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Mark Important Points in Margin Date: ___________ The Bohr Model of the Hydrogen Atom Unit 6A: Atomic Theory (Quantum/Electronic Structure) Knowledge/Understanding Goals: developments leading to the Bohr model of the atom the Bohr model and its limitations how the modern quantum mechanical model of the atom grew out of the Bohr model Skills: calculate the frequency/wavelength of light emitted using the Rydberg equation calculate the energy associated with a quantum number using Bohr’s equation Significant Developments Prior to 1913 Discovery of the Electron (1897): J.J. Thompson determined that cathode rays were actually particles emitted from atoms that the cathode was made of. These particles had an electrical charge, so they were named “electrons”. Cathode Ray Experiment: https://www.youtube.com/watch?v=GzMh4q-2HjM Use this space for additional notes. AP Chem Page 1 of 6 Mark Important Points in Margin The Bohr Model of the Hydrogen Atom Discovery of the Nucleus (1909): Ernest Rutherford’s famous “gold foil experiment” determined that atoms contained a dense, positively-charged region that comprised most of the atom’s mass. This region was named the “nucleus”, after the nucleus of a cell. Gold Foil Experiment: http://www.mhhe.com/physsci/chemistry/essentialchemistry/flash/ruther14.swf Rutherford (“Planetary”) Model of the Atom (1911): The atom was believed to be like a miniature solar system, with electrons orbiting the nucleus in much the same way as planets orbit the sun. Electrons could be found orbiting anywhere within the low density “electron cloud” region. Use this space for additional notes. AP Chem Page 2 of 6 Mark Important Points in Margin The Bohr Model of the Hydrogen Atom Rydberg Formula (1888): Johannes Rydberg developed a generalized formula that could describe the wavenumbers of all of the spectral lines in hydrogen (and similar elements). There are several series of spectral lines for hydrogen, each of which converge at different wavelengths. Rydberg described the Balmer series in terms of a pair of integers (n1 and n2, where n1 < n2), and devised a single formula with a single constant (now called the Rydberg constant) that relates them. (RH = 1.097 x 107 1/m) 1 1 1 RH 2 2 λvac n1 n2 Rydberg’s equation was later found to be consistent with other series discovered later, including the Lyman series (in the ultraviolet region; first discovered in 1906) and the Paschen series (in the infrared region; first discovered in 1908). Those series and their converging wavelengths are: Series Wavelength n1 n2 91 nm 1 2→∞ Balmer 365 nm 2 3→∞ Paschen 820 nm 3 4→∞ Lyman Use this space for additional notes. AP Chem Page 3 of 6 Mark Important Points in Margin The Bohr Model of the Hydrogen Atom Bohr’s Model of the Atom (1913) In 1913, Niels Bohr combined atomic, spectroscopy, and quantum theories into a single theory. Bohr hypothesized that electrons moved around the nucleus as in Rutherford’s model, but that these electrons had only certain allowed quantum values of energy, which could be described by a quantum number (n). The value of that quantum number was the same n as in Rydberg’s equation, and that using quantum numbers in Rydberg’s equation could predict the wavelengths of light emitted when the electrons gained or lost energy by moved from one quantum level to another. Bohr’s model gained wide acceptance, because it related several prominent theories of the time. The theory worked well for hydrogen, giving a theoretical basis for Rydberg’s equation. Bohr defined the energy associated with a quantum number (n) in terms of Rydberg’s constant: En RH n2 http://highered.mheducation.com/olcweb/cgi/pluginpop.cgi?it=swf::800::600::/sites/dl/free/0072482621/59229/ Bohr_Nav.swf::The%20Bohr%20Atom Use this space for additional notes. AP Chem Page 4 of 6 Mark Important Points in Margin The Bohr Model of the Hydrogen Atom The Bohr model worked well for hydrogen. However, the equations could not be solved exactly for atoms with more than one electron, because of the additional effects that electrons exert on each other (Coulomb force kq q F d12 2 ). By the mid-1920s, quantum physics was changing. The concept of “allowed states” gave way to probability distributions, governed by Werner Heisenberg’s uncertainty principle, which states that there is a limit on how much certainty can exist in the state of a sub-atomic particle. For example, the more exactly an electron’s position is specified, the less the exactly the velocity or momentum can be specified. Or, as soon as you observe light energy, it loses its duality. (must act as either a wave or a particle) In 1925, Erwin Schrödinger used the “wave equation”—an equation that describes how a wave changes with time—to describe where electrons would be found (in terms of probability) if the electron behaved as a wave rather than as a particle. Schrödinger found that by treating each electron as a unique wave function governed by the wave equation, the energies of the electrons could be predicted by the solutions to the wave equation without the need for an empirically-derived number (the Rydberg constant). This use of Schrödinger’s equation to construct a probability map for the electrons in an atom is the basis for the modern quantum-mechanical model of the atom. Use this space for additional notes. AP Chem Page 5 of 6 Mark Important Points in Margin The Bohr Model of the Hydrogen Atom Probability Maps: graphical depictions of where certain electrons are likely to be found at any given moment around the nucleus. Each map represents a specific orbital, capable of holding 2 electrons. The shapes of each orbital are determined using Schrödinger’s equation. Use this space for additional notes. AP Chem Page 6 of 6