha particles t = foil thickness 45 90 135 180 cphys351 c4:4 Rutherford’s ingredients: Newtonian Mechanics (F = ma) 1 q1 q 2 1 q1 q2 F ;PE Coulomb Interaction 2 4 0 r 4 0 r => Distance of closest approach Conservation of Energy Ei (a at large distance) E f (a at turn around) KE 0 0 PE 1 Ze2e 1 2Ze 2 KE R 4 0 R 4 0 KE Example: The maximum KE of alpha particles from natural sources is 7.7 MeV. What is the distance of closest approach for a gold nucleus? (ZAu = 79) cphys351 c4:5 Electron Orbits: planetary models of the atom for the purposes of this discussion, take electron orbits to be circular Hydrogen: single electron atom 1 e2 1 e2 FE ; PE 2 4 0 r 4 0 r 2 mv 2 1 e Fc FE 12 mv 2 12 KE - 12 PE r 4 0 r also v e 4 0 mr 2 1 e E KE PE - 12 PE PE 12 PE 8 0 r Example 4.1: The ionization energy of Hydrogen is 13.6 eV (the energy required to liberate the electron from the atom). Find the orbital radius and speed of the electron in a hydrogen atom. cphys351 c4:6 Problems with the nuclear atom: accelerating charges radiate orbits cannot be stable!! considerable problems with atomic spectra cphys351 c4:7 gas discharge tube Atomic Spectra emission line spectra (from thin, hot gas or vapor) spectrum tube contains rarified gas or vapor through which a high voltage is discharged prism collimating slit screen or film typical emission spectra Hydrogen Helium emission spectra vs. absorption spectra Mercury 700nm 400nm cphys351 c4:8 Hydrogen spectral series: patterns in the spectra 10 100 1 1 Balmer R 2 - 2 n 2 n 1 1000 n 3,4,5, R 0.01097nm-1 1 1 1 Lyman R 2 - 2 n 2,3,4, 1 n n 1 1 1 Paschen R 2 - 2 n 4,5,6, 3 n n 1 1 1 Brackett R 2 - 2 n 5,6,7, 4 n n 1 1 1 Pfund R 2 - 2 n 6,7,8, 5 n n 10000 (visible light) (UV) (IR) (IR) (IR) cphys351 c4:9 Bohr Atom electron in orbit about nucleus atomic size ~ electron orbit radius (or see example 4.1) = 0.053 nm compare de Broglie wavelength with radius v h mv e 40 mr (from " planetary orbit" ) h 40 r e m with r 0.053nm, 0.33nm 2 r cphys351 c4:10 h n n 2rn n pn ... Bohr’s original hypothesis: quantize angular momentum of circular orbits h L mvr Ln n n 2 h nh 2rn mvn rn n n n 2 mvn Bohr’s hypothesis justified by de Broglie wave theory cphys351 c4:11 Energy in the Bohr Atom n n 2rn free electron n= ... E > 0eV E = 0eV ... h 40 rn 2rn n e m n n2h 20 2 rn n a0 2 me h 20 a 0 r1 0.05292 nm 2 me e2 me 4 1 En 2 2 2 80 rn 8 0 h n n=3 E = -3.40eV n=2 E = -13.6eV n=1 E1 E n 2 , E1 -2.18 10 -18 J -13.6eV n cphys351 c4:12 Origin of Line Spectra Discrete Energy levels + conservation of energy + photons hc Ei E f h E f 1 Ei Ei - E f hc E1 ni 2 (any atom ) , Ef E1 nf 2 -E1 1 1 2 - 2 hc n f ni 1 -E1 1 hc n f 2 1 (hydrogen ) -E1 R ! hc series limit (ni ) n f =1 -> Lyman, n f =2 -> Balmer, n f =3 -> Paschen, etc. cphys351 c4:13 Example 4.2: An electron collides with a hydrogen atom in its ground state(lowest energy) and excites it to a state of n = 3. How much energy was given to the hydrogen atom in this inelastic collision? Example 4.3: Hydrogen atoms in state of high quantum number have been created in the laboratory. (a) Find the quantum number of the Bohr orbit in a hydrogen atom whose radius is 0.0100mm. (b) What is the energy of a hydrogen atom in this state? Example 4.4: Find the longest wavelength present in the Balmer series of hydrogen cphys351 c4:14 The Correspondence Principle A new theory should encompass an old theory where the old theory was successful. Quantum theory approximates the results of classical mechanics when: quantum numbers are large h -> 0 cphys351 c4:15 Classical treatment of radiation from “planetary” hydrogen: frequency of emitted light = frequency of orbits (+ harmonics) v f 2r e f e 3 2 4 mr v 0 40 mr n 2h 20 me 4 2 - E1 2 with rn f 3 2 2 3 3 h n me 8 0 h n Quantum transition from n -> n- p with p << n - E1 2np - p 2 1 1 h - E1 - 2 2 2 2 h ( n p ) n ( n p ) n - E1 2 p p f 3 h n cphys351 c4:16 Refining the Bohr Atom nuclear motion: electron and nucleus orbit each other (each orbit center of mass). Two body problem => center of mass motion + relative motion (with reduced mass) mM m' mM m' e 4 E'n 2 8 0 h 2 1 m' E1 2 2 n m n m' hydrogen : 0.99945 m cphys351 c4:17 Example 4.6: A “positronium” atom consists of an electron and a positron. Compare the spectrum of positronium to that of hydrogen Example 4.7: Muons are elementary particles with mass 207me and +/-e of charge. A muonic atom is formed by a negative muon with a proton. Find the radius of the first Bohr orbit and the ionization energy of the atom. cphys351 c4:18 Atomic spectra Atoms have discrete set of allowed energies ALL changes in atom’s energy have to be to an allowed state Absorption and emission spectra from conservation of energy h DE Franck-Hertz Experiment: inelastic scattering of electrons by atoms ->atom only absorbs energy to DE = e DV A DV DV cphys351 c4:19 The Laser: bright, monochromatic, coherent light source Excited State: state above ground state decays to lower states, with emission of photon (or other mechanism for energy transfer). Metastable State: “sort of stable” state state with a longer life time than ordinary excited states lifetime ~ 1E-3 s vs. 1E-8 s for ordinary states Three kinds of transitions h DE h h h h Induced Absorption Spontaneous Emission Induced Emission (Stimulated) cphys351 c4:20 fast emission to metastable state pumping process h h’ h laser transition: stimulated emission Energy levels for 4-level laser h Light Amplification by Stimulated Emission of Radiation cphys351 c4:21 Other considerations: “recycling” inducing photons and selecting lasing transition: the laser cavity Fabret-Perot Interferometer = standing waves “Tunable” Dye Lasers Semiconductor Lasers Chemical Lasers cphys351 c4:22 Chapter 4 exercises:3,4,5,6,7,8,11,12,13,14,15,16,18,19,21,22,29,30,31,32,33,35 cphys351 c4:23