GATE PH topic:solid-state-physics PYQs & Answers — Page 5

Questions 41–50 of 65. Imported answers require independent review unless marked reviewed.

As shown in the figure, inverse magnetic susceptibility

is plotted as a function of temperature

for three different materials in paramagnetic states.

(Curie temperature of ferromagnetic material

Néel temperature of antiferromagnetic material

)

Choose the correct statement from the following

Your answerChoose one option.

Material 1 is antiferromagnetic (

), 2 is paramagnetic, and 3 is ferromagnetic (

Material 1 is paramagnetic, 2 is antiferromagnetic (

), and 3 is ferromagnetic (

Material 1 ferromagnetic (

), 2 is antiferromagnetic (

), and 3 is paramagnetic.

Material 1 is ferromagnetic (

), 2 is paramagnetic, and 3 is antiferromagnetic (

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Consider an atomic gas with number density

m⁻³, in the ground state at 300 K. The valence electronic configuration of atoms is

. The paramagnetic susceptibility of the gas

. The value of

(rounded off to two decimal places) is _____.

(Given: Magnetic permeability of free space

H m⁻¹

Bohr magneton

A m²

Boltzmann constant

J K⁻¹)

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The number of distinct ways the primitive unit cell can be constructed for the two dimensional lattice as shown in the figure is _____.

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Consider a one-dimensional non-magnetic crystal with one atom per unit cell. Assume that the valence electrons (i) do not interact with each other and (ii) interact weakly with the ions. If

is the number of valence electrons per unit cell, then at 0 K,

Your answerChoose one option.

the crystal is metallic for any value of

the crystal is non-metallic for any value of

the crystal is metallic for even values of

the crystal is metallic for odd values of

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Consider a two dimensional crystal with 3 atoms in the basis. The number of allowed optical branches (

) and acoustic branches (

) due to the lattice vibrations are

Your answerChoose one option.

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Consider a simple cubic monoatomic Bravais lattice which has a basis with vectors

is the lattice parameter