Solid State — Page 3 | NEET Chemistry

Q21

Structure of a mixed oxide is cubic close packed ( ccp ). The cubic unit cell of mixed oxide is composed of oxide ions. One fourth of the tetrahedral voids are occupied by divalent metal A and the octahedral voids are cooupied by a monovalent metal B. The formula of the oxide is

A ABO 2

B A 2 BO 2

C A 2 B 3 O 4

D AB 2 O 2

Correct Answer

Option D

Solution

Number of atoms in cubic close packing = 4 = O 2- Number of tetrahedral voids = 2 × N = 2 × 4 Number of A 2+ ions = 8 $\times$

{1 \over 4}

= 2 Number of octahedral voids = Number of B + ions = N = 4 Ratio of ions will be, O 2– : A 2+ : B + = 4 : 2 : 4 = 2 : 1 : 2 Formula of oxide = AB 2 O 2

Q22

A metal crystallises with a face-centred cubic lattice. The edge of the unit cell is 408 pm. The diameter of the metal atom is

A 288 pm

B 408 pm

C 144 pm

D 204 pm

Correct Answer

Option A

Solution

Given

a

= 408 pm For the face centred cubic structure r =

{a \over {2\sqrt 2 }}

=

{{408} \over {2\sqrt 2 }}

= 144 pm $\therefore$ Diameter = 2r = 2 $\times$ 144 = 288 pm

Q23

The number of octahedral void(s) per atom present in a cubic close-packed structure is

A 1

B 3

C 2

D 4

Correct Answer

Option A

Solution

Number of octahedral voids is same as number of atoms.

Q24

A solid compound XY has NaCl structure. If the radius of the cation is 100 pm, the radius of the anion ( Y

-

) will be

A 275.1 pm

B 322.5 pm

C 241.5 pm

D 165.7 pm

Correct Answer

Option C

Solution

For NaCl crystal,

{{{r_ + }} \over {{r_ - }}} = 0.414

Given, r + = 100 pm $\therefore$

{{100} \over {{r_ - }}} = 0.414

$\Rightarrow$

{r_ - } = {{100} \over {0.414}}

= 241.5 pm

Q25

AB crystallizes in a body centered cubic lattice with edge length '

a

' equal to 387 pm. The distance between two oppositely charged ions in the lattice is

A 335 pm

B 250 pm

C 200 pm

D 300 pm

Correct Answer

Option A

Solution

For a bcc lattice, 2(r + + r – ) =

\sqrt 3 a

$\therefore$ r + + r – =

{{\sqrt 3 \times 387} \over 2}

= 335 pm

Q26

Lithium metal crystallises in a body-centred cubic crystal. If the length of the side of the unit cell of lithium is 351 pm, the atomic radius of lithium will be

A 151.8 pm

B 75.5 pm

C 300.5 pm

D 240.8 pm

Correct Answer

Option A

Solution

Since Li crystallises in body-centred cubic crystal, atomic radius, r =

{{\sqrt 3 a} \over 4}

. $\therefore$ r =

{{\sqrt 3 } \over 4} \times 351

= 151.8 pm

Q27

Copper crystallises in a face-centred cubic lattice with a unit cell length of 361 pm. What is the radius of copper atom in pm?

A 157

B 181

C 108

D 128

Correct Answer

Option D

Solution

Since Cu crystallises in a face-centred cubic lattice, Atomic radius, r =

{a \over {2\sqrt 2 }}

$\therefore$ r =

{{361} \over {2\sqrt 2 }}

= 128 pm

Q28

With which one of the following elements silicon should be doped so as to give p -type of semiconductor?

A Selenium

B Boron

C Germanium

D Arsenic

Correct Answer

Option B

Solution

The semiconductors formed by the introduction of impurity atoms containing one elecron less than the parent atoms of insulators are termed as p-type semiconductors.

Therefore silicon containing 14 electrons has to be doped with boron containing 13 electrons to give a p-type semi-conductor.

Q29

If

a

stands for the edge length of the cubic systems: simple cubic, body centred cubic and face centred cubic, then the ratio of radii of the spheres in these systems will be respectively

A

{1 \over 2}a:{{\sqrt 3 } \over 2}a:{{\sqrt 2 } \over 2}a

B

1a:\sqrt 3 a:\sqrt 2 a

C

{1 \over 2}a:{{\sqrt 3 } \over 4}a:{1 \over {2\sqrt 2 }}a

D

{1 \over 2}a:\sqrt 3 a:{1 \over {\sqrt 2 }}a

Correct Answer

Option C

Solution

For Simple cubic : r + + r – =

{a \over 2}

For Body centred : r + + r – =

{{a\sqrt 2 } \over 4}

For Face centered: r + + r – =

{a \over {2\sqrt 2 }}

$\therefore$ Ratio of radii of the three will be =

{1 \over 2}a:{{\sqrt 3 } \over 4}a:{1 \over {2\sqrt 2 }}a

Q30

Which of the following statements is not correct?

A The number of carbon atoms in a unit cell of diamond is 4

B The number of Bravais lattices in which a crystal can be categorized is 14

C The fraction of the total volume occupied by the atoms in a primitive cell is 0.48.

D Molecular solids are generally volatile.

Correct Answer

Option C

Solution

Packing fraction for a cubic unit cell is given by f =

{{Z \times {4 \over 3}\pi {r^3}} \over {{a^3}}}

where a = edge length, r = radius of cation and anion.

Efficiency of packing in simple cubic or primitive cell = π/6 = 0.52 or 52 % It means 52 % of unit cell is occupied by atoms and 48 % is empty.