1. Chemistry 330 Chapter 11 Quantum Mechanics – The Concepts

2. The Early Years Before 1890 – there were two camps – Classical Physics – thermodynamics, mechanics, kinetic theory, optics, and electricity and magnetism. MatterWaves

3. Energy and Momentum (Classical) Successful with large particles Total energy consists of – Kinetic term – Potential term Kinetic energy Potential energy

4. Energy and Position The application of Newtonian physics gives an exact solution for – Energy – Position – Momentum

5. The Walls Come Tumbling Down!! The Photoelectric effect (Heinrich Hertz – 1887) X-rays (Wilhelm Roentgen – 1895) Radioactivity (Henri Becquerel – 1896) The Discovery of the electron (J.J. Thomson – 1897)

6. Tumblin’ Down (cont’d) Nature of Radioactivity (Marie Curie – 1899) Quantum hypothesis (Max Planck – 1900) Explanation of the photoelectric effect (Albert Einstein – 1905) The discovery of the  -particle (Geiger, Marsden, Rutherford – 1909) The Bohr Model of the Atom (Neils Bohr – 1913)

7. Blackbody Radiation Example – a pinhole in an otherwise closed container. – The radiation is reflected many times within the container and comes to thermal equilibrium with the walls at a temperature T. – Radiation leaking out through the pinhole is characteristic of the radiation within the container.

8. An Example of a Blackbody

9. The Energy Distribution Energy density increases in the visible region as the temperature is raised Maximum shifts to shorter wavelengths. The total energy density (the area under the curve) increases as the temperature is increased (as T 4 ).

10. The Spectral Distribution

11. Blackbody Radiation Rayleigh and Jeans – Electromagnetic field was a collection of oscillators with their own characteristic frequency Wien’s displacement law

12. Predictions vs. Experimental

13. The Planck Hypothesis Energy of the oscillators has only certain allowed values! Set the energy of the oscillator inversely proportional to the wavelength Energy gap – 0 in classical physics – Finite – E = h = h c/ in Planck’s treatment

14. The Planck Hypothesis (cont’d) The Planck distribution accounts very well for the experimentally determined distribution of radiation.

15. The Photoelectric effect Electrons are ejected from a metal when the incident radiation has a frequency above a value characteristic of the metal  – the binding energy of the electron

16. Einstein Applies Planck’s Hypothesis Incident radiation is composed of photons that have energy proportional to the frequency of the radiation. o – the threshold frequency

17. The Photoelectric effect

18. Heat Capacities Low-temperature molar heat capacities – Experimental (points) – Einstein (solid curve)

19. The Discrete Nature of Atomic Spectra Atomic spectrum for hydrogen consisted of discrete, sharp lines! Balmer Equation – 1885 R H = Rydberg Constant = 109 678 cm -1

20. The Bohr Model of the Hydrogen Atom Neils Bohr – laws of classical electrodynamics did not apply to systems at the atomic level Postulates – Energy of the H atom is quantized – Electron is promoted from a low to high energy level by the absorption of a photon – The amount of energy absorbed and emitted by the atom is quantized – Only orbits of certain angular momenta are allowed

21. Bohr and Balmer The Bohr Model successfully explains the Balmer equation

22. The De Broglie Hypothesis Planck and Einstein are correct! Particles must have wave-like properties De Broglie’s matter waves

23. An Illustration of the de Broglie Relation The wave is associated with a particle A particle with high momentum has a wavefunction with a short wavelength, and vice versa.

24. The Davisson-Germer Experiment The scattering of an electron beam from a nickel crystal shows a variation of intensity Characteristic of a diffraction experiment in which waves interfere constructively and destructively in different directions.

25. Experimental Verification of Wave- Particle Duality

26. The Classical Wave Equation From classical physics  =  (x,y,z) e i  t

27. The Square of the Wavefunction For stationary states The function  is called the amplitude of the wave.

28. Schrödinger and de Broglie Combine the de Broglie hypothesis with the classical wave equation

29. The Energy Operators The kinetic energy operator The potential energy operator

30. The Hamiltonian The sum of the operators for the kinetic and the potential energy yields the Hamiltonian

31. The Born Interpretation Max Born – the wavefunction  is a probability amplitude Square modulus (  *  or  2 ) is a probability density. The probability of finding a particle in the region dx located at x is proportional to  2 dx.

32. The Born Interpretation in 3D Space Relates the probability of finding the particle in the volume element d  = dx dy dz At location r – proportional to the product of d  and the value of  2 at that location.