Figure 2: A hexagonal close-packed layer of atoms in two dimensions.(b)Figure 3: Conventional unit cells for: (a) the fcc structure; (b) the bcc structure.(a)a)A hexagonal close-packed layer in two dimensions is shown in figure 2.By identifying a suitable unit cell, calculate the packing fraction of this structure.b) Two possible cubic crystal structures are shown in figure 3. Part (a) shows the fcc struc-ture, in which atoms are touching along a face-diagonal. Part (b) shows the bcc structure,in which atoms are touching along a body diagonal of the cube.Calculate the packing fractions of each of these structures. Which one of them is close-packed?c) Copper (Cu) has an fcc structure, where the mass of a Cu atom is 63 in atomic mass units.The density of Cu is 8.9x10³ kgm-³.Tungsten (W) typically has a bcc structure, where the mass of a W atom is 184 in atomicmass units. The density of W is 19.3x10³ kgm-³.(i) Use the above data to find the radius of a Cu atom, and of a W atom.(ii) Which atom has the larger radius, and why?You may use the fact that 1 atomic mass unit is equivalent to 1.66 × 10-27 kg.

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A hexagonal close-packed layer in two dimensions is shown in figure 2. By identifying a suitable unit cell, calculate the packing fraction of this structure.

Chemistry: Principles and Practice

3rd Edition

ISBN:9780534420123

Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer

Publisher:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer

Chapter11: Liquids And Solids

Section: Chapter Questions

Problem 11.87QE

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Concept explainers

Crystallography

Crystallography is the category of science that focuses on the atomic and molecular arrangements with their bonding constituting the crystal structure. It is derived experimentally and originated in the year 1912. It is a combination of two words; those are crystal, meaning a cold drop, and graph, meaning writing.

Question

Figure 2: A hexagonal close-packed layer of atoms in two dimensions.
(b)
Figure 3: Conventional unit cells for: (a) the fcc structure; (b) the bcc structure.
(a)
a)
A hexagonal close-packed layer in two dimensions is shown in figure 2.
By identifying a suitable unit cell, calculate the packing fraction of this structure.
b) Two possible cubic crystal structures are shown in figure 3. Part (a) shows the fcc struc-
ture, in which atoms are touching along a face-diagonal. Part (b) shows the bcc structure,
in which atoms are touching along a body diagonal of the cube.
Calculate the packing fractions of each of these structures. Which one of them is close-
packed?
c) Copper (Cu) has an fcc structure, where the mass of a Cu atom is 63 in atomic mass units.
The density of Cu is 8.9x10³ kgm-³.
Tungsten (W) typically has a bcc structure, where the mass of a W atom is 184 in atomic
mass units. The density of W is 19.3x10³ kgm-³.
(i) Use the above data to find the radius of a Cu atom, and of a W atom.
(ii) Which atom has the larger radius, and why?
You may use the fact that 1 atomic mass unit is equivalent to 1.66 × 10-27 kg.

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Step 5: Determination of effective number of atoms (Z)

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