Chapter 33 Early Quantum Theory and Models of Atom

Revolution of classical physics 2 World was well explained except a few puzzles? M-M experimenttheory of relativity Black body radiationquantum theory Revolution of Q-theory: (1900 – 1926) → now? Two foundations of modern physics “two dark clouds in the sky of physics”

Blackbody radiation 3 All objects emit radiation → thermal radiation 1) Total intensity of radiation ∝ T 4 2) Continuous spectrum of wavelength Blackbody: absorbs all the radiation falling on it Idealized model Blackbody radiation → easiest

Classical theories 4 Wien’s law: Experiment Intensity Wavelength Wien Rayleigh-Jeans Planck

Planck’s quantum hypothesis 5 Planck’ formula (1900): Max Planck (Nobel 1918) Completely fit the data! Planck’s constant: The energy of any molecular vibration could be only some whole number multiply of hf.

Concept of quantum 6 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 continuous (a) discrete (b)

Photon theory of light 7 Little attention to quantum idea Albert Einstein (Nobel 1921) Until Einstein’s theory of light Molecular vibration The light ought to be emitted, transported, and absorbed as tiny particles, or photons. → radiation → quantum of radiation

Energy of photon 8 Solution: Example1: Calculate the energy of a photon with Example2: Estimate the number of visible light photons per sec in radiation of 50W light bulb. Solution: Average wavelength: invisible light photons?

Photoelectric effect 9 Photoelectric effect: electron emitted under light Stopping potential / voltage: If voltage V changes photocurrent I also changes Saturated photocurrent

Experimental results 10 1) E kmax is independent of the intensity of light 2) E kmax changes over the frequency of light 3) If f < f 0 (cutoff frequency), no photoelectrons

Explanation by photon theory 11 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 energy electron (be absorbed) Minimum energy to get out: work function W 0 Photoelectric equation

Compare with experiment 12 1) Intensity of light ↗ n ↗, f doesn’t change 2) linear relationship 3)

Energy of photon 13 Example3: The threshold wavelength for a metal surface is 350 nm. What is the E kmax when the wavelength changes to (a) 280 nm, (b) 380 nm? Solution: No ejected electrons!

Compton effect 14 Compton’s x-ray scattering experiment (Nobel 1927) Scattering: light propagate in different direction EM waves: forced vibration → same f ( = 0 )

Experimental results 15 1) Besides 0, another peak > 0 ( f < f 0 ) Can not be explained by model of EM waves 2) Δ = - 0 depends on the scattering angle  Ordinary scattering & Compton scattering

Explanation by photon theory 16 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

Compton shift 17 Conservation of momentum: Compton shiftCompton wavelength

X-ray scattering 18 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?

Some questions 19 An collision between photon and free electron 1) Why there is still a peak of 0 ? 3) Why not absorb the photon ? 4) Why not consider in photoelectric effect? 2) What is the difference from photoelectric effect?

*Photon interaction 20 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

Wave-particle duality 21 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.

Wave nature of matter 22 L. de Broglie extended the wave-particle duality Symmetry in nature: For a particle with momentum p, wavelength: Wave particle L. de Broglie ( Nobel 1929) It’s called de Broglie wave or matter-wave

de Broglie wavelength 23 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)

Experiments of de Broglie wave 24 1) Davisson-Germer experiment 2) G. P. Thomson’s experiment (Nobel 1937) 3) Other experiments & other particles

What is an electron? 25 An electron is neither a wave nor a particle de Broglie wave → a wave of probability It is the set of its properties that we can measure “A logical construction” —— B. Russell

Early models of atom 26 1) J. J. Thomson’s plum-pudding model 2) Rutherford’s planetary model (nuclear model) α particle scattering experiment Stability of atom & discrete spectrum

Atomic spectra 27 Light spectrum of atom: line spectrum (discrete) Characteristic of the material → “fingerprint” Emission spectrum & Absorption spectrum

Spectrum of Hydrogen 28 Hydrogen: simplest atom → simplest spectrum Balmer’s formula for visible lines: Rydberg constant: Balmer series I R range Visible light U V range (Infrared Ray) (UltraViolet ray)

General formula 29 There are other series in the UV and I R regions k = 1 → Lyman series ( ultraviolet ) k = 2 → Balmer series ( visible ) k = 3 → Paschen series ( infrared ) … Lyman Balmer Paschen

Bohr’s three postulates 30 Rutherford’s model + quantum idea Neils Bohr (Nobel 1922) 1) Stationary states: stable & discrete energy level 2) Quantum transition: (“jump”) emit or absorb a photon: 3) Quantum condition: (for angular momentum)

Bohr model (1) 31 Rutherford’s model + quantum idea Bohr radius: The orbital radius of electron is quantized

Bohr model (2) 32 Kinetic energy: Total energy: Potential energy: Energy is also quantized

Energy levels 33 n = 1: ground state, E 1 = eV; n = 2: 1 st exited state, E 2 = - 3.4eV; n = 3: 2 nd exited state, E 3 = eV; … 1) Quantization of energy (energy levels) Negative energy → bound state 2) Binding / ionization energy → E = 13.6eV

Transition & radiation 34 Jumping from upper state n to lower state k : Theoretical value of R : In accord with the experimental value!

Energy level diagram 35 n=1(ground) n=2(1 st exited) n=3(2 nd exited) n=4(3 rd exited) … -13.6eV -3.4eV -1.51eV -0.85eV Lyman Balmer Paschen E = 0

Transition of atom 36 Example6: Hydrogen atom in 3 rd excited state, (a) how many types of photon can it emit? (b) What is the maximum wavelength? Solution: (a) n = eV -3.4eV -1.51eV -0.85eV 6 types of photon

Single-electron ions 37 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:

38 (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

Value of Bohr’s theory 39 Niels Bohr Institute & Copenhagen School 1) Precisely explained the discrete spectrum 2) Lyman series & Pickering series 3) Ensures the stability of atoms Semi-classical: other atoms, line intensity, … New theory → quantum mechanics

*de Broglie’s hypothesis applied to atoms 40 Stable orbit for electron → “standing wave” de Broglie wave: Circular standing wave: Combine two equations: It is just the quantum condition by Bohr!