Which would you expect to be the more ductile element, (a) Ag or Mo? (b) Zn or Si? In each case explain your reasoning.

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Identify the crystal structures of Ag (Silver) and Mo (Molybdenum). Silver typically crystallizes in a face-centered cubic (FCC) structure, while Molybdenum crystallizes in a body-centered cubic (BCC) structure.

Understand the implications of these crystal structures on ductility. FCC structures, like that of Silver, generally allow for easier slip because they have a higher number of slip systems (12 {111}<110> slip systems). This is due to the close packing and multiple slip planes available in the FCC structure.

Compare this to the BCC structure of Molybdenum, which has fewer slip systems (48 {110}<111>, {112}<111>, and {123}<111> slip systems) and generally experiences more resistance to dislocation motion, especially at lower temperatures, making it less ductile.

Consider the electronic configuration and bonding. Silver, being a noble metal with a single electron in the outermost s-orbital, has more metallic character and greater malleability and ductility. Molybdenum, a transition metal, has partially filled d orbitals that contribute to stronger, more directional bonding, reducing its ductility.

Conclude that based on the crystal structure and electronic properties, Silver (Ag) is expected to be more ductile than Molybdenum (Mo).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ductility

Ductility is a measure of a material's ability to deform under tensile stress, which is often characterized by the material's ability to be stretched into a wire. Metals typically exhibit high ductility due to the presence of metallic bonds that allow atoms to slide past one another without breaking the overall structure. This property is crucial in applications where materials need to be shaped or drawn into wires.

Metallic Bonding

Metallic bonding is a type of chemical bonding that occurs between metal atoms, characterized by a 'sea of electrons' that are free to move around. This delocalization of electrons allows metals to conduct electricity and heat efficiently, as well as contributing to their malleability and ductility. The strength and nature of these bonds can vary between different metals, influencing their physical properties.

Comparison of Silver (Ag) and Molybdenum (Mo)

Silver (Ag) is known for its high ductility and malleability, making it one of the most ductile metals. In contrast, Molybdenum (Mo) is a transition metal that, while strong and resistant to heat, is less ductile than silver. The differences in their atomic structure and bonding lead to silver being more easily drawn into wires compared to molybdenum, which is more brittle.

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Related Practice

Textbook Question

The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.22. Construct a molecular-orbital diagram for a chain containing six lithium atoms and use it to answer the following questions: (e) How many nodes are in the lowest-energy unoccupied molecular orbital (LUMO)?

Textbook Question

Repeat Exercise 12.51 for a linear chain of eight lithium atoms. (b) How many nodes are in the lowest-energy molecular orbital? (c) How many nodes are in the highestenergy molecular orbital? (d) How many nodes are in the highest-energy occupied molecular orbital (HOMO)? (e) How many nodes are in the lowest-energy unoccupied molecular orbital (LUMO)?

Textbook Question

Repeat Exercise 12.51 for a linear chain of eight lithium atoms. (f) How does the HOMO–LUMO energy gap for this case compare to that of the four-atom case?

Textbook Question

Which of the following statements does not follow from the fact that the alkali metals have relatively weak metal–metal bonding? (a) The alkali metals are less dense than other metals. (b) The alkali metals are soft enough to be cut with a knife. (c) The alkali metals are more reactive than other metals. (d) The alkali metals have higher melting points than other metals. (e) The alkali metals have low ionization energies.

Textbook Question

For each of the following groups, which metal would you expect to have the highest melting point: (b) rubidium, molybdenum, or indium?

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