Q: A face-centered cubic (FCC) unit cell contains atoms at each corner and at the center of each face. How many total atoms are present in one FCC unit cell?

$$1/8 \times 8 + 1/2 \times 6 = 4$$ atoms

Q: Calculate the density of a metal that crystallizes in a primitive cubic unit cell with an edge length of $$3.00$$ Å and an atomic mass of $$50.0$$ amu. (Avogadro's number = $$6.02 \times 10$$^{23}$$ mol$$^{-1}$$, 1$ Å = 1$$ \times $$10^{-8} cm)$$

$$d = \frac{1 \times 50.0 \text{ amu}}{(3.00 \text{ Å})^3$} \times \frac{1 \text{ g}}{6.02 \times 10$$^{23}$$ \text{ amu}} \times \frac{(1 \times 10$$^{-8}$$ \text{ cm})^3$}{1 \text{ Å}^3} = 3.08 \text{ g/cm}^3$$

Question 1

Which of the following best describes the difference between crystalline and amorphous solids, as illustrated by SiO$$_2 in $$the provided images?

Accepted Answer

Crystalline solids have a highly ordered arrangement of particles, while amorphous solids lack long-range order.

Question 2

A face-centered cubic (FCC) unit cell contains atoms at each corner and at the center of each face. How many total atoms are present in one FCC unit cell?

Accepted Answer

$$1/8 	imes 8 + 1/2 	imes 6 = 4$$ atoms

Question 3

Which type of solid is most likely to have the highest melting point?

Accepted Answer

Covalent network solid

Question 4

Given a body-centered cubic (BCC) unit cell, what is the relationship between the edge length $$l$$ and the atomic radius $$r$$?

Accepted Answer

$$l = \frac{4r}{\sqrt{3}}$$

Question 5

Which of the following solids is an example of a molecular solid?

Accepted Answer

Dry ice (CO$$_2)$$

Question 6

Calculate the density of a metal that crystallizes in a primitive cubic unit cell with an edge length of $$3.00$$ Å and an atomic mass of $$50.0$$ amu. (Avogadro's number = $$6.02 	imes 10$$^{23}$$ mol$$^{-1}$$, 1$ Å = 1$$ 	imes $$10^{-8} cm)$$

Accepted Answer

$$d = \frac{1 	imes 50.0 	ext{ amu}}{(3.00 	ext{ Å})^3$} 	imes \frac{1 	ext{ g}}{6.02 	imes 10$$^{23}$$ 	ext{ amu}} 	imes \frac{(1 	imes 10$$^{-8}$$ 	ext{ cm})^3$}{1 	ext{ Å}^3} = 3.08 	ext{ g/cm}^3$$

Question 7

Which of the following best explains why metallic solids are good conductors of electricity?

Accepted Answer

They have delocalized valence electrons that can move freely throughout the solid.

Question 8

Which of the following statements about close packing in solids is correct?

Accepted Answer

Hexagonal close packing follows an ABAB pattern, while cubic close packing follows an ABCABC pattern.

Question 9

Which of the following solids would you expect to have the lowest melting point?

Accepted Answer

Argon (Ar)

Question 10

A unit cell contains atoms at the corners, faces, and center. If an atom is located at the center of the unit cell, what fraction of that atom belongs to the unit cell?

Accepted Answer

$$1$$

Question 11

Which of the following is a correct empirical formula for a compound with 1 atom at each corner (gray), 1 atom at the center (red), and 6 atoms at the faces (blue) of a cubic unit cell?

Accepted Answer

CaTiO$$_3$$

Question 12

Which of the following best describes the bonding in a covalent network solid such as diamond?

Accepted Answer

Atoms are connected in a continuous network by covalent bonds.

Question 13

Which of the following is a property of ionic solids?

Accepted Answer

They are hard and brittle with high melting points.

Question 14

What is the packing efficiency of a face-centered cubic (FCC) unit cell?

Accepted Answer

$$74\%$$

Question 15

Which of the following best explains why NaCl has a lower melting point than MgO?

Accepted Answer

NaCl has ions with lower charges (+1, -1) compared to MgO (+2, -2), resulting in weaker ionic bonds.

Question 16

Which of the following is a real-world application of nanomaterials, as discussed in the study materials?

Accepted Answer

Stained glass windows colored by gold nanoparticles

Question 17

Which of the following statements about polymers is correct?

Accepted Answer

Addition polymers are formed when a bond breaks and the electrons make two new bonds.

Structures of Solids: Crystalline and Amorphous Solids

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