Qualitative introduction to quantum theory

BS1030, Chemistry for Life Scientists November 11, 2008 Qualitative introduction to quantum theory Prof. Judith Klein-Seetharaman School of Biological Sciences j.klein-seetharaman@rhul.ac.uk Overview • Today: Study of atomic structure - from classical mechanics to quantum theory – Energy is quantized – Wave-particle duality Atkins & Jones Chapter 1.1-1.6 • Next week: Application of quantum theory to describe atomic structure – – – – The uncertainty principle The Schroedinger equation Quantum numbers Atomic orbitals Atkins & Jones Chapter 1.7-1.22 • Third week: Bonding and shapes of molecules – Types of bonds – MO theory 2 Atkins & Jones Chapter 2+3 Atomic Structure • Dalton: 3 Atomic Structure • Dalton: featureless spheres • J.J. Thomson: discovery of the electron as the first subatomic particle (neg. charge) • Robert Millikan: determined the charge of the electron • But atom is neutral • J.J. Thomson: atom is a blob of a positively charged jelly with electrons like raisins • Ernest Rutherford: shoot positive charges from atoms against a thin platinum foil – What do you expect to find? In JJ Thomson’s model? In alternative models? 4 Shooting alpha particles on a thin foil 1 in 20,000 is deflected with very large angle Most go through 5 Rutherford’s Atom Model • Nucleus many times smaller than itself with electrons occupying the rest of the space • What are the electrons doing in the atom? 6 The answer came from… 7 8 The answer came from… • The study of light emitted by heated atoms 9 The answer came from… • The study of light emitted by heated atoms 10 What is light? • electromagnetic radiation – Oscillating electric and magnetic fields traveling at the speed of light – # of cycles is frequency 1Hz = s-1 One cycle per second – Amplitude l*v=c – Wavelength Wavelength x Frequency = speed of light 11 What is the speed of light • In vacuum: 2.998 * 10^8 m/s • Radar waves leave earth, bounce off the moon and come back in 2.5 seconds (478,000 miles) 12 Short or long wavelength? 13 What is the wavelength of red? of blue? which frequency? other waves? 14 Continuous Spectrum 15 Atomic spectra • are LINE spectra… 16 There are patterns in the lines… • First Joseph Balmer, a swiss school teacher in 1885 • Then Johann Rydberg, a swedish spectroscopist 17 What does it mean? 18 What does it mean? • The electrons in an atom can only have certain energies. • Energy is quantized. 19 Next puzzle: black body radiation 20 Next puzzle: black body radiation • With increasing temperature, the total energy emitted increases and the maximum intensity shifts to shorter wavelengths. 21 Stefan-Boltzmann Law Wien’s Law 22 Can you determine the temperature on the surface of the sun? • Max intensity at 490nm 23 A red giant is a late stage in the evolution of a star. The average wavelength maximum is 700nm. • What is the temperature of the star? 24 What is the wavelength emitted by the human body? 25 Why does the wavelength shift with T? • Classical physics puts no restriction on how small a quantum can be transferred between matter and radiation • Thus, classical physics says any hot body should emit any wavelength • Even a human body would glow in the dark • There would be no darkness • Something is wrong! “Ultraviolet catastrophe” 26 Planck’s answer E = hn • Energy exchange between matter and radiation is quantized • Low frequencies, not enough energy to stimulate oscillations • h=Planck constant • Can reproduce Wien’s and StefanBoltzmann laws perfectly 27 The nail in the coffin: Photoelectric effect • No electrons are ejected if the frequency of the radiation is below a threshold value characteristic of the metal. • Immediate ejection of electrons however low the intensity of the radiation. • The kinetic energy of the ejected electrons increases linearly with the frequency of the incident radiation. 28 Einstein’s explanation • Einstein proposed that electromagnetic radiation consists of particles, which were later called photons • Each photon is a packet of energy • Questions – A. What is the energy of a photon e.g. of blue light? – B. Why kinetic energy linear? 29 Bohr Frequency Condition • The frequency in a line spectrum of an atom arises from transition between two energy levels 30 Light is also waves • Best evidence: Diffraction 31 From waves to particles back to waves • Line spectrum of atoms – Bohr’s frequency condition • Black body radiation – Planck’s quantization of energy • Photoelectric effect – Einstein’s particle interpretation • Diffraction – Clearly a wave-related property 32 Wave-Particle Duality • In the wave model, the intensity of the radiation is proportional to the square of the amplitude of the wave. • In the particle model, the intensity is proportional to the number of photons present. 33 Generalization to all particles • French scientist Louis de Broglie proposed that all particles should have wavelike properties 34 The wave-like behavior of electrons can be experimentally observed 35 Electron Microscope • Electrons have wavelengths suitable to image biological samples down to nearatomic resolution 36 The Dr. Jekyll & Mr. Hyde of Physics The Electron: Wave & Particle 37 Crime Scene Investigators Ernest Rutherford New Zealand Physicist (1871-1937) Nobel Prize in Chemistry 1908 Max Planck German Physicist (1858-1947) Nobel Prize in Physics 1918 Robert Millikan American Physicist (1868-1953) Nobel Prize in Physics 1923 Albert Einstein German Physicist (1879-1955) Nobel Prize in Physics 1921 Joseph John Thomson British Physicist (1856-1949) Nobel Prize in Physics 1906 Niels Bohr Danish Physicist (1885-1962) Nobel Prize in Physics 1922 38 Now you (should) know: • • • • • • Why we need quantum mechanics That Energy is quantized That matter shows particle/wave duality What are characteristics of particles What are characteristics of waves How to calculate energies, frequencies, wavelengths… 39