Solid State Test

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Solid State Test - 57

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Weekly Quiz Competition

Question 1
1 / -0

A crystal lattice is a periodic structure in

A
$$2$$ dimension

B
$$3$$ dimension

C
vacuum space

D
none

Solution

$$\text{A crystal lattice is a regular arrangement of the constituent atoms or ions or molecules in }three-dimensional$$ $$\text{space. A crystal lattice also called a space lattice or simply, a lattice. There are only 14 possible three-}$$$$\text{dimensional lattices. These are called Bravais’ lattices.}$$

Option B is correct.
Question 2
1 / -0

The neon atoms has a radius of $$160\,pm.$$ What is the edge of the unit cell of a face centered structured of neon ?

A
$$490 \,pm$$

B
$$320 \,pm$$

C
$$453 \,pm$$

D
$$481 \,pm$$

Solution

For body centered cubic crystals, the relation between side of unit cell (a) and radius of atom (r) is :
$$a\sqrt2$$ = $$4r$$
Given, r = 160 pm

Hence, a = $$\cfrac{4r}{\sqrt2}$$ = $$\cfrac{4\space \times \space 160}{\sqrt2}$$ = 452.6 pm ≈ 453 pm.

Thus, option C is correct.
Question 3
1 / -0

Which of the following has the smallest packing efficiency for atoms of a single type ?

A
Body centered cubic

B
Face centered cubic

C
Simple cubic

D
None of these

Solution

The packing efficiency of the following cubic unit cells are :
BCC - 68%
FCC - 74%
Simple cubic- 52.4%

Thus, option C is correct.
Question 4
1 / -0

The numbers of tetrahedral and octahedral holes in a hexagonal primitive unit cell are :

A
$$8, 4$$

B
$$6, 12$$

C
$$2, 1$$

D
$$12, 6$$

Solution

A hexagonal primitive unit cell contains 6 atoms in the crystal structure i.e. n = 6
We know that, for hcp,

The number of octahedral voids will be equal to the number of atoms in the crystal structure.
No. of octahedral voids = 6.

The number of tetrahedral voids will be equal to two times the number of atoms in the crystal structure .
No. of tetrahedral voids = 2 x 6 = 12.

Thus, option D is correct.
Question 5
1 / -0

The number of atoms present in a hexagonal close-packed unit cell is :

A
$$4$$

B
$$6$$

C
$$8$$

D
$$12$$

Solution

The closest packing of spheres in two dimensions has hexagonal symmetry where every sphere has six nearest neighbours. Hexagonal close-packing corresponds to a ABAB stacking of such planes.

The hexagonal closest packed (hcp) has a coordination number of 12 and contains 6 atoms per unit cell.

Thus, option B is correct.
Question 6
1 / -0

The unit cell present in ABCABC, closest packing of atoms is :

A
hexagonal

B
tetragonal

C
face centered cube

D
primitive cube

Solution

ABCABCABC... patterns corresponds to ccp (cubic close packing) or fcc (face centered cubic) unit cell in which occupied space is 74% and empty space is 26%.

Thus, option C is correct.
Question 7
1 / -0

Ferrous oxide has a cubic structure and edge length of the unit cell is $$5.0 \,\mathring {A}.$$ Assuming the density of ferrous oxide to be $$3.84 \,g/cm^3,$$ the no. of $$Fe^{2+}$$ and $$O^{2-}$$ ions present in each unit cell be : $$(use : N_{A} = 6 \times 10^{23})$$ :

A
$$4Fe^{2+}$$ and $$4O^{2-}$$

B
$$2Fe^{2+}$$ and $$2O^{2-}$$

C
$$1Fe^{2+}$$ and $$1O^{2-}$$

D
$$3Fe^{2+}$$ and $$4O^{2-}$$

Solution

Mass of unit cell $$= d \times V$$
$$= (5 \times 10^{-8})^{3} \times 3.84 \times 6 \times 10^{23}$$
$$= 288$$ a.m.u.
Mass of formula unit of $$FeO = 56 + 16 = 72$$ a.m.u.
$$\therefore$$ no. of formula unit $$= \dfrac{288}{72} = 4$$
Question 8
1 / -0

In the close packing of atoms, there are :

A
one tetrahedral void and two octahedral voids per atom

B
two tetrahedral voids and one octahedral void per atom

C
two of each tetrahedral and octahedral voids per atom

D
one of each tetrahedral and octahedral void per atom

Solution

In the close packing of atoms, the number of tetrahedral voids per atom is two and the number of octahedral voids per atom is one. These are applicable for cubic closed packing (CCP) and hexagonal closed packing (hcp).

Thus, option B is correct.
Question 9
1 / -0

The unit cell present in ABAB, closest packing of atoms is :

A
hexagonal

B
tetragonal

C
face centered cube

D
primitive cube

Solution

The closest packing of spheres in two dimensions has hexagonal symmetry where every sphere has six nearest neighbors. Hexagonal close-packing corresponds to a ABAB stacking of such planes. Each atom has twelve nearest neighbors in hcp.
Thus, option A is correct.
Question 10
1 / -0

Graphite has h.c.p. arrangements of carbon atoms and the parallel planes are $$3.35 \,\mathring {A}$$ apart. Determine density of graphite:

A
$$2.46 \,g/cc$$

B
$$0.41 \,g/cc$$

C
$$1 \,g/cc$$

D
$$1.41 \,g/cc$$

Solution

In hcp arrangement total height
$$h = 4 \times \sqrt{ \dfrac{2}{3}}r$$
as per given
$$\dfrac{h}{2} = 2 \sqrt{\dfrac{2}{3}}r = 3.35 \,\mathring {A} = 3.35 \times 10^{-8} \,cm.$$
Volume of unit cell $$= 24 \sqrt{2}r^{3}$$
$$= 24 \sqrt{2} \left ( \sqrt{\dfrac{3}{2}} \times \dfrac{1}{2} \times 3.35 \times 10^{-8} \right )^{3}$$
$$= 2.93 \times 10^{-22} \,cm^{3}$$
Effective no. of atoms in hexagonal unit cell $$= 6$$
$$\therefore density = \dfrac{6 \times 12}{6.023 \times 10^{23} \times 2.93 \times 10^{-22}}$$
$$= 0.41 \,g/cc$$

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Re-Attempt Weekly Quiz Competition

Solid State Test - 57

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Solid State Test - 57

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SHARING IS CARING

Question 1

$$2$$ dimension

$$3$$ dimension

vacuum space

none

Solution

Question 2

$$490 \,pm$$

$$320 \,pm$$

$$453 \,pm$$

$$481 \,pm$$

Solution

Question 3

Body centered cubic

Face centered cubic

Simple cubic

None of these

Solution

Question 4

$$8, 4$$

$$6, 12$$

$$2, 1$$

$$12, 6$$

Solution

Question 5

$$4$$

$$6$$

$$8$$

$$12$$

Solution

Question 6

hexagonal

tetragonal

face centered cube

primitive cube

Solution

Question 7

$$4Fe^{2+}$$ and $$4O^{2-}$$

$$2Fe^{2+}$$ and $$2O^{2-}$$

$$1Fe^{2+}$$ and $$1O^{2-}$$

$$3Fe^{2+}$$ and $$4O^{2-}$$

Solution

Question 8

one tetrahedral void and two octahedral voids per atom

two tetrahedral voids and one octahedral void per atom

two of each tetrahedral and octahedral voids per atom

one of each tetrahedral and octahedral void per atom

Solution

Question 9

hexagonal

tetragonal

face centered cube

primitive cube

Solution

Question 10

$$2.46 \,g/cc$$

$$0.41 \,g/cc$$

$$1 \,g/cc$$

$$1.41 \,g/cc$$

Solution

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