Chapter 6

In the transition metals (the \(d\) -block), the electron configuration of cations is different than what you might expect. Instead of the \(\mathrm{d}\) electrons being lost first, \(s\) electrons are lost first. For example, the electron configuration of iron, \(\mathrm{Fe}\), is \([\mathrm{Ar}] 4 s^{2} 3 d^{6}\); but the electron configuration of \(\mathrm{Fe}^{2+}\) is \([\mathrm{Ar}] 3 d^{6} ;\) the \(4 \mathrm{~s}\) electrons are eliminated to make the cation. Write out the electron configurations of (a) \(\mathrm{Zn}^{2+}\) (b) \(\mathrm{Pt}^{2+}\) (c) \(\mathrm{Cr}^{3+}\) (d) \(\mathrm{Ti}^{4+}\).

Identify the specific element that corresponds to each of the following electron configurations: (a) \(1 s^{2} 2 s^{2}\), (b) \(1 s^{2} 2 s^{2} 2 p^{4}\), (c) \([\mathrm{Ar}] 4 s^{1} 3 d^{5}\), (d) \([\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{4}\) (e) \(1 s\).

Identify the group of elements that corresponds to each of the following generalized electron configurations: (a) [noble gas] \(n s^{2} n p^{5}\) (b) [noble gas] \(n s^{2}(n-1) d^{2}\) (c) [noble gas] \(n s^{2}(n-1) d^{10} n p^{1}\) (d) [noble gas] \(n s^{2}(n-2) f^{6}\)

The following electron configurations represent excited states. Identify the element, and write its ground-state condensed electron configuration. (a) \(\mathrm{ls}^{2} 2 \mathrm{~s}^{2} 3 p^{2} 4 p^{1}\), (b) \([\mathrm{Ar}] 3 d^{10} 4 s^{1} 4 p^{4} 5 s^{1}\), (c) \([\mathrm{Kr}] 4 d^{6} 5 s^{2} 5 p^{1}\)

The series of emission lines of the hydrogen atom for which \(n_{f}=3\) is called the Paschen series. (a) Determine the region of the electromagnetic spectrum in which the lines of the Paschen series are observed. (b) Calculate the wavelengths of the first three lines in the Paschen series - those for which \(n_{i}=4,5\), and 6 .

Bohr's model can be used for hydrogen-like ions - ions that have only one electron, such as \(\mathrm{He}^{+}\) and \(\mathrm{Li}^{2+}\). (a) Why is the Bohr model applicable to \(\mathrm{He}^{+}\) ions but not to neutral He atoms? (b) The ground-state energies of \(\mathrm{H}, \mathrm{He}^{+}\), and \(\mathrm{Li}^{2+}\) are tabulated as follows:

Under appropriate conditions, molybdenum emits Xrays that have a characteristic wavelength of \(0.711 \AA\). These X-rays are used in diffraction experiments to determine the structures of molecules. (a) Why are X-rays, and not visible light, suitable for the determination of structure at the atomic level? (b) How fast would an electron have to be moving to have the same wavelength as these X-rays?

In the television series Star Trek, the transporter beam is a device used to "beam down" people from the Starship Enterprise to another location, such as the surface of a planet. The writers of the show put a "Heisenberg compensator" into the transporter beam mechanism. Explain why such a compensator would be necessary to get around Heisenberg's uncertainty principle.

Which of the quantum numbers governs (a) the shape of an orbital, (b) the energy of an orbital, (c) the spin properties of the electron, (d) the spatial orientation of the orbital?

The "magic numbers" in the periodic table are the atomic numbers of elements with high stability (the noble gases): \(2,10,18,36,54\), and \(86 .\) In terms of allowed values of orbitals and spin quantum numbers, explain why these electron arrangements correspond to special stability.

Scientists have speculated that element 126 might have a moderate stability, allowing it to be synthesized and characterized. Predict what the condensed electron configuration of this element might be.

The discovery of hafnium, element number 72, provided a controversial episode in chemistry. G. Urbain, a French chemist, claimed in 1911 to have isolated an element number 72 from a sample of rare earth (elements 58-71) compounds. However, Niels Bohr believed that hafnium was more likely to be found along with zirconium than with the rare earths. D. Coster and \(G\). von Hevesy, working in Bohr's laboratory in Copenhagen, showed in 1922 that element 72 was present in a sample of Norwegian zircon, an ore of zirconium. (The name hafnium comes from the Latin name for Copenhagen, Hafnia). (a) How would you use electron configuration arguments to justify Bohr's prediction? (b) Zirconium, hafnium's neighbor in group \(4 \mathrm{~B}\), can be produced as a metal by reduction of solid \(\mathrm{ZrCl}_{4}\) with molten sodium metal. Write a balanced chemical equation for the reaction. Is this an oxidation- reduction reaction? If yes, what is reduced and what is oxidized? (c) Solid zirconium dioxide, \(\mathrm{ZrO}_{2}\), is reacted with chlorine gas in the presence of carbon. The products of the reaction are \(\mathrm{ZrCl}_{4}\) and two gases, \(\mathrm{CO}_{2}\) and \(\mathrm{CO}\) in the ratio \(1: 2 \mathrm{Write}\) a balanced chemical equation for the reaction. Starting with a 55.4-g sample of \(\mathrm{ZrO}_{2}\), calculate the mass of \(\mathrm{ZrCl}_{4}\) formed, assuming that \(\mathrm{ZrO}_{2}\) is the limiting reagent and assuming \(100 \%\) yield. (d) Using their electron configurations, account for the fact that \(\mathrm{Zr}\) and \(\mathrm{Hf}\) form chlorides \(\mathrm{MCl}_{4}\) and oxides \(\mathrm{MO}_{2}\).

The first 25 years of the twentieth century were momentous for the rapid pace of change in scientists' understanding of the nature of matter. (a) How did Rutherford's experiments on the scattering of \(\alpha\) particles by a gold foil set the stage for Bohr's theory of the hydrogen atom? (b) In what ways is de Broglie's hypothesis, as it applies to electrons, consistent with J. J. Thomson's conclusion that the electron has mass? In what sense is it consistent with proposals that preceded Thomson's work, that the cathode rays are a wave phenomenon?