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6 Electronic Structure of Atoms Solutions to Exercises (b) De Broglie's hypothesis is that electrons exhibit both particle and wave properties. Thomson's conclusion that electrons have mass is a particle property, while the nature of cathode rays is a wave property. De Broglie's hypothesis actually rationalizes these two seemingly contradictory observations about the properties of electrons. 6.102 (a) 92 p, 146 n, 92 e; U: 92 p, 143 n, 92 e In keeping with the definition isotopes, only the number of neutrons is different in the two nuclides. Since the two isotopes have the same number of electrons, they will have the same electron configuration. (b) U: (c) From Figure 6.31, the actual electron configuration is The energies of the 6d and 5f orbitals are very close, and electron configurations of many actinides include 6d electrons. (d) 238 92 U 90 Th He has 90 144 90 238 p, n, U has lost 2p,2n,2e. These are organized into 2 4 He shown in the nuclear reaction above. (e) From Figure 6.31, the electron configuration of Th is [Rn]7s²6d². This is not really surprising because there are so many rare earth electron configurations that are exceptions to the expected orbital filling order. However, Th is the only rare earth that has two d valence electrons. Furthermore, the configuration of Th is different than that of Ce, the element above it on the periodic chart, so the electron configuration is at least interesting. 6.103 In each case, radiant energy from the sun in shown as hv. heat hv hv heat electrical work (electricity) inert black material photovoltaic cell hv chemical energy green leaf Energy from the sun irradiates the earth without external intervention. In the absence of an appropriate receiver, the energy is dissipated as heat, as the diagram for the inert black material shows. When sunlight hits a material that can convert the energy to a useable form, such as a leaf or a photovoltaic cell, the sun becomes a sustainable energy source. 165