E45Supplement_2+2011

E45Supplement_2+2011 - E45 Supplement to Lecture No 4...

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E45 Supplement to Lecture No. 4 Recall that Rutherford’s experiments provided a very surprising result. Atoms were not solid but were mostly empty space. Prior to Rutherford’s experiments, the structure of atoms was thought to be similar to the structure of raisin bread. Imagining the atom to be a slice of raisin bread, the positive charge was represented by the bread; the electrons were represented by raisins stuck in the bread. The positive charge of the atom had been thought of as filling the entire volume of the atom. Rutherford’s experiments indicated that the positive charge did not occupy a large volume; the positive charge was found to reside in the nucleus, which occupied a very small fraction (approximately 10 -12 ) of the overall volume of an atom. Note that Rutherford’s experiment provided no information on the locations of the electrons in gold atoms. The mass of an alpha particle is over 7,000 times greater than the mass of an electron. As the high velocity α particles in Rutherford’s experiment moved through the gold foil, the electrons of the gold atoms had the same effect on the trajectories of the α particles as a pile of baseballs (each of which weighs approximately 0.25 lbs.) would have on the trajectory of a 1,750 pound ball of iron. As mentioned in the last set of notes, in order to get information on the location and energy of an electron in an atom, we need to recognize that an electron is not merely a particle. An electron is so small that it is a particle-wave, or wave-particle. The wave nature of the electron was made obvious by the interference pattern exhibited by a beam of electrons that passed through a thin crystal of nickel (i.e., the equivalent of the double- slit experiment, which resulted in interference patterns for water waves and light waves.). In order to determine the energies and locations of electrons within atoms, it was necessary to first determine the rules that govern the movement of electrons. Stated differently, since the movement of electrons appears to be similar to the movement of waves (e.g., water waves and light), we needed to determine what aspect of the electron is waving. That is, what aspect of an electron is equivalent to the electric (and magnetic) field of a light wave? To identify what aspect of an electron is waving during the movement of an electron, and to determine the laws that govern the movement of the electron, we accepted de Broglie’s hypothesis that λ = h/p. That is, whatever it is that happens to be waving, its wavelength is h/p. A second hypothesis is needed to accompany de Broglie’s hypothesis. Together, the two hypotheses will allow us to identify what is waving and to construct an equation that describes all that we can ever know about the energies and positions of electrons in atoms.
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