Solid State Test

Result

Solid State Test - 78

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Weekly Quiz Competition

Question 1
1 / -0

Packing fraction in FCC lattice is

A
$$\cfrac { 1 }{ 6 } \pi \quad $$

B
$$\cfrac { \sqrt { 2 } }{ 6 } \pi $$

C
$$\cfrac { \sqrt { 3 } }{ 8 } \pi \quad $$

D
$$\cfrac { \sqrt { 2 } }{ 3 } \pi $$

Solution

For a face-centered cubic unit cell, the number of atoms is four. A line can be drawn from the top corner of a cube diagonally to the bottom corner on the same side of the cube, which is equal to 4r. Using geometry, and the side length, a can be related to r as:

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

Packing fraction = $$\dfrac{Number \ of\ atom \times volume \ of \ atom}{volume \ of \ unit \ cell} $$

$$ \Rightarrow \dfrac{4 \times \frac{4}{3} \pi r^{3}}{(2\sqrt{2}r)^{3}} $$

$$ \therefore $$ Packing fraction = $$ \dfrac{\pi \sqrt{2}}{6} $$
Question 2
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Sodium oxide as anti-fluorite structure. The percentage of the tetrahedral voids occupied by the sodium ions is

A
$$12$$%

B
$$25$$%

C
$$50$$%

D
$$100$$%

Solution
Question 3
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Consider the bcc unit cells of the solids $$1$$ and $$2$$ with the position of atoms as shown below. The radius of atom $$B$$ is twice that of atom $$A$$. The unit cell edge length is $$50 \%$$ more in solid $$2$$ than in $$1$$. What is the approximate packing efficiency in solid $$2$$?

A
$$45 \%$$

B
$$65 \%$$

C
$$90 \%$$

D
$$75 \%$$

Solution

Solution:- Given $$r_B=2r_A$$

Packing fraction for Solid 2 is :

$$p.f. = \dfrac{\left(z_{eff} \times \dfrac{4}{3}\pi r^3_A\right)_A + \left(z_{eff} \times \dfrac{4}{3} \pi r^3_B\right)_B}{a^3}$$

$$2(r_A + r_B) = \sqrt{3}a$$
$$\Rightarrow 2(r_A + 2r_A) = \sqrt{3}a$$
$$\Rightarrow 2\sqrt{3} r_A = a$$

$$\Rightarrow p.f. = \dfrac{1 \times \dfrac{4}{3}\pi r^3_A + \dfrac{4}{3}\pi (8r^3_A)}{8 \times 3\sqrt{3}r^3_A} = \dfrac{9 \times \dfrac{4}{3}\pi}{8 \times 3\sqrt{3}} = \dfrac{\pi}{2\sqrt{3}}$$

p. efficiency $$= \dfrac{\pi}{2\sqrt{3}} \times 100 \simeq 90 \%$$

Option C is correct.
Question 4
1 / -0

Iodine molecules are held in the crystal lattice by?

A
London forces

B
Dipole-dipole interactions

C
Covalent bonds

D
Ionic bonds

Solution
Question 5
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In $${Na}_{2}O$$ structure

A
$${ O }^{ 2- }$$ ions constitute CCP and $${Na}^{+}$$ ions occupy all the octahedral holes

B
$${ O }^{ 2- }$$ ions constitute CCP and $${Na}^{+}$$ ions occupy all the tetahedral holes

C
$${ O }^{ 2- }$$ ions constitute CCP and $${Na}^{+}$$ ions occupy $$50$$% of tetrahedral holes and $$100$$% octahedral holes

D
$${Na}^{+}$$ ions constitute CCP and $${ O }^{ 2- }$$ ions occupy half of octahedral holes

Solution

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Question 6
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Frenkel defect is noticed in

A
$$AgBr$$

B
$$ZnS$$

C
$$AgI$$

D
All
Question 7
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Which void is smallest in close packing?

A
tetrahedral

B
octahedral

C
cubic

D
square

Solution
Question 8
1 / -0

If the unit cell length of sodium chloride crystal is $$600pm$$, then its density will be

A
$$2.165g/{ cm }^{ 3 }$$

B
$$3.247g/{ cm }^{ 3 }$$

C
$$1.79g/{ cm }^{ 3 }$$

D
$$1.082g/{ cm }^{ 3 }$$

Solution
Question 9
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An alkali metal has density $$4.5g/{ cm }^{ 3 }$$. It has cubic unit cell with an edge length $$400pm$$. Reaction of $$7.68{ cm }^{ 3 }$$ chunk of the metal with an excess of $$HCl$$ solution gives a colorless gas that occupies $$4.54L$$ at $${0}^{o}C$$ and $$1$$ bar. The unit cell of metal is

A
Simple cubic

B
BCC

C
FCC

D
End-centered

Solution
Question 10
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A solid element (monoatomic) exists in cubic crystal. If its atomic radius is $$1.0\mathring { A } $$ and the ratio of packing fraction and density is $$0.1{cm}^{3}/g$$, then the atomic mass of the element is $$\left( { N }_{ A }=6\times { 10 }^{ 23 } \right) $$

A
$$8\pi $$

B
$$16\pi $$

C
$$80\pi $$

D
$$4\pi $$

Solution