ph126f09_lec20-NQ.pdf

Physics 126 Fall 2009 Lecture #20 Atomic Structure  Prof. David Gerdes phys126lecture@umich.edu About Exam #3 ?? Location: same as Exams #1 & #2 ?? Time: Thursday 12/3, 8:00 ? 10:00 pm ?? Class on Wed. 12/2 will be a review from 2-4pm. ?? Practice exams and solutions posted. ?? Notecards: 1 new + 2 old (both sides ok) ?? Material covered: Lectures 15-21 (Sections 26.6 ?30.9) What is the world made of? ?? Building blocks of the world: historical ?? Greece: earth, air, fire, and water ?? India: earth, fire, and water ?? Buddhists: earth, air, fire, water, and void ?? China: earth, wood, metal, fire, water ?? Movie ?The Fifth Element?: earth, wind, fire, water, and Leeloo (+love) + 1800?s: Birth of Modern Chemistry ?? In 1869 Mendeléev published the first effective version of the periodic table of the elements ?? He was impressed with certain regularities of the chemical properties of elements ?? Elements with related properties arrayed in periodic table ?? Prediction of unknown elements Mendeleyev 1834 - 1907 Periodic Table Known Properties of Atoms (~1900) ?? Atoms are small. Size approximately 0.1 nm ?? Atoms are stable ?? Atoms contain electrons, but are electrically neutral, so they must contain some positive stuff too ?? The positive stuff makes up most of the atom?s mass ?? Atoms of a given type are identical ?? Atoms have their unique spectral ?fingerprint? J.J. Thomson?s ?Plums in Pudding? Model ?? In 1903, he proposed a subatomic model of the atom ?? He was awarded a Nobel Prize in 1906 for his discovery of the electron ?? This model was not correct, but it was consistent with the evidence at the time Positive goo Electrons 1856-1940 Rutherford Probes Atomic Structure ?? Was J.J Thomson?s student ?? Performed his famous Geiger-Marsden experiment (1909) and showed ?the Plum pudding model? of the atom was incorrect ?? Send in ? particles (Helium nucleus) to pass through a thin piece of gold foil ?? ? particles: emitted from 214 Bi at very high energy ?? Nobel Prize in Chemistry 1908 1871 ? 1937 Rutherford?s Experiment 214 Bi particles Collimator Thin film target ?Scintillation detector? Thompson prediction Occasional reality! Rutherford Quote: ?? 1 in 8000 ? particles bounced back towards the source ?It was quite the most incredible event that ever happened to me in my life. It was as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.? ?? Conclusion: atoms have a dense region containing most of their mass and positive electric charge, associated with a strong central electric field The Line Spectrum of Hydrogen ?? Dilute atomic gases (like Hydrogen) emit and absorb light of very specific frequencies ?? Explaining this became a primary goal in understanding atoms Neils Bohr Anyone who says they can contemplate quantum mechanics without becoming dizzy has not understood the concept in the least. The opposite of a fact is falsehood, but the opposite of one profound truth may very well be another profound truth. Niels Bohr (1885-1962) Theories, Models, and Facts ?? Theories: ?? The most general, overarching structures in science ?? A small number of very general rules ?? Wide explanatory and predictive power ?? Models: ?? Often constructed to solve one particular problem ?? May contain ad-hoc hypotheses ?? Limited explanatory power, hard to generalize ?? Often an interim step on the way to a theory ?? Facts: ?? The raw material of theories and models ?? Need a theory or a model to connect to other facts Bohr Model of the Hydrogen Atom (1913) Postulate #1: Stationary States The electron travels in circular orbits about the positively charged nucleus. However, only certain orbits are allowed. The electron does not radiate energy when it is in one of these orbits. Classically, any orbit is allowed. Bohr?s Postulate #2 Postulate #2: Transitions between States If an electron jumps from one orbit, also known as an energy level, to another, it gains or loses energy in the form of a photon of light. The energy of the photon equals the difference between the energy of the orbits. Classically, radiation is associated with the orbital frequency, not with transitions between orbits. Bohr?s Postulate #3 Postulate #3: Quantization of Angular Momentum Angular momentum comes in multiples of Planck?s constant: Classically, any value of angular momentum is allowed. Calculation of H-atom energy levels: ?? The Coulomb force between the electron and the proton provides the centripetal force to keep the electron in its circular orbit: ?? The electron?s total energy is its KE plus its PE: Note: total energy is negative. ?? Angular momentum quantized: (1) (2) (3) H-atom energy levels, cont?d ?? Use (3) to eliminate v from (1): ?? Finally, substitute (4) into energy equation (2), to obtain the allowed energy levels for the hydrogen atom: (4) Radii of allowed Bohr orbits! Electron volt: practical unit of energy for atomic processes. 1 eV = 1.602 x 10 -19 J = energy gained by an electron when accelerated through a potential difference of one volt. Energy Level Diagram for H ?? Ground state (the lowest energy): E 1 = -13.6 eV ?? First excited state: n=2 ?? The highest energy level: E=0 eV at n=infinity ?? When E=0, the electron is completely removed from the nucleus (r=infinity) ?? Ionization energy: energy required to raise an electron from n to n=infinity The Bohr Model and Hydrogen Spectral Lines ?? Recall, we are trying to explain this: ?? Bohr: each line corresponds to a transition between two stationary states. ?? The energy of the photon is Hydrogen Atomic Fingerprints Lyman series Transitions to n=1 Balmer series Transitions to n=2 Paschen series Transitions to n=3 Successes of the Bohr Model ?? It gives the correct numerical values of the energy levels in the H atom and correctly predicts the size of the H atom. ?? The electron can be in one of a discrete set of stationary states with quantized energy levels. ?? The atom can make a transition between energy level by emitting or absorbing a photon. ?? Angular momentum is quantized. ?? Stationary states can be described by quantum numbers (n is called the principal quantum number). ?? The quantum jump ? the discontinuous transition between energy levels. Problems with the Bohr Model ?? Failed to predict energy levels for atoms with more than one electron ?? Why are atoms stable? Classically, an electron in circular motion will radiate continuously ? the electron would eventually crash into the nucleus ?? Could not account for the intensities or the fine structure of the spectral lines ?? Could not explain the binding of atoms into molecules David Gerdes