Q: A metal crystallizes in a face-centered cubic (FCC) structure with an atomic radius of $$1.62\ \text{\AA}. $$What is the edge length $$a of $$the unit cell?

$$a = 2\sqrt{2} \times 1.62\ \text{\AA} = 4.58\ \text{\AA}$$

Q: A certain metal has a face-centered cubic structure with an edge length $$a = 4.08\ \text{\AA}. $$What is the volume of the unit cell in $$\text{cm}^3$$?

$$6.8 \times 10$$^{-24}$$\ \text{cm}^3$$

Q: Which of the following is the correct formula for the percent occupied volume in a unit cell?

$$\text{Percent occupied} = \frac{\text{volume of atoms in cell}}{\text{volume of unit cell}} \times 100\%$$

Q: If the density of a metal is $$6.37\ \text{g/cm}^3$$ and the volume of its unit cell is $$6.8 \times 10$$^{-24}$$\ \text{cm}^3$$, what is the mass of one unit cell?

$$4.33 \times 10$$^{-23}$$\ \text{g}$$

Question 1

In a face-centered cubic (FCC) unit cell, what is the relationship between the edge length $$a$$ and the atomic radius $$r$$?

Accepted Answer

$$a = 2\sqrt{2}r$$

Question 2

Which of the following best describes the coordination number in a crystal lattice?

Accepted Answer

The number of nearest neighbor atoms directly surrounding a given atom

Question 3

A metal crystallizes in a face-centered cubic (FCC) structure with an atomic radius of $$1.62\ 	ext{\AA}. $$What is the edge length $$a of $$the unit cell?

Accepted Answer

$$a = 2\sqrt{2} 	imes 1.62\ 	ext{\AA} = 4.58\ 	ext{\AA}$$

Question 4

What is the formula for the volume of a cubic unit cell with edge length $$a$$?

Accepted Answer

$$V = a^3$

Question 5

If the atomic radius of a metal in an FCC structure is doubled, how does the volume of the unit cell change?

Accepted Answer

It increases by a factor of 8

Question 6

Which of the following best explains why the density of a metal can be calculated using its unit cell parameters?

Accepted Answer

Because the unit cell's mass and volume can be determined and scaled up to the macroscopic sample

Question 7

A certain metal has a face-centered cubic structure with an edge length $$a = 4.08\ 	ext{\AA}. $$What is the volume of the unit cell in $$	ext{cm}^3$$?

Accepted Answer

$$6.8 	imes 10$$^{-24}$$\ 	ext{cm}^3$$

Question 8

Which of the following is the correct formula for the percent occupied volume in a unit cell?

Accepted Answer

$$	ext{Percent occupied} = \frac{	ext{volume of atoms in cell}}{	ext{volume of unit cell}} 	imes 100\%$$

Question 9

A body-centered cubic (BCC) unit cell contains how many atoms per unit cell?

Accepted Answer

2

Question 10

Given a metal with a face-centered cubic structure, atomic mass $$M$$, and density $$\rho$$, which formula correctly relates these to the edge length $$a of $$the unit cell?

Accepted Answer

$$a = \left(\frac{4M}{N_A \rho}\$$right)^{1/3}$$

Question 11

If the density of a metal is $$6.37\ 	ext{g/cm}^3$$ and the volume of its unit cell is $$6.8 	imes 10$$^{-24}$$\ 	ext{cm}^3$$, what is the mass of one unit cell?

Accepted Answer

$$4.33 	imes 10$$^{-23}$$\ 	ext{g}$$

Question 12

Which of the following statements about primitive, body-centered, and face-centered unit cells is correct?

Accepted Answer

Primitive cells have atoms only at the corners, BCC has atoms at corners and center, FCC has atoms at corners and face centers

Question 13

A sample of a metal crystallizes in an FCC structure. If the atomic mass is $$60\ 	ext{g/mol}$$ and the edge length is $$4.00\ 	ext{\AA}$$, what is the density of the metal? ($$N_A = 6.022 	imes 10$$^{23}$$\ 	ext{mol}^{-1})$$

Accepted Answer

$$6.24\ 	ext{g/cm}^3$$

Question 14

Which of the following is a correct statement about the packing efficiency of FCC, BCC, and simple cubic unit cells?

Accepted Answer

FCC has the highest packing efficiency, followed by BCC, then simple cubic

Question 15

If a unit cell has a coordination number of 12, which type of unit cell is it most likely to be?

Accepted Answer

Face-centered cubic

Question 16

A student calculates the percent occupied volume in an FCC unit cell and gets a value much lower than expected. Which of the following is the most likely error?

Accepted Answer

They used the atomic radius instead of the edge length in the unit cell volume calculation

Question 17

Which of the following best describes the purpose of building unit cell models in a laboratory setting?

Accepted Answer

To visualize and understand the arrangement of atoms in different types of unit cells

Question 18

A metal has a body-centered cubic structure with an atomic radius $$r. $$What is the relationship between the edge length $$a$$ and $$r$$?

Accepted Answer

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

Question 19

If the number of atoms per unit cell in a face-centered cubic structure is 4, how is this number derived?

Accepted Answer

8 corner atoms $$	imes 1/8 + 6 $$face atoms $$	imes 1/2$$

Unit Cell Models and Calculations in Solid State Chemistry

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