Solid State Test

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Solid State Test - 17

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Weekly Quiz Competition

Question 1
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Which type of 'defect' has the presence of cations in the interstitial sites ?

A
Frenkel defect

B
Metal deficiency defect

C
Schottky defect

D
Vacancy defect
Question 2
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Percentage of free space in cubic close-packed structure and in body centred packed structure are, respectively:

A
$$30\%$$ and $$26\%$$

B
$$26\%$$ and $$32\%$$

C
$$32\%$$ and $$48\%$$

D
$$48\%$$ and $$26\%$$

Solution

Packing fraction of cubic close packing and body centred packing are 0.74 and 0.68 respectively.
Therefore the free space are respectively 26% and 32%.
Question 3
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In a monoclinic unit cell, the relation of sides and angles are, respectively :

A
$$a=b\neq c$$ and $$\alpha =\beta =\gamma =90^o$$

B
$$a\neq b\neq c$$ and $$\alpha =\beta =\gamma =90^o$$

C
$$a\neq b\neq c$$ and $$\beta =\gamma =90^o\neq \alpha$$

D
$$a\neq b\neq c$$ and $$\alpha \neq \beta \neq \gamma \neq 90^o$$

Solution

monoclinic crystal is one of the 7 crystal system. In monoclinic system, the crystal is describe by vectors of unequal lengths,

So, we have $$a\neq b\neq \ c$$ and $$\beta = \gamma = 90^0 \neq \alpha$$

Option C is correct.
Question 4
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The packing efficiency of the two-dimensional square unit cell shown in the given figure is :

A
$$39.27\%$$

B
$$68.02\%$$

C
$$74.05\%$$

D
$$78.54\%$$

Solution

Let $$a=2\sqrt2r$$
Let us consider the square plane and $$L$$ be the length of square (given).
$$\text{Area} = L^{2}$$
By applying pythagoras theorem,
$$L^{2}$$ + $$L^{2}$$ = $$(2r)^{2}$$
$$4r^{2}=$$ $$2L$$
$$\dfrac{\sqrt{2L}}{2}=r$$
$$\text{Area} =$$ $$2 \pi \times \dfrac{\sqrt{(2L)}}{4}^{2}$$
Packing efficiency $$ =\displaystyle \frac{2\times\pi

\mathrm{r}^{2}}{(2\sqrt{2}\mathrm{r})^{2}}=\frac{2\pi

\mathrm{r}^{2}}{8\mathrm{r}^{2}}=\frac{\pi}{4}= 78.5\%$$
Question 5
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Directions For Questions

In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between them. A space-filling model of this structure called hexagonal close-packed (HCP), is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of these three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with a third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be 'r'.

...view full instructions

The empty space in this HCP unit cell is :

A
$$74\%$$

B
$$47.6\%$$

C
$$32\%$$

D
$$26\%$$

Solution

As we know,
Packing fraction = 74 %
Empty space = 26 %
Question 6
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The number of hexagonal faces that are present in a truncated octahedron is:

A
$$8$$

B
$$9$$

C
$$10$$

D
$$11$$

Solution

The number of hexagonal faces that are present in a truncated octahedron is 8.

A truncated octahedron is constructed from a regular octahedron with side length 3a by the removal of six right square pyramids, one from each point. It has 6 squares and 8 hexagons.
Question 7
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A compound is formed by cation $$C$$ and anion $$A$$. The anions form hexagonal close packed (hcp) lattice and the cations occupy $$75\%$$ of octahedral voids. The formula of the compound is :

A
$$C_2A_3$$

B
$$C_3A_2$$

C
$$C_3A_4$$

D
$$C_4A_3$$

Solution

Anions (A) are in hcp, so the number of anions $$(A)=6$$

Cations (C) are in $$75\% \,O.V.,$$ so number of cations (C)
$$=6\times \dfrac{75}{100}$$

$$=\dfrac{18}{4}$$

$$=\dfrac{9}{2}$$

$$\Rightarrow$$ So, the formula of compound will be

$$C_{\frac{9}{2}}A_6\Rightarrow C_9A_{12}$$

$$C_9A_{12}\Rightarrow C_3A_4$$
Question 8
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The vacant space in a $$bcc$$ unit cell is:

A
$$23\%$$

B
$$32\%$$

C
$$26\%$$

D
$$48\%$$

Solution

Packing fraction of BCC unit cell is 68%. Therefore, the vacant space in BCC unit cell is $$32%$$.
Question 9
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In tetragonal crystal system, which of the following is true?

A
All axial lengths and all axial angles are equal

B
All three axial lengths are equal

C
All three axial angles are equal

D
Two axial angles are equal but the third is different

Solution

In tetragonal system
$$a=b\ne c,$$ and $$\alpha =\beta =\gamma ={90}^{o}$$
Here all three axial angles are equal but all lengths in tetragonal system are not same.

Hence, option $$C$$ is correct.
Question 10
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Amorphous solids are:

A
Solid substances in real sense

B
Liquids in real sense

C
Supercooled liquids

D
Substances with definite melting point

Solution

Amorphous solids are supercooled liquids and they are irregularly arranged in nature of their structure. They never possess a definite melting point.

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Solid State Test - 17

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Solid State Test - 17

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Question 1

Frenkel defect

Metal deficiency defect

Schottky defect

Vacancy defect

Question 2

$$30\%$$ and $$26\%$$

$$26\%$$ and $$32\%$$

$$32\%$$ and $$48\%$$

$$48\%$$ and $$26\%$$

Solution

Question 3

$$a=b\neq c$$ and $$\alpha =\beta =\gamma =90^o$$

$$a\neq b\neq c$$ and $$\alpha =\beta =\gamma =90^o$$

$$a\neq b\neq c$$ and $$\beta =\gamma =90^o\neq \alpha$$

$$a\neq b\neq c$$ and $$\alpha \neq \beta \neq \gamma \neq 90^o$$

Solution

Question 4

$$39.27\%$$

$$68.02\%$$

$$74.05\%$$

$$78.54\%$$

Solution

Question 5

$$74\%$$

$$47.6\%$$

$$32\%$$

$$26\%$$

Solution

Question 6

$$8$$

$$9$$

$$10$$

$$11$$

Solution

Question 7

$$C_2A_3$$

$$C_3A_2$$

$$C_3A_4$$

$$C_4A_3$$

Solution

Question 8

$$23\%$$

$$32\%$$

$$26\%$$

$$48\%$$

Solution

Question 9

All axial lengths and all axial angles are equal

All three axial lengths are equal

All three axial angles are equal

Two axial angles are equal but the third is different

Solution

Question 10

Solid substances in real sense

Liquids in real sense

Supercooled liquids

Substances with definite melting point

Solution

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