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Inside the Modern Atom Review of Waves Properties: Wavelength (l): distance between two successive crests Frequency (f): number of wave crests passing per second Speed of wave: v=fl Amplitude (A): maximum displacement Energy: E A2 Interference Only waves experience interference this is just adding up the parts of a wave: Where two crests (or troughs) meet, they add Where a crest and trough meet, they cancel Light: Particles vs. Waves Light was originally thought to be a particle E.g., look at sharp shadows, photoelectric effect, etc. also, Newton endorsed the view that light was made up of particles Particles behave completely differently when they encounter slits... E.g., suppose you fired bullets at one slit? What does that look like? Just a simple curve... What if you fired bullets at two slits? Just two separate curves So what happens when you fire light at it? Interference like water waves! The Photoelectric Effect • When light hits certain metals, e- are ejected •Only the frequency (color) of the light affected the energy of the ejected e• Higher frequency light ejected e- with higher energy The Atomic Spectra Light from bulbs, stars, etc. show a continuous spectrum when seen through a prism A hot gas, however, has an emission line spectrum made of a few, discrete lines of color Why don't hot gases show continuous spectra? Absorption Emission Quantum Hypothesis: Energy is quantized What is quantization? It only comes in discrete chunks instead of a continuous range of energies Planck suggested Energy is quantized in units of h and was proportional to the oscillators frequency: E = hf Continuous Discrete Quantum Hypothesis: Light is quantized Einstein proposed that light is also quantized and its energy is also determined by its frequency via E = hf Each individual packet of light energy is called a photon and an EM wave is made of these individual "particles" Brighter light → more photons strike metal each second → more e- ejected/sec (but it does not increase the energy of each e-) Higher frequency light ejects e- with more energy because each photon has more energy to give E hf h 6.626 1034 J s Kmax hf Structural Models of the Atom Aristotle’s “Point” Model e Thompson “Plumb Pudding” Model r Rutherford “Point Nucleus” Model 200 2 r 2a0 Ze Bohr “Planetary” Model QM “Probability” Model Quantum Hypothesis: Orbits are quantized Bohr suggested that the orbits of electrons are also quantized An electron can go from one level to another by absorbing or emitting a photon of light If light energy is quantized and electron orbits are also quantized, that would explain why atomic spectra are discrete (since atoms/electrons only absorb or emit a single photon at a time) The Bohr Model of the Hydrogen Atom Bohr’s Quantum Conditions I. There are discrete stable “tracks” for the electrons. Along these tracks, the electrons move without energy loss. II. The electrons are able to “jump” between the tracks. Ei-Ef=hf In the Bohr model, a photon is emitted when the electron drops from a higher orbit (Ei) to a lower energy orbit (Ef). Predicted Energy Levels Instead of looking at orbits, we now look at energy levels, which are the certain, allowed energy states Lowest energy level (corresponding to innermost orbit in Bohr theory) is called the ground state and higher energy states are excited states The structure of the atom is shown schematically on an energy-level diagram labeled with a quantum number n As quantum number ↑, Energy associated with that state ↑ Transition of the electron from one orbit to another is now represented as the atom going from one energy level to another Transition achieved by absorption or emission of a photon with an energy corresponding to the difference in energy between the two levels, or states When white light hits an atom, only photons with the right energy are absorbed! Energy, Light, & Orbits are quantized! This is why it's called quantum mechanics: everything is quantized (comes in discrete chunks instead of a continuous range of values) -- matter (the Bohr "orbitals"), light, and even energy are ALL quantized! DeBroglie further hypothesized that since electrons also behave as waves, they must also have a electron wavelength: λ = h/mv wave de Broglie Waves in the Hydrogen Atom In this example, three complete wavelengths are contained in the circumference of the orbit In general, the circumference must equal some integer number of wavelengths 2 r = n λ ; n = 1, 2, … Heisenberg Uncertainty Principle Heisenberg proposed that the wave aspect of an electron makes it impossible to know both the position and momentum to arbitrary precision Heisenberg Uncertainty Principle (HUP): Δx • Δ(mv) ≥ h/4π E.g., if you have a periodic wave (or a standing wave) you can't really tell what its position is (it's spread out over the whole string, e.g.). But you can tell exactly what its wavelength is. Now if you send a wave pulse down the string, you can't tell what its wavelength is (doesn't make sense for a pulse) but you can tell exactly what its position is. The Atomic Structure So we can't say where exactly the electron is (it's not like a billiard ball, or like a wave, or like a puffy cloud, or like anything else we know from ordinary experience) "Now we know how the electrons and light behave. But what can I call it? If I say they behave like particles I give the wrong impression; also if I say they behave like waves. They behave in their own inimitable way, which technically could be called a quantum mechanical way. They behave in a way that is like nothing that you have ever seen before. Your experience with things that you have seen before is incomplete. The behavior of things on a very tiny scale is simply different. An atom does not behave like a weight hanging on a spring and oscillating. Nor does it behave like a miniature representation of the solar system with little planets going around in orbits. Nor does it appear to be somewhat like a cloud or fog of some sort surrounding the nucleus. It behaves like nothing you have ever seen before." -- Richard P. Feynman, The Character of Physical Law Since we can't talk about its exact location, it's more useful to concentrate on the electron's energy Some Atomic Physics Atom can gain or lose energy by absorption or emission of photons or by collisions Pauli Exclusion Principle: two electrons cannot occupy the same quantum state at the same time Number of quantum states in a given energy level given by 2n2 If even one electron is in a higher energy level, the atom is said to be in an excited state Properties of each element determined by the groundstate configuration of its atoms (e.g., valence electrons, etc.) Four Known Forces Two familiar kinds of interactions: gravity (masses attract one another) and electromagnetism (same-sign charges repel, opposite-sign charges attract) What causes radioactive decays of nuclei ? Must be a force weak enough to allow most atoms to be stable. What binds protons together into nuclei ? Must be a force strong enough to overcome repulsion due to protons’ electric charge Previously, we peered inside the atom We recalled that electrons orbit the atom’s massive nucleus and determine an element’s chemical behavior. We explored the proton and neutron content of nuclei and the phenomena of radioactivity, fission, and fusion they make possible. Today we’ll look inside the nucleons themselves. Fundamental particles in the Standard Model are: Leptons Quarks Intermediate Gauge Bosons Anti-matter Each kind of elementary particle has a counterpart with the same mass, but the opposite electric charge, called its “anti-particle”. Electron: m= .0005 GeV, charge = +1, symbol e- Positron: m = .0005 GeV, charge = -1, symbol e+ The anti-particle has a bar over its symbol: Anti-proton is written p , anti-neutrino is v Anti-matter is rare in the explored universe It’s created in cosmic rays and particle accelerators and some radioactive decays. When a particle and its anti-particle collide, they “annihilate” one another in a flash of energy. Stability diagram Heavy elements can fission into lighter elements. Elements from helium to iron were manufactured in the cores of stars by fusion. Heavier elements are metastable and were made during supernovae explosions. Light elements can undergo fusion into heavier elements. Chain reaction For reaction to be self-sustaining, must have CRITICAL MASS. Fusion Light nuclei are more stable when combined Tremendous energy released Hydrogen bombs and Fusion power?