Solid State — Page 2 | JEE Chemistry

Q11

In a compound atoms of element Y from ccp lattice and those of element X occupy 2/3rd of tetrahedral voids. The formula of the compound will be :

A X4Y3

B X2Y3

C X2Y

D X3Y4

Correct Answer

Option A

Solution

From the given data, we have Number of

Y

atoms in a unit cell

=4

Number of

X

atoms in a unit cell

= 8 \times {2 \over 3} = {{16} \over 3}

From the above we get the formula of the compound as

{X_{16/3}}{Y_4}\,\,

or

{X_4}{Y_3}

Q12

The radius of the largest sphere which fits properly at the centre of the edge of a body centred cubic unit cell is : (Edge length is represented by 'a')

A 0.134 a

B 0.067 a

C 0.047 a

D 0.027 a

Correct Answer

Option B

Solution

a = 2(R + r) $\Rightarrow$

{a \over 2} = \left( {R + r} \right)

......(1) For bcc,

\sqrt 3 a

= 4R Using (i) and (ii)

{a \over 2} = \left( {{{a\sqrt 3 } \over 4} + r} \right)

$\Rightarrow$ r =

a\left( {{{2 - \sqrt 3 } \over 4}} \right)

$\Rightarrow$ r = 0.067 a

Q13

Given below are two statements. Statement I : Frenkel defects are vacancy as well as interstitial defects. Statement II : Frenkel defect leads to colour in ionic solids due to presence of F-centres. Choose the most appropriate answer for the statements from the options given below :

A Statement I is false but Statement II is true

B Both Statement I and Statement II are true

C Statement I is true but Statement II is false

D Both Statement I and Statement II are false

Correct Answer

Option C

Solution

To answer this question, let's analyze each statement separately.

Statement I: Frenkel defects are vacancy as well as interstitial defects.

This statement is true.

A Frenkel defect, also known as a dislocation defect, occurs in a crystalline solid when an atom or ion leaves its normal site and moves to an interstitial site, creating a vacancy defect at its original position and an interstitial defect at the new position.

However, it's crucial to note that the vacancy and interstitial are created by the same atom or ion moving from one site to another within the crystal.

So, the Frenkel defect involves both a vacancy and an interstitial defect, but they are correlated because they involve the displacement of the same atom or ion.

Statement II: Frenkel defect leads to color in ionic solids due to presence of F-centres.

This statement is false.

The color in ionic solids is usually caused by F-centers (color centers), which are defects formed when an anion vacancy is occupied by one or more electrons.

These electrons can absorb visible light, giving the crystal a characteristic color.

However, the Frenkel defect, involving an atom or ion moving from its lattice site to an interstitial site, does not directly lead to the creation of F-centers.

Instead, the coloration associated with F-centers is most commonly linked with Schottky defects (which involve paired vacancies of cations and anions but do not include displaced atoms to interstitial sites) or directly with anion vacancies that are not necessarily related to Frenkel defects.

Conclusion: Given the explanations above, the correct answer is Option C: Statement I is true but Statement II is false.

Q14

Element 'B' forms ccp structure and 'A' occupies half of the octahedral voids, while oxygen atoms occupy all the tetrahedral voids, The structure of bimetallic oxide is :

A AB2O4

B A2BO4

C A4B2O

D A2B2O

Correct Answer

Option A

Solution

We know, for cubic unit cell, only FCC has octahedral and tetrahedral voids.

B forms ccp structure means B forms FCC structure.

For FCC, z = 4 We know for octahedral voids z = 4.

In this lattice, A present in half of octahedral voids.

$\therefore$ For A, z = 2 For tetrahedral voids, 2z = 8.

In this lattice, oxygen present in all the tetrahedral voids.

$\therefore$ Simplest formula :

{A_{4 \times {1 \over 2}}}{B_4}{O_8}

=

{A_2}{B_4}{O_8}

=

A{B_2}{O_4}

Q15

Given below are two statements. One is labelled as Assertion A nd the other is labelled as Reason R. Assertion A : Sharp glass edge becomes smooth on heating it upto its melting point. Reason R : The viscosity of glass decreases on melting. Choose the most appropriate answer from the options given below.

A A is true but R is false

B Both A and R are true but R is NOT the correct explanation of A.

C A is false but R is true.

D Both A and R are true and R is the correct explanation of A.

Correct Answer

Option B

Solution

On heating the glass, it melts and takes up rounded shape at the edges, which has minimum surface area.

This is due to the property of surface tension of liquids and not due to decrease in viscosity.

Viscosity generally decreases as the temperature increases.

Hence, both A and R are true but R is not the correct explanation of A.

Q16

An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of the faces of the cube. The empirical formula for this compound would be :

A AB

B A2B

C AB3

D A3B

Correct Answer

Option C

Solution

Number of A ions in the unit cell.

= {1 \over 8} \times 8 = 1

Number of

B

ions in the unit cell

= {1 \over 2} \times 6 = 3

Hence empirical formula of the compound

= A{B_3}

Q17

The parameters of the unit cell of a substance are a = 2.5, b = 3.0, c = 4.0,

\alpha

= 90

^\circ

,

\beta

= 120

^\circ

,

\gamma

= 90

^\circ

. The crystal system of the substance is :

A Hexagonal

B Orthorhombic

C Monoclinic

D Triclinic

Correct Answer

Option C

Solution

a $\ne$ b $\ne$ c and $\alpha$ = $\gamma$ = 90

^\circ

$\ne$ $\beta$ are parameters of monoclinic unit cell.

Q18

Which premitive unit cell has unequal edge lengths (a

\ne

b

\ne

c) and all axial angles different from 90o?

A Hexagonal

B Tetragonal

C Triclinic

D Monoclinic

Correct Answer

Option C

Solution

In Triclinic unit cell a $\ne$ b $\ne$ c & $\alpha$ $\ne$ $\beta$ $\ne$ $\gamma$ $\ne$ 90o

Q19

A hard substance melts at high temperature and is an insulator in both solid and in molten state. This solid is most likely to be a/an :

A Covalent solid

B Molecular solid

C Ionic solid

D Metallic solid

Correct Answer

Option A

Solution

Covalent or network solid are insulator (except graphite) and have very high melting point.

Q20

The edge length of a face centered cubic cell of an ionic substance is 508 pm. If the radius of the cation is 110 pm, the radius of the anion is :

A 288 pm

B 398 pm

C 618 pm

D 144 pm

Correct Answer

Option D

Solution

For an Fcc crystal

{r_{cation}} + {r_{anion}} = {{edge\,\,length} \over 2};

\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,110 + {r_{anion}}\,\, = {{508} \over 2}

{r_{anion}} = 254 - 110 = 144pm