Solid State Test

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Solid State Test - 31

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Weekly Quiz Competition

Question 1
1 / -0

If the co-ordination number of an element in its crystal lattice is 8, then packing is :

A
fcc

B
hcp

C
bcc

D
none of the above

Solution

The co-ordination numbers of an element in fcc, hcp and bcc crystal lattice are $$12$$, $$12$$ and $$8$$ respectively. Hence, if the coordination number of an element in its crystal lattice is $$8$$, then packing is bcc.
Question 2
1 / -0

In a simple cubic cell, each point on a corner is shared by:

A
2 unit cells

B
1 unit cell

C
8 unit cells

D
4 unit cells

Solution

In a simple cubic cell, each point on a corner is shared by $$8$$ unit cells.
Thus, each point on a corner contributes one-eight to the unit cell.

Hence, the correct option is $$\text{C}$$
Question 3
1 / -0

The available space occupied by spheres of equal size in three dimensions in both hcp and ccp arrangement is:

A
74 %

B
70 %

C
60.4 %

D
52.4 %

Solution

$$\text { Solution:}-\quad(z=\text { no. of atoms per unit cell) } \\$$
$$\text { [Percentage of occupied volume }=z \times \dfrac{\text { Volume of sphere }}{\text { volume of cube /hexagon}}]$$

$$z=4,$$
$$4 \pi=a \sqrt{2} \\$$
$$r=a \sqrt{2} \\$$
$$\text { percentage }=4\times \dfrac{4 / 3 \pi \gamma^{3}}{a^{3}} \times 100 \%$$
$$=\dfrac{16}{3} \times \dfrac{\pi \gamma^{3}}{a^{3}} \\$$
$$=\dfrac{\pi}{3 \sqrt{2}} \times 100 \\$$
$$\text { (%of occupied Vol. } =74 \% \text { ) }$$

$$\text { for hcp, }$$

$$z=6 \quad 2 r=a \\$$
$$r=9 / 2 \\$$
$$\text { percentage }=6 \times \dfrac{4 / 3 \pi \gamma^{3}}{3 \sqrt{2} a^{3}}$$
$$

$$\text { (Volume of hexagon } \left.=3 \sqrt{2} \mathrm{a}^{3}\right) \\$$
$$\quad=\dfrac{\pi \gamma^{3}}{3 \sqrt{2} a^{3}} \times 100 \\$$
$$=\dfrac{\pi}{3 \sqrt{2}} \times 100$$

$$\text { (%of occupied Vol. } =74 \% \text { ) }$$

$$\text { Hence correct ans is }(A)$$
Question 4
1 / -0

For an orthorhombic system, axial ratios are $$a\neq b\neq c$$ and the axial angles are:

A
$$\;\alpha=\beta=\gamma\neq 90^{\circ}$$

B
$$\;\alpha=\beta=\gamma=90^{\circ}$$

C
$$\;\alpha\neq \beta=\gamma=90^{\circ}$$

D
$$\;\alpha\neq\beta\neq\gamma=90^{\circ}$$

Solution

For orthorhombic system axial ratios are $$a\neq b\neq c$$ and the axial angles are $$\;\alpha=\beta=\gamma=90^{\circ}$$. Thus, all the three edge lengths are unequal but all the angles are equal. They are equal to $$90^0$$.
Question 5
1 / -0

An element crystallizes in a structure having a fcc unit cell with edge length $$200$$ pm. Calculate its density (in g cm$$^{-3}$$) if $$200$$ g of this element contain $$24\times10^{23}$$ atoms.

