The unit cell of nickel arsenide is shown here. (b) What is the empirical formula?

The unit cell of a compound containing potassium, aluminum, and fluorine is shown here. (a) What type of lattice does this crystal possess (all three lattice vectors are mutually perpendicular)?

Consider the unit cells shown here for three different structures that are commonly observed for metallic elements. (a) Which structure(s) corresponds to the densest packing of atoms?

Consider the unit cells shown here for three different structures that are commonly observed for metallic elements. (b) Which structure(s) corresponds to the least dense packing of atoms?

Sodium metal (atomic weight 22.99 g/mol) adopts a body-centered cubic structure with a density of 0.97 g/cm3. (a) Use this information and Avogadro’s number (N_A = 6.022 × 10²³/mol) to estimate the atomic radius of sodium. (b) If sodium didn't react so vigorously, it could float on water. Use the answer from part (a) to estimate the density of Na if its structure were that of a cubic close-packed metal. Would it still float on water?

Calcium crystallizes in a body-centered cubic structure at 467°C. (a) How many Ca atoms are contained in each unit cell?

Calcium crystallizes in a body-centered cubic structure at 467°C. (b) How many nearest neighbors does each Ca atom possess? (c) Estimate the length of the unit cell edge, a, from the atomic radius of calcium (1.97 Å). (d) Estimate the density of Ca metal at this temperature.

Calcium crystallizes in a face-centered cubic unit cell at room temperature that has an edge length of 5.588 Å.

a. Calculate the atomic radius of a calcium atom.

b. Calculate the density of Ca metal at this temperature.

An element crystallizes in a face-centered cubic lattice. The edge of the unit cell is 4.078 Å, and the density of the crystal is 19.30 g>cm3. Calculate the atomic weight of the element and identify the element.

Which of these statements about alloys and intermetallic compounds is false? (a) Bronze is an example of an alloy. (b) 'Alloy' is just another word for 'a chemical compound of fixed composition that is made of two or more metals.' (c) Intermetallics are compounds of two or more metals that have a definite composition and are not considered alloys. (d) If you mix two metals together and, at the atomic level, they separate into two or more different compositional phases, you have created a heterogeneous alloy. (e) Alloys can be formed even if the atoms that comprise them are rather different in size.

Determine if each statement is true or false: (b) Substitutional alloys have 'solute' atoms that replace 'solvent' atoms in a lattice, but interstitial alloys have 'solute' atoms that are in between the 'solvent' atoms in a lattice.

For each of the following alloy compositions, indicate whether you would expect it to be a substitutional alloy, an interstitial alloy, or an intermetallic compound: (a) Fe_0.97Si_0.03 (b) Fe_0.60Ni_0.40 (c) SmCo₅.

Indicate whether each statement is true or false: (c) Nonmetallic elements are never found in alloys.

An increase in temperature causes most metals to undergo thermal expansion, which means the volume of the metal increases upon heating. How does thermal expansion affect the unit cell length? What is the effect of an increase in temperature on the density of a metal?

State whether each sentence is true or false: (b) Metals have high electrical conductivities because they are denser than other solids.

The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.21. Construct a molecular-orbital diagram for a chain containing six lithium atoms and use it to answer the following questions: a. How many molecular orbitals are there in the diagram?

The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.21. Construct a molecular-orbital diagram for a chain containing six lithium atoms and use it to answer the following questions: c. How many nodes are in the highest-energy molecular orbital?

The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.21. 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)?

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?

Which would you expect to be the more ductile element: a. Ag or Mo

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.

Tausonite, a mineral composed of Sr, O, and Ti, has the cubic unit cell shown in the drawing. (a) What is the empirical formula of this mineral?

The unit cell of a compound containing Co and O has a unit cell shown in the diagram. The Co atoms are on the corners, and the O atoms are completely within the unit cell. a. What is the empirical formula of this compound? b. What is the oxidation state of the metal?