Solid State Test

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Solid State Test - 10

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Weekly Quiz Competition

Question 1
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Minimum interplanar spacing required for Bragg ’s diffraction is:

A
λ/4

B
λ/2

C
λ

D
2 λ

Solution

Explanation: Maximum value of incident angle can be 90 °for which sine is 1. Hence d = λ/2 ( n λ= 2.d.sin θ)
Question 2
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Which of the following Bravais lattices exist as face centered unit cell?

A
Orthorhombic

B
Monoclinic

C
Tetragonal

D
None of the mentioned

Solution

Orthorhombic lattice exists as all four types of unit cells. Besides primitive cell, monoclinic lattice exists only as end centered cell while tetragonal exists only as body centered lattices.
Question 3
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Comprehension Type
This section contains a passage describing theory, experiments, data, etc. Two questions related to the paragraph have been given. Each question has only one correct answer out of the given 4 options (a), (b), (c) and (d).
Perovskite (A), a mineral containing calcium (o), oxygen and titanium crystallises in the following cubic unit cell:

Q.

What is the Formula of A?

A
CaTiO₂

B
CaTiO₃

C
Ca₂ TiO₃

D
Ca(TiO)₂

Solution

(b)
Calcium appears at eight corners, hence number of calcium atoms = 8/8 =1
Oxygen appears on six faces and two faces share one oxygen atom hence, number of oxygen atoms = 6/2 =3
Titanium appears at the centre, thus, number of Ti-atom = 1/1 =1
Thus, A is CaTi0₃ .
Let the oxidation number of Ti = x
CaTi0₃
(+2) + x + 3 ( - 2 ) = 0
2 + x - 6 = 0
x = + 4
Question 4
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Perovskite (A), a mineral containing calcium (o), oxygen and titanium crystallises in the following cubic unit cell:

Q. What is the oxidation number of titanium in the given lattice?

A
+2

B
+3

C
+4

D
-4

Solution

(c)
Calcium appears at eight corners,hence number of calcium atoms = 8/8 =1
Oxygen appears on six faces and two faces share one oxygen atom hence, number of oxygen atoms = 6/2 =3
Titanium appears at the centre, thus, number of Ti-atom = 1/1 =1
Thus, A is CaTi0₃ .
Let the oxidation number of Ti = x CaTi0₃
(+2) + x + 3 ( - 2 ) = 0
2 + x - 6 = 0
x = + 4
Question 5
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Matching List Type
Choices for the correct combination of elements from Column I and Column II are given as options (a), (b), (c) and (d), out of which one is correct.

Match the primitive unit cells given in Column I with their axial angles axial distances given in Column II and select the correct answer from the codes given

A
a

B
b

C
c

D
d

Solution

(i) Triclinic, a b c and α βγ= 90 °Thus, (i)→(r)

(ii) Hexagonal, a = b c, α= β= 90 °,γ= 120 °Thus, (ii) →(s)

(iii) C u b ic ,a = b = c , α= β=γ= 90 °Thus, (iii) →(p)

(iv) Tetragonal, a = b c, α= β=γ= 90^o

Thus, (iv) →(q)
Question 6
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One Integer Value Correct Type
This section contains 5 questions, when worked out will result in an integer value from 0 to 9 (both inclusive)
Q. A unit cell is characterised by how many parameters?

A
6

B
5

C
4

D
3

Solution

(6) Edge length : a, b, c and angles between the edges : α,β,γ
Question 7
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How many types of primitive unit cells are there?

A
1

B
7

C
5

D
9

Solution

Primitive unit cells are

(i) Cubic

(ii) Tetragonal

(iii) Orthorhombic

(iv) Hexagonal

(v) Rhombohedral

(vi) Monoclinic

(vii) Triclinic
Question 8
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In which of the following Bravais lattices, not all axial angles are right angles?

A
Tetragonal

B
Rhombohedral

C
Orthorhombic

D
Cubic

Solution

A rhombohedral is a prism whose base is shaped as a non-square rhombus. Hence two of its six faces are rhombuses while others are rectangles. This results in a geometry for which two of the axial angles are right angles but the third is not.
Question 9
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A second order Bragg ’s diffraction of X-rays from a set of parallel planes separated by 1.155 occurs at an angle 60 °using wavelength of x. What is the value of x?

A
1

B
9

C
0

D
8

Solution

(1) By Bragg 's equation,

n = 2 (second order diffraction)
Question 10
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Number of unit cells in 240 g of element X (atomic mass 40) which crystallises in bcc pattern in yN ₀ . What is the value of y?

A
1

B
2

C
3

D
4

Solution

(3)

Number of atoms in one unit cell of bcc structure =2
Thus, number of unit cells =
Thus, y = 3