A
$$10.4$$

B
$$2.6$$

C
$$41.6$$

D
$$83.2$$

Solution

Weight of $$24\times10^{23}$$ atoms $$=200$$ g
$$\therefore\,$$ Weight of $$4$$ atoms $$=\displaystyle\frac{200}{24\times10^{23}}\times4$$ g
The fcc structure contains $$4$$ atoms in a unit cell.
Density $$=\displaystyle\frac{\text{Mass of unit cell}}{\text{Volume of unit cell}}$$ $$=\displaystyle\frac{200\times4}{24\times10^{23}\times(200\times10^{-10})^3}$$ $$=41.6$$ g cm$$^{-3}$$
Hence, the density of the unit cell is $$41.6$$ g cm$$^{-3}$$.
Question 6
1 / -0

Which of the following is a primitive unit cell?

A
Simple cubic

B
Body-centred cubic

C
Face-centred cubic

D
Both body-centred and face-centred cubic
Question 7
1 / -0

The more efficient mode of packing of identical atoms in one layer is :

A
square close packing pattern

B
hexagonal close packing pattern

C
trigonal closed packing

D
none of the above

Solution

The more efficient mode of packing of identical atoms in one layer is hexagonal close packing pattern.
This is because the empty space in hexagonal closed packing is much less than that in square close packing.
Question 8
1 / -0

A tetrahedral void in a crystal implies that:

A
the shape of the void is tetrahedral

B
molecules forming the void are tetrahedral in shape

C
the void is surrounded tetrahedrally by four spheres

D
the void is surrounded by six spheres

Solution

A tetrahedral void in a crystal implies that the void is surrounded tetrahedrally by four spheres. The four spheres are located at the four corners of the tetrahedron.
Question 9
1 / -0

A metallic crystal crystallizes into a lattice containing a sequence of layers AB AB AB.... . Any packing of spheres leaves out voids in the lattice. What percentage of the volume of this lattice is empty space?

A
$$\;74\%$$

B
$$\;26\%$$

C
$$\;50\%$$

D
$$\;33\%$$

Solution

AB AB AB describes the hexagonal close-packed arrangement of spheres.

The available space occupied by spheres of equal size in three dimensions in the hexagonal close packed arrangement is 74%.

The vacant space is $$100-74=26$$%.

Hence, the correct option is $$\text{B}$$
Question 10
1 / -0

The number of octahedral sites in a cubical close packed array of $$N$$ spheres is :

A
$$\dfrac N2$$

B
2N

C
N

D
4N

Solution

The ratio of spheres and octahedral void in ccp is $$1:1$$. Therefore, for N spheres, the number of octahedral voids will be N.
The number of octahedral sites in a cubical close packed array of N spheres is N.
For example, a ccp lattice contains $$4$$ atoms per unit cell. It has $$4$$ octahedral voids and $$8$$ tetrahedral voids.

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Re-Attempt Weekly Quiz Competition

Solid State Test - 31

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Solid State Test - 31

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Question 1

fcc

hcp

bcc

none of the above

Solution

Question 2

2 unit cells

1 unit cell

8 unit cells

4 unit cells

Solution

Question 3

74 %

70 %

60.4 %

52.4 %

Solution

Question 4

$$\;\alpha=\beta=\gamma\neq 90^{\circ}$$

$$\;\alpha=\beta=\gamma=90^{\circ}$$

$$\;\alpha\neq \beta=\gamma=90^{\circ}$$

$$\;\alpha\neq\beta\neq\gamma=90^{\circ}$$

Solution

Question 5

$$10.4$$

$$2.6$$

$$41.6$$

$$83.2$$

Solution

Question 6

Simple cubic

Body-centred cubic

Face-centred cubic

Both body-centred and face-centred cubic

Question 7

square close packing pattern

hexagonal close packing pattern

trigonal closed packing

none of the above

Solution

Question 8

the shape of the void is tetrahedral

molecules forming the void are tetrahedral in shape

the void is surrounded tetrahedrally by four spheres

the void is surrounded by six spheres

Solution

Question 9

$$\;74\%$$

$$\;26\%$$

$$\;50\%$$

$$\;33\%$$

Solution

Question 10

$$\dfrac N2$$

2N

N

4N

Solution

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