Solid State & Group Theory

QUESTION: 1

Nickel forms a face centered cubic unit cell with a = 351.8 pm. The value of crystallographic radius of a nickel atom is

A.
124.4 pm
B.
120 pm
C.
118 pm
D.
100 pm

Solution:

QUESTION: 2

The unit cell of an element of atomic mass 96 and density 10.3 g/cm^–3 is a cube with edge length of 314 pm the structure of the crystal lattice is

A.
bcc
B.
fcc
C.
scc
D.
diamond

Solution:

The structure of solid should be bcc.

*Answer can only contain numeric values

QUESTION: 3

Lithium boron hydride crystallizes in an orthorhombic system with 4 molecules per unit cell. The unit cell dimensions are If the molar mass is 21.76. The density of crystal is ______g/cm^-3. (Round off to two decimal places).x1

Solution:

*Answer can only contain numeric values

QUESTION: 4

A metal crystallizes in simple cubic unit cell. The length of the edge of the unit cell 'a' is 6.22 The radius of each atom of the metal is ______() (Round of to two decimal places).

Solution:

For simple cubic structure

QUESTION: 5

In n-type semi conductors the correct statement is/are
(i) The fermi energy level lies in between donor band and valence band
(ii) The fermi energy level lies in donor band and conduction band
(iii) The fermi energy increases with increasing temperature
(iv) The fermi energy decreases with increasing temperature

A.
(i) and (ii)
B.
(ii) and (iii)
C.
(iii) and (iv)
D.
(ii) and (iv)

Solution:

QUESTION: 6

The diamond unit cell

can be representd as

A.
B.
C.
D.

Solution:

Corners are represented by 0, 1.
Face centres (left, right, top, bottom) by (½)
Face centres front and back by 0, 1
Td Vd centres by 1/4 and 3/4.

QUESTION: 7

In an ionic oxide, oxide ions are arranged in hcp array and positive ion occupy two thirds of octahedral void simplest formula of metal M is

A.
M₂O₆
B.
M₄O₆
C.
M₃O₂
D.
M₆O₄

Solution:

QUESTION: 8

In case of Fullerene the correct relation between number of faces (F), number of vertices (V) and number of edges (E) is

A.
F + V = E
B.
F + V = E + 1
C.
F + V = E – 1
D.
F + V = E + 2

Solution:

F + V = E + 2
Correct option is (d)

QUESTION: 9

The point group of Admantane is

A.
C_2V
B.
C_3V
C.
D_2h
D.
TD

Solution:

Tetrahedral (Td)
Correct option is (d)

QUESTION: 10

The point group of Bicyclo 1, 1, 1-pentane is

A.
C_2V
B.
D_5h
C.
D_3h
D.
none of these

Solution:

Point group = D_3h

*Answer can only contain numeric values

QUESTION: 11

The first order reflection of a beam of X-rays from a given crystal occur at 15^o. The 3rd order reflection will occurs at angle of _____ degree. (Round off to two decimal places).

Solution:

*Answer can only contain numeric values

QUESTION: 12

A metal (atomic weight = 26.08), crystallizes in the cubic system with Its density is 2.7g/cm^-3. The radius of the atom of this metal will be _____ (Round off to two decimal places).

Solution:

*Answer can only contain numeric values

QUESTION: 13

The distance between the body-centered atom and one corner atom in sodium a =0.424 nm is ____nm. (Round off to two decimal places).

Solution:

The atom at the center of the cube is supposed to touch the two nearest corner atoms. The longest diagonal at which all these three atoms lie will be length 4r.
Therefore, distance between center atom and the corner atom = 2r

*Answer can only contain numeric values

QUESTION: 14

The ionic radii of Cs⁺ and Cl^-1 ions are 1.69 and 1.81 respectively. The co-ordinate number of Cs⁺ is _____(answer should be an integer).

Solution:

As the radius ratio lies between 0.732 and 1.0 the co-ordinate number of Cs⁺ is 8.

*Answer can only contain numeric values

QUESTION: 15

For primitive cubic crystal with a = 3 x 10¹⁰m, the smallest diffraction angle θ, for (110) plane for is ______(Round off to two decimal places).

Solution:

QUESTION: 16

The first order diffraction of X-rays from a ceratin set of crystal planes occurs at an angle of 11.8º from the planes, if the planes are 0.281 nm a part the wavelength of X-rays is

A.
0.123 nm
B.
0.312 nm
C.
0.115 nm
D.
0.125 nm

Solution:

QUESTION: 17

Match the crystal system unit cells mentioned in column-I with their characteristic feature mentioned in column-II

A.
P-(i), (iv) ; Q-(i), (ii) ; R-(ii) ; S-(ii), (iii)
B.
P-(ii), (iv) ; Q-(i), (iii) ; R-(iii) ; S-(iii)
C.
P-(iv) ; Q-(iii) ; R-(iv) ; S-(i), (iv)
D.
P-(i) ; Q-(ii), (iv) ; R-(ii) ; S-(iii), (iv)

Solution:

QUESTION: 18

The improper axis present in staggered ferrocene is

A.
S₅
B.
S₁₀
C.
S₅and S₁₀
D.
S₃ and S₅

Solution:

The point group of ferrocene is D₅d. It has S₂n improper axis called S₁₀.

QUESTION: 19

The Mulliken Notation for the following irreducible representation

A.
B.
C.
D.

Solution:

*Answer can only contain numeric values

QUESTION: 20

The number of classes in CH₄ molecule is/are ________(answer should be an integer).

Solution:

The number of classes in CH₄ molecule is 5.

20 Questions MCQ Test GATE Chemistry Mock Test Series | Solid State & Group Theory

Nickel forms a face centered cubic unit cell with a = 351.8 pm. The value of crystallographic radius of a nickel atom is

The unit cell of an element of atomic mass 96 and density 10.3 g/cm^–3 is a cube with edge length of 314 pm the structure of the crystal lattice is

Lithium boron hydride crystallizes in an orthorhombic system with 4 molecules per unit cell. The unit cell dimensions are If the molar mass is 21.76. The density of crystal is ______g/cm^-3. (Round off to two decimal places).x1

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