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## Chapter 33 Early Quantum Theory and Models of Atom

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**Chapter 33**Early Quantum Theory and Models of Atom**Revolution of classical physics**World was well explained except a few puzzles? “two dark clouds in the sky of physics” M-M experiment theory of relativity Black body radiation quantum theory Two foundations of modern physics Revolution of Q-theory: (1900 – 1926) → now? 2**Blackbody radiation**All objects emit radiation → thermal radiation 1) Total intensity of radiation ∝ T4 2) Continuous spectrum of wavelength Blackbody: absorbs all the radiation falling on it Idealized model Blackbody radiation → easiest 3**Experiment**Intensity Wien Rayleigh-Jeans Wavelength Planck Classical theories Wien’s law: 4**Planck’s quantum hypothesis**Planck’ formula (1900): Max Planck (Nobel1918) Completely fit the data! Planck’s constant: The energy of any molecular vibration could be only some whole number multiply of hf. 5**(a)**(b) continuous discrete Concept of quantum The energy of any molecular vibration could be only some whole number multiply of hf. f : frequency of oscillation Quantum→ discrete amount / not continuous hf : quantum of energy n : quantum number 6**Photon theory of light**Little attention to quantum idea Until Einstein’s theory of light Molecular vibration → radiation Albert Einstein (Nobel1921) → quantum of radiation The light ought to be emitted, transported, and absorbed as tiny particles, or photons. 7**Energy of photon**Example1: Calculate the energy of a photon with Solution: Example2: Estimate the number of visible light photons per sec in radiation of 50W light bulb. Solution: Average wavelength: invisible light photons? 8**Photoelectric effect**Photoelectric effect: electron emitted under light If voltage V changes photocurrentI also changes Saturated photocurrent Stopping potential / voltage: 9**Experimental results**1) Ekmaxis independent of the intensity of light 2) Ekmaxchanges over the frequency of light 3)If f < f0 (cutoff frequency), no photoelectrons 10**energy**Explanation by photon theory The result can’t be explained by classical theory An electron is ejected from the metal by a collision (inelastic) with a single photon. photon (be absorbed) electron Minimum energy to get out: work function W0 Photoelectric equation 11**Compare with experiment**1)Intensity of light ↗ n ↗, f doesn’t change 2) linear relationship 3) 12**Energy of photon**Example3:The threshold wavelength for a metal surface is 350 nm. What is the Ekmax when the wavelength changes to (a) 280 nm, (b) 380 nm? Solution: No ejected electrons! 13**Compton effect**Compton’s x-ray scattering experiment (Nobel 1927) Scattering:light propagate in different direction EM waves: forced vibration → same f(=0) 14**Experimental results**1) Besides 0, another peak > 0 ( f < f0 ) 2) Δ=-0 depends on the scatteringangle Ordinary scattering & Compton scattering Can not be explained by model of EM waves 15**Explanation by photon theory**What happens in the view of photon theory? A single photon strikes an electron and knocks it out of the atom. (elastic collision) Conservation of energy: Energy loss → > 0 16**Compton shift**Conservation of momentum: Compton shift Compton wavelength 17**X-ray scattering**Example4:X-rays with 0= 0.2 nm are scattered from a material. Calculate the wavelength of the x-rays at scattering angle (a) 45°and (b) 90°. Solution: Maximum shift? 18**4) Why not consider in photoelectric effect?**Some questions An collision between photon and free electron 1) Why there is still a peak of 0 ? 2) What is the difference from photoelectric effect? 3) Why not absorb the photon ? 19***Photon interaction**Four important types of interaction for photons: 1) Scattered from an electron but still exist 2) Knock an electron out of atom (absorbed) 3) Absorbed by an atom → excited state 4) Pair production: such as electron and positron Inverse process → annihilation of a pair 20**Wave-particle duality**Sometimes light behaves like a wave sometimes it behaves like a stream of particles Wave-particle duality as a fact of life Bohr’s principle of complementarity: To understand any given experiment of light, we must use either the wave or the photon theory, but not both. 21**Wave**particle Wave nature of matter L. de Broglie extended the wave-particle duality Symmetry in nature: It’s called de Broglie wave or matter-wave For a particle with momentum p, wavelength: L. de Broglie ( Nobel 1929) 22**de Broglie wavelength**Example5:Calculate the de Broglie wavelength of (a) a 70kg man moving with speed 5m/s; (b) an electron accelerated through 100V voltage. Solution: (a) Much too small to be measured (b) 23**Experiments of de Broglie wave**1) Davisson-Germer experiment 2) G. P. Thomson’s experiment (Nobel 1937) 3) Other experiments & other particles 24**What is an electron?**An electron is neither a wave nor a particle It is the set of its properties that we can measure “A logical construction” —— B. Russell de Broglie wave → a wave of probability 25**Early models of atom**1) J. J. Thomson’s plum-pudding model α particle scattering experiment 2) Rutherford’s planetary model (nuclear model) Stability of atom & discrete spectrum 26**Atomic spectra**Light spectrum of atom: line spectrum (discrete) Emission spectrum & Absorption spectrum Characteristic of the material → “fingerprint” 27**UV range**IR range Visible light (UltraViolet ray) (Infrared Ray) Spectrum of Hydrogen Hydrogen: simplest atom → simplest spectrum Balmer’s formula for visible lines: Balmer series Rydberg constant: 28**General formula**There are other series in the UV and IR regions k = 1 → Lyman series ( ultraviolet ) k = 2 →Balmer series ( visible ) k = 3 →Paschen series ( infrared ) … Lyman Balmer Paschen 29**Bohr’s three postulates**Rutherford’s model + quantum idea 1) Stationary states: stable & discrete energy level Neils Bohr (Nobel1922) 2) Quantum transition: (“jump”) emit or absorb a photon: 3) Quantum condition: (for angular momentum) 30**Bohr model (1)**Rutherford’s model + quantum idea Bohr radius: The orbital radius of electron is quantized 31**Bohr model (2)**Kinetic energy: Potential energy: Total energy: Energy is also quantized 32**Energy levels**1) Quantization of energy (energy levels) n = 1: ground state, E1=-13.6eV; n = 2: 1st exited state, E2=-3.4eV; n = 3: 2nd exited state, E3=-1.51eV; … Negative energy → bound state 2) Binding / ionization energy → E=13.6eV 33**Transition & radiation**Jumping from upper state n to lower state k : Theoretical value of R : In accord with the experimental value! 34**-0.85eV**-1.51eV -3.4eV Paschen Balmer -13.6eV Lyman Energy level diagram E =0 … n=4(3rd exited) n=3(2nd exited) n=2(1st exited) n=1(ground) 35**-0.85eV**-1.51eV 4 -3.4eV 3 2 -13.6eV 1 Transition of atom Example6:Hydrogen atom in 3rd excited state, (a) how many types of photon can it emit? (b) What is the maximum wavelength? Solution: (a)n = 4 6 types of photon 36**Single-electron ions**Example7:Calculate (a) the ionization energy of He+; (b) radiation energy when jumping from n=6 to n=2. (c) Can that photon be absorbed by H? Solution: (a) For single-electron ions: 37**(b) radiation energy if jumping from n=6 to n=2**(c) Can that photon be absorbed by H? So it can be absorbed by Hydrogen atom 38**Value of Bohr’s theory**1) Precisely explained the discrete spectrum 2) Lymanseries & Pickering series 3) Ensures the stability of atoms Semi-classical: other atoms, line intensity, … New theory → quantum mechanics Niels Bohr Institute & Copenhagen School 39***de Broglie’s hypothesis applied to atoms**Stable orbit for electron → “standing wave” de Broglie wave: Circular standing wave: Combine two equations: It is just the quantum condition by Bohr! 40