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WHY CAN'T WE SEE ATOMS?. “seeing an object” = detecting light that has been reflected off the object's surface light = electromagnetic wave; “visible light”= those electromagnetic waves that our eyes can detect
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WHY CAN'T WE SEE ATOMS? • “seeing an object” • = detecting light that has been reflected off the object's surface • light = electromagnetic wave; • “visible light”= those electromagnetic waves that our eyes can detect • “wavelength” of e.m. wave (distance between two successive crests) determines “color” of light • wave hardly influenced by object if size of object is much smaller than wavelength • wavelength of visible light: between 410-7m (violet) and 7 10-7 m (red); • diameter of atoms: 10-10m • generalize meaning of seeing: • seeing is to detect effect due to the presence of an object • quantum theory “particle waves”, with wavelength 1/(m v) • use accelerated (charged) particles as probe, can “tune” wavelength by choosing mass m and changing velocity v • this method is used in electron microscope, as well as in “scattering experiments” in nuclear and particle physics
WHAT IS INSIDE AN ATOM? • THOMSON'S MODEL OF ATOM • (“RAISIN CAKE MODEL”): • atom = sphere of positive charge (diameter 10-10 m), • with electrons embedded in it, evenly distributed (like raisins in cake) • Geiger & Marsden’s SCATTERING EXPERIMENT: • (Geiger, Marsden, 1906 - 1911) (interpreted by Rutherford, 1911) • get particles from radioactive source • make “beam” of particles using “collimators” (lead plates with holes in them, holes aligned in straight line) • bombard foils of gold, silver, copper with beam • measure scattering angles of particles with scintillating screen (ZnS) .
Geiger, Marsden, Rutherford expt. • result: • most particles only slightly deflected (i.e. by small angles), but some by large angles - even backward • measured angular distribution of scattered particles did not agree with expectations from Thomson model (only small angles expected), • but did agree with that expected from scattering on small, dense positively charged nucleus with diameter < 10-14 m, surrounded by electrons at 10-10 m
Rutherford model • RUTHERFORD MODEL OF ATOM:(“planetary model of atom”) • positive charge concentrated in nucleus (<10-14 m); • negative electrons in orbit around nucleus at distance 10-10 m; • electrons bound to nucleus by Coulomb force. • problem with Rutherford atom: • electron in orbit around nucleus is accelerated (centripetal acceleration to change direction of velocity); • according to theory of electromagnetism (Maxwell's equations), accelerated electron emits electromagnetic radiation (frequency = revolution frequency); • electron loses energy by radiation orbit decays, • changing revolution frequency continuous emission spectrum (no line spectra), and atoms would be unstable (lifetime 10-10 s ) • we would not exist to think about this!!
Bohr model of hydrogen (Niels Bohr, 1913) • Bohr model is radical modification of Rutherford model; discrete line spectrum attributed to “quantum effect”; • electron in orbit around nucleus, but not all orbits allowed; • three basic assumptions: • 1. angular momentum is quantized L = n·(h/2) = n ·ħ, n = 1,2,3,...electron can only be in discrete specific orbits with particular radii discrete energy levels • 2. electron does not radiate when in one of the allowed levels, or “states” • 3. radiation is only emitted when electron makes “transition” between states, transition also called “quantum jump” or “quantum leap” • from these assumptions, can calculate radii of allowed orbits and corresponding energy levels: • radii of allowed orbits: rn = a0 n2 n = 1,2,3,…., a0 = 0.53 x 10-10 m = “Bohr radius” n = “principal quantum number” • allowed energy levels: En = - E0 /n2 , E0 = “Rydberg energy” • note: energy is negative, indicating that electron is in a “potential well”; energy is = 0 at top of well, i.e. for n = , at infinite distance from the nucleus.
Ground state and excited states • ground state = lowest energy state, n = 1; this is where electron is under normal circumstances; electron is “at bottom of potential well”; energy needed to get it out of the well = “binding energy”; binding energy of ground state electron = E0 = energy to move electron away from the nucleus (to infinity), i.e. to “liberate” electron; this energy also called “ionization energy” • excited states = states with n > 1 • excitation = moving to higher state • de-excitation = moving to lower state • energy unit eV = “electron volt” = energy acquired by an electron when it is accelerated through electric potential of 1 Volt; electron volt is energy unit commonly used in atomic and nuclear physics; 1 eV = 1.6 x 10-19 J • relation between energy and wavelength: E = h f = hc/ , hc = 1.24 x 10-6eV m
Excitation and de-excitation • PROCESSES FOR EXCITATION: • gain energy by collision with other atoms, molecules or stray electrons; kinetic energy of collision partners converted into internal energy of the atom; kinetic • energy comes from heating or discharge; • absorb passing photon of appropriate energy. • DE-EXCITATION: • spontaneous de-excitation with emission of photon which carries energy = difference of the two energy levels; • typically, lifetime of excited states is 10-8 s (compare to revolution period of 10-16 s )
Excitation: • states of electron in hydrogen atom:
MICROWAVE COOKING • water molecule has rotational energy levels close together small energy difference can absorb microwaves; • microwaves: wavelength 3cm, frequency 10GHz = 1010 Hz; energy of photon = h f 4.13x10-5 eV • it is water content that is critical in microwave cooking; most dishes and containers do not absorb microwaves are not heated by them, but get hot from hot food. • IONIZATION: • if energy given to electron > binding energy, the atom is ionized, i.e. electron leaves atom; surplus energy becomes kinetic energy of freed electron. • this is what happens, e.g. in photoelectric effect • ionizing effect of charged particles exploited in particle detectors (e.g. Geiger counter) • aurora borealis, aurora australis: cosmic rays from sun captured in earth’s magnetic field, channeled towards poles; ionization/excitation of air caused by charged particles, followed by recombination/de-excitation;
Matter waves • Louis de Broglie (1925): any moving particle has wavelength associated with it: = h/p = h/(mv) • example: electron in atom has 10-10 m; car (1000 kg) at 60mph has 10-38 m; wave effects manifest themselves only in interaction with things of size comparable to wavelength we do not notice wave aspect of our cars. • note: Bohr's quantization condition for angular momentum is identical to requirement that integer number of electron wavelengths fit into circumference of orbit. • experimental verification of de Broglie's matter waves: • beam of electrons scattered by crystal lattice shows diffraction pattern (crystal lattice acts like array of slits); experiment done by Davisson and Germer (1927) • Electron microscope
QUANTUM MECHANICS • = new kind of physics based on synthesis of dual nature of waves and particles; developed in 1920's and 1930's. • Schrödinger equation: (Erwin Schrödinger, 1925) • is a differential equation for matter waves; basically a formulation of energy conservation. • its solution called “wave function”, usually denoted by ; • |(x)|2 gives the probability of finding the particle at x; • applied to the hydrogen atom, the Schrödinger equation gives the same energy levels as those obtained from the Bohr model; • the most probable orbits are those predicted by the Bohr model; • but probability instead of Newtonian certainty! • Uncertainty principle: (Werner Heisenberg, 1925) It is impossible to simultaneously know a particle's exact position and momentum (or velocity) p x ħ = h/(2) (remember h is a very small quantity: h = 6.63 x 10-34 J s = 4.14 x 10-15 eV) (note that here p means “uncertainty” in our knowledge of the momentum p) • note that there are many such uncertainty relations in quantum mechanics, for any pair of “incompatible” observables.
