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Electrons and Atoms Properties of electromagnetic radiation wavelike behavior described by wavelength, frequency, and amplitude. students should know the general spectrum of light from radio waves to cosmic rays. Visible light = ROY G BIV c Observations regarding light. A solid heated to incandescence emits all wavelengths of visible light. The spectrum is continuous. Gases under low pressure under high voltage emit discontinuous light. Bright lines are seen generating atomic spectra or line spectra. They are unique to each atom. 1885: Apparently through trial and error, Johann Balmer determines an equation that accurately predicts the four visible lines in the H spectra. The equation is: (where n greater than 2) 1 1 22 n 2 3.2881x1015 s 1 1900: Max Planck, after evaluating the spectra of Black body radiation which did not correlate to the classical physics model ( which placed no limit on the E of a system) proposes that E is discontinuous. The difference between specific values is a quantum and it is proportional to frequency. E h where h = 6.626 x 10-34 J s 1905: Einstein explains the photoelectric effect which had been observed decades earlier. When visible light shines on certain metals, electrons are ejected from the surface. The stunning observation was that super bright red light would result in no electrons leaving the surface of the metal, but extremely faint blue light would cause some electrons to leave the surface and they all possessed the same KE. Classical physics had always related the E of light as a function of brightness (amplitude) but not its frequency. Einstein proposes that light has particle like properties which we call photons. The number of electrons ejected depends on the intensity but the KE of the electrons depends on the frequency of the light. The fundamental interpretation relevant to electrons is that they are not capable of accumulating energy. They are restricted to certain allowed energies -- and can make quantum jumps. The Rutherford Model of the atom Rutherford's model derived from the classic gold foil experiment with Alpha particles was that the atom is a vast empty space with electrons traveling around an extremely tiny unbelievably dense nucleus. But a charged particle that is in a circular path radiates energy and thus should fall into the nucleus (Classical Physics) 1913: The Bohr Model of the atom Bohr is aware of this inconsistency as well as Planck's and Einstein's proposals. He asserts the following and thus creates a replacement model of the atom. 1. e- are in circular orbits (their motion is classically defined) 2. e- has a fixed set of allowed orbits and no energy is emitted as the electron moves. Arbitrarily, he states that angular momentum is quantized. mvr nh 2 3. e- may pass from one allowed orbit to another but only if fixed discrete quantities of E (quanta) are involved (h). These orbits are described with values of n, where n = 1, 2, 3, 4..... Bohr defines the energy of a hydrogen electron as En RH 2 n where RH is equal to 2.179 x 10-18 J Most often we are interested in ∆E so the useful equation is: 18 E 2.179x10 1 1 J 2 2 ni n f As an electron approaches a nucleus, it drops in potential energy and emits light. Thus, the energy of the electron becomes negative. Notice the resemblance to Balmer's equation for the hydrogen line spectrum calculated almost 30 years earlier! Although the Bohr model was impressive it failed to predict bright line spectra for elements beyond H. The failure increased dramatically with increased atomic number. Why would the model fail for multi-electron species? 1924-27: Louis De Broglie proposes that e- may display wave like character. According to his hypothesis, the wavelength of a particle is related to the particle momentum, p, and Planck's constant, h. Momentum is the product of mass and velocity. Lambda is the wavelength of the matter wave. h h p mv note that the units work. Also note that the velocity in this equation is not to be confused with the velocity term for the KE of an electron. It is only when wavelengths are comparable to ~ atomic dimensions that waveparticle duality is important. If m is large, lambda is not measurable. If electrons were treated as 3D standing waves, then they could only constructively interfere if crest met crest; the number of wavelengths that fit a given circumference must be an integral number: 2r n Since we already know the De Broglie equation, substitute the equation: 2 r nh mv Rearrange and voila, the Bohr postulate: mvr nh 2 If an electron behaves as a wave, how do you specify a position of a wave at a particular moment? Maybe its wavelength, E, and amplitude could be measured, but the idea of position becomes nebulous. Heisenberg uncertainty principle: there is a limit to which both the eposition and momentum can be known. If you can't say where the electron is, we certainly don't know how it got there. Wave Mechanics Schrodinger proposed various complex mathematical equations that described 3D wave patterns. They required a set of quantum numbers and produce a "wave function." When specific terms are assigned for these quantum numbers, an orbital is defined. Orbital: a region of space around the nucleus where the probability of finding an electron is >90%.