Solid State Test

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Solid State Test - 38

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Weekly Quiz Competition

Question 1
1 / -0

Tetragonal crystal system has the following unit cell dimensions.

A
$$a = b = c$$ and $$\alpha = \beta = \gamma = 90^{\circ}$$

B
$$a = b \neq c$$ and $$\alpha = \beta = \gamma = 90^{\circ}$$

C
$$a \neq b \neq c$$ and $$\alpha = \beta = \gamma = 90^{\circ}$$

D
$$a = b \neq c$$ and $$\alpha = \beta = 90^{\circ}, \gamma = 120^{\circ}$$
Question 2
1 / -0

The closest-packing sequence $$ABC\ ABC .....$$ represents:

A
primitive cubic packing

B
body-centered cubic packing

C
face-centered cubic packing

D
hexagonal packing

Solution

The closest-packing sequence $$ABAB.....$$ represents hexagonal packing.
The closest-packing sequence $$AAAA.....$$ represents primitive cubic packing.
The closest-packing sequence $$ABCABC.....$$ (with spheres of the third layer placed into octahedral voids) represents face-centered cubic packing.

Hence, option $$C$$ is correct.
Question 3
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If the temperature of 500 mL of air increases from 27°C to 42°C under constant pressure, then the increases in volume shall be

A
15 mL

B
20 mL

C
25 mL

D
30 mL

Solution
Question 4
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How many tetrahedral voids are occupied in diamond?

A
$$25$$%

B
$$50$$%

C
$$75$$%

D
$$100$$%

Solution

One half or 50% tetrahedral voids are occupied in diamond. Its unit cell is similar to face centered cubic unit cell.
Question 5
1 / -0

Directions For Questions

Packing refers to the arrangement of constituent units in such a way that the forces of attraction among the constituent particles is maximum and the constituents occupy the maximum available space. In two-dimensions, there are square close packing and hexagonal close packing. In three-dimensions, however, there are hexagonal close packing, cubic close packing and body-centred cubic packing.
(i) $$hcp: AB\ AB\ AB\ AB ....$$ arrangement
Coordination no. $$= 12$$
% occupied space $$= 74$$
(ii) $$ccp : ABC \ ABC ....$$ arrangement
Coordinate no $$= 12$$
% occupied space $$= 74$$
(iii) $$bcc : 68$$% space is occupied
Coordination no. $$= 8$$.

...view full instructions

The space occupied by spheres in bcc arrangement is

A
$$74$$%

B
$$70$$%

C
$$68$$%

D
$$60.4$$%

Solution

The space occupied by spheres in bcc arrangement is 68%.
The empty space is 32%.

Packing fraction $$\displaystyle =\dfrac {Z \times \dfrac {4}{3}\pi r^3}{a^3}= \dfrac {2 \times \dfrac

{4}{3} \pi r^3}{(\dfrac {4r}{\sqrt{2}})^3}=0.68=68$$%
Question 6
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A solid solution of $$CdBr_{2}$$ in $$AgBr$$ contains:

A
schottky defects

B
frenkel defects

C
colour centres

D
frenkel as well as schottky defects

Solution

Frenkel Defect: This defect is shown by ionic solids. The smaller ion is dislocated from its normal site to an interstitial site. Frenkel defect is shown by ionic substance in which there is a large difference in the size of ions.

Schottky Defect: It is basically a vacancy defect in ionic solids. In order to maintain electrical neutrality, the number of missing cations and anions are equal. Schottky defect is shown by ionic substances in which the cation and anion are of almost similar sizes.

The radius ratio for CdBr2 and AgBr is intermediate. Thus, it shows both frenkel and schottky defects.
Question 7
1 / -0

The total volume of atoms present in a face-centered cubic unit cell of a metal is: $$(r$$ is atomic radius)

A
$$\dfrac {16}{3}\pi r^{3}$$

B
$$\dfrac {20}{3}\pi r^{3}$$

C
$$\dfrac {24}{3}\pi r^{3}$$

D
$$\dfrac {12}{3}\pi r^{3}$$

Solution

$$Z_{eff}$$ in $$FCC$$ unit cell= $$6\times \cfrac {1}{2}+\cfrac {1}{8}\times 8$$
$$=4$$
Volume of one atom=$$\dfrac{4}{3}\pi r^3$$
Volume of atoms in $$FCC$$=$$4\times \cfrac {4}{3}\pi r^3$$
$$=\cfrac {16}{3} \pi r^3$$
Question 8
1 / -0

Directions For Questions

Packing refers to the arrangement of constituent units in such a way that the forces of attraction among the constituent particles is maximum and the constituents occupy the maximum available space. In two-dimensions, there are square close packing and hexagonal close packing. In three-dimensions, however, there are hexagonal close packing, cubic close packing and body-centred cubic packing.
(i) $$hcp: AB\ AB\ AB\ AB ....$$ arrangement
Coordination no. $$= 12$$
% occupied space $$= 74$$
(ii) $$ccp : ABC \ ABC ....$$ arrangement
Coordinate no $$= 12$$
% occupied space $$= 74$$
(iii) $$bcc : 68$$% space is occupied
Coordination no. $$= 8$$.

...view full instructions

The empty space left in hcp in three-dimensions is__________.

A
$$26$$%

B
$$74$$%

C
$$52.4$$%

D
$$80$$%

Solution

The space left in hcp in three-dimensions is 26%.
The space occupied by spheres in the hcp arrangement is 74%.

Packing fraction is

$$\displaystyle\dfrac {6 \times \dfrac {4}{3}\pi r^3}{ a^2csin60^o}= 0.74$$

i.e. 74 %

The space left in hcp in three-dimensions is 26 %

a=2r, c=$$2\sqrt{\dfrac{2}{3}}a$$

Hence, the correct option is $$\text{A}$$
Question 9
1 / -0

The packing fraction of the element that crystallises in simple cubic arrangement is:

A
$$\dfrac {\pi}{4}$$

B
$$\dfrac {\pi}{6}$$

C
$$\dfrac {\pi}{3}$$

D
$$\dfrac {\pi}{2}$$

Solution

In simple unit cell $$a = 2r$$
$$Z = 1$$
$$\therefore$$ Packing fraction $$= \dfrac {\text {Occupied volume}}{\text {Total volume}}$$
$$= \dfrac {\dfrac {4}{3}\pi r^{3}}{a^{3}} = \dfrac {\dfrac {4}{3}\pi r^{3}}{(2r)^{3}} = \dfrac {\pi}{6}$$
Question 10
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A certain sample of cuprous sulphide is found to have the composition $$Cu_{192}S_{100}$$ because of incorporation of $$Cu^{2+}$$ and $$Cu^+$$ ions in the crystal then ratio of $$Cu^{2+}$$ and $$Cu^{+}$$ ions is:

A
0.08 : 1.00

B
1 : 23

C
1 : 24

D
1 : 1

Solution

Let, $$x$$ number of $$Cu^{+2}$$ are present in $$192$$ $$Cu$$ atoms
Now, $$2x+192-x=100\times 2$$
$$x=8$$

$$Cu^{+2}=8$$ , $$Cu^{+}=192$$
$$Cu^{+2}: Cu^{+}\Rightarrow 8:192=1:23$$

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Solid State Test - 38

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Solid State Test - 38

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Question 1

$$a = b = c$$ and $$\alpha = \beta = \gamma = 90^{\circ}$$

$$a = b \neq c$$ and $$\alpha = \beta = \gamma = 90^{\circ}$$

$$a \neq b \neq c$$ and $$\alpha = \beta = \gamma = 90^{\circ}$$

$$a = b \neq c$$ and $$\alpha = \beta = 90^{\circ}, \gamma = 120^{\circ}$$

Question 2

primitive cubic packing

body-centered cubic packing

face-centered cubic packing

hexagonal packing

Solution

Question 3

15 mL

20 mL

25 mL

30 mL

Solution

Question 4

$$25$$%

$$50$$%

$$75$$%

$$100$$%

Solution

Question 5

$$74$$%

$$70$$%

$$68$$%

$$60.4$$%

Solution

Question 6

schottky defects

frenkel defects

colour centres

frenkel as well as schottky defects

Solution

Question 7

$$\dfrac {16}{3}\pi r^{3}$$

$$\dfrac {20}{3}\pi r^{3}$$

$$\dfrac {24}{3}\pi r^{3}$$

$$\dfrac {12}{3}\pi r^{3}$$

Solution

Question 8

$$26$$%

$$74$$%

$$52.4$$%

$$80$$%

Solution

Question 9

$$\dfrac {\pi}{4}$$

$$\dfrac {\pi}{6}$$

$$\dfrac {\pi}{3}$$

$$\dfrac {\pi}{2}$$

Solution

Question 10

0.08 : 1.00

1 : 23

1 : 24

1 : 1

Solution

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