Chapter 1

Arrange the elements in each of the following sets in order of decreasing atomic radius: (a) bromine, chlorine, iodine; (b) gallium, selenium, arsenic; (c) calcium, potassium, zinc; (d) barium, calcium, strontium.

Place the following ions in order of increasing ionic radius: \(\mathrm{S}^{2-}, \mathrm{Cl}^{-}, \mathrm{P}^{3-}\).

Which ion of each of the following pairs has the larger radius: (a) \(\mathrm{Ca}^{2+}, \mathrm{Ba}^{2+} ;\) (b) \(\mathrm{As}^{3-}, \mathrm{Se}^{2-} ;\) (c) \(\mathrm{Sn}^{2+}, \mathrm{Sn}^{4+}\) ?

Which member of each pair has the smaller first ionization energy: (a) \(\mathrm{Ca}\) or \(\mathrm{Mg}\); (b) \(\mathrm{Mg}\) or \(\mathrm{Na}\); (c) \(\mathrm{Al}\) or \(\mathrm{Na}\) ?

Which member of each pair is likely to have the smaller second ionization energy: (a) \(\mathrm{Ca}\) or \(\mathrm{Mg}\); (b) \(\mathrm{Mg}\) or \(\mathrm{Na}\); (c) \(\mathrm{Al}\) or \(\mathrm{Na}\) ?

Place each of the following sets of elements in order of decreasing ionization energy. Explain your choices. (a) Selenium, oxygen, tellurium; (b) gold, tantalum, osmium; (c) lead, barium, cesium.

Which element of each of the following pairs has the higher electron affinity: (a) aluminum or indium; (b) bismuth or antimony; (c) silicon or lead?

(a) What is the inert-pair effect? (b) Why is the inert-pair effect observed only for heavy elements?

(a) What is a diagonal relationship? (b) How does it arise? (c) Give two examples to illustrate the concept.

Which of the following pairs of elements exhibit a diagonal relationship: (a) \(\mathrm{Li}\) and \(\mathrm{Mg}\); (b) \(\mathrm{Ca}\) and \(\mathrm{Al}\); (c) \(\mathrm{F}\) and S?

Which of the following pairs of elements do not exhibit a diagonal relationship: (a) Be and \(\mathrm{Al}\); (b) As and \(\mathrm{Sn}\); (c) Ga and \(S_{n}\) ?

Why are s-block metals more reactive than p-block metals?

Which of the following elements are transition metals: (a) radium; (b) radon; (c) hafnium; (d) niobium?

Identify the following elements as metals, nonmetals, or metalloids: (a) lead; (b) sulfur; (c) zinc; (d) silicon; (e) antimony; (f) cadmium.

Identify the following elements as metals, nonmetals, or metalloids: (a) aluminum; (b) carbon; (c) germanium; (d) arsenic; (e) selenium; (f) tellurium.

Ionization energies usually increase on going from left to right across the periodic table. The ionization energy for oxygen, however, is lower than that of either nitrogen or fluorine. Explain this anomaly.

In the spectroscopic technique known as photoelectron spectroscopy (PES), ultraviolet radiation is directed at an atom or a molecule. Electrons are ejected from the valence shell, and their kinetic energies are measured. Because the energy of the incoming ultraviolet photon is known and the kinetic energy of the outgoing electron is measured, the ionization energy, \(I\), can be deduced from the fact that the total energy is conserved. (a) Show that the speed \(v\) of the ejected electron and the frequency \(\nu\) of the incoming radiation are related by \(h v=I+\frac{1}{2} m_{\mathrm{e}} v^{2}\) (b) Use this relation to calculate the ionization energy of a rubidium atom, given that radiation of wavelength \(58.4 \mathrm{~nm}\) produces electrons with a speed of \(2450 \mathrm{~km} \cdot \mathrm{s}^{-1}\); recall that \(1 \mathrm{~J}=1 \mathrm{~kg} \cdot \mathrm{m}^{2} \cdot \mathrm{s}^{-2}\).

In the heavier transition-metal elements, especially the lanthanoids and actinoids, there are numerous exceptions to the regular order of orbital occupation predicted by the building-up principle. Suggest why more exceptions would be noted for these clements.

Millikan measured the charge of the electron in electrostatic units, esu. The data that he collected included the following series of charges found on oil drops: \(9.60 \times 10^{-10} \mathrm{esu}, 1.92 \times 10^{-9} \mathrm{esu}\), \(2.40 \times 10^{-9} \mathrm{esu}, 2.88 \times 10^{-9} \mathrm{esu}\), and \(4.80 \times 10^{-9}\) esu. (a) From this series find the likely charge on the electron in electrostatic units. (b) Predict the number of electrons on an oil drop with the charge \(6.72 \times 10^{-9}\) esu.

Atomic orbitals may be combined to form molecular orbitals. In such orbitals, there is a nonzero probability of finding an electron on any of the atoms that contribute to that molecular orbital. Consider an electron that is confined in a molecular orbital that extends over two adjacent carbon atoms. The electron can move freely between the two atoms. The C-C distance is \(139 \mathrm{pm}\). (a) Using the one-dimensional particle-in-the-box model, calculate the energy required to promote an electron from the \(n=1\) to the \(n=2\) level, assuming that the length of the box is determined by the distance between two carbon atoms. (b) To what wavelength of radiation does this correspond? (c) Repeat the calculation for a linear chain of 1000 carbon atoms. (d) What can you conclude about the energy separation between energy levels as the size of the atom chain increases?

The electron in a hydrogen atom is excited to a 4d-orbital. Calculate the energy of the photon released if the electron were then to move to each of the following orbitals: (a) \(1 \mathrm{~s}\); (b) \(2 \mathrm{p}\); (c) \(2 \mathrm{~s}\); (d) \(4 \mathrm{~s}\). (e) If the outermost electron in a potassium atom were excited to a 4d-orbital and then fell to the same orbitals, describe qualitatively how the emission spectrum would differ from that of hydrogen (do not do any calculations). Explain your answer.

Francium is thought to be the most reactive of the alkali metals. Because it is radioactive and available in only very small amounts it is difficult to study. However, we can predict its properties based on its location in Group 1 of the periodic table. Estimate the following properties of francium: (a) atomic radius; (b) ionic radius of the \(+1\) cation; (c) ionization energy.