Q: A crystalline solid has a cubic unit cell with an edge length of $$400\ \mathrm{pm}$$ and contains 2 atoms per unit cell. If the molar mass of the element is $$60\ \mathrm{g/mol}$$, what is the density of the solid? ($$N_A = 6.022 \times 10$$^{23}$$\ \mathrm{mol}^{-1})$$

$$\rho = \frac{2 \times 60}{(4.00 \times 10$$^{-8}$$)^3$$ \times 6.022 \times $$10^{23}$$} = 3.11\ \mathrm{$$g/cm^3$$}$

Question 1

Which equation correctly represents Bragg's Law for X-ray diffraction in crystals?

Accepted Answer

$$n\lambda = 2d \sin	heta$$

Question 2

A metal crystallizes in a body-centered cubic (BCC) structure. If the atomic radius is $$r$$, what is the edge length $$a of $$the unit cell?

Accepted Answer

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

Question 3

Which of the following best describes the arrangement of atoms in a face-centered cubic (FCC) unit cell?

Accepted Answer

Atoms at the corners and at the center of each face

Question 4

Calculate the number of atoms per unit cell in a simple cubic structure.

Accepted Answer

1

Question 5

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

Accepted Answer

Ionic solid

Question 6

Sodium chloride (NaCl) crystallizes in a structure where Cl$$^-$$ ions form a face-centered cubic lattice and Na$$^+$$ ions occupy all octahedral holes. What is the coordination number of Na$$^+ in $$this structure?

Accepted Answer

6

Question 7

Which of the following statements about metallic bonding is correct?

Accepted Answer

Metal atoms release their valence electrons, forming a 'sea' of mobile electrons around fixed cations.

Question 8

A crystalline solid has a cubic unit cell with an edge length of $$400\ \mathrm{pm}$$ and contains 2 atoms per unit cell. If the molar mass of the element is $$60\ \mathrm{g/mol}$$, what is the density of the solid? ($$N_A = 6.022 	imes 10$$^{23}$$\ \mathrm{mol}^{-1})$$

Accepted Answer

$$ho = \frac{2 	imes 60}{(4.00 	imes 10$$^{-8}$$)^3$$ 	imes 6.022 	imes $$10^{23}$$} = 3.11\ \mathrm{$$g/cm^3$$}$

Question 9

Which of the following best explains why silicon is a semiconductor?

Accepted Answer

It has a small energy gap between the valence and conduction bands.

Question 10

Which of the following is a property of silicates that makes them important in Earth's crust?

Accepted Answer

They form extended network covalent structures with each Si atom bonded to four O atoms.

Question 11

Which of the following statements about n-type semiconductors is correct?

Accepted Answer

They are formed by doping a Group 14 element with a Group 15 element.

Question 12

Which of the following unit cell types has the highest packing efficiency?

Accepted Answer

Face-centered cubic (FCC)

Question 13

A solid is classified as a molecular solid. Which property is it most likely to exhibit?

Accepted Answer

Low melting point and poor electrical conductivity

Question 14

Which of the following best describes the structure of a fullerene (e.g., C$$_{60}$$)?

Accepted Answer

A spherical network of carbon atoms arranged in pentagons and hexagons

Question 15

Which of the following is true for the band gap in conductors, semiconductors, and insulators?

Accepted Answer

Conductors have no band gap, semiconductors have a small band gap, and insulators have a large band gap.

Question 16

Which of the following best describes the difference between hexagonal closest packing (HCP) and cubic closest packing (CCP)?

Accepted Answer

HCP has an ABAB stacking sequence, while CCP has an ABCABC stacking sequence.

Question 17

Which of the following is the correct formula for the density $$\rho of a $$crystalline solid in terms of the number of atoms per unit cell $$n$$, molar mass $$M$$, Avogadro's number $$N_A$$, and unit cell edge length $$a$$?

Accepted Answer

$$\rho = \frac{nM}{a^3$ N_A}$$

Question 18

Which of the following is a characteristic of an extrinsic semiconductor?

Accepted Answer

Its electrical properties are modified by the addition of impurity atoms.

Question 19

Which of the following statements about the rock salt structure of NaCl is correct?

Accepted Answer

Cl$$^-$$ ions form a face-centered cubic lattice and Na$$^+$$ ions occupy all octahedral holes.

Solids: Structure, Properties, and Classification (Chapter 13 Study Notes)

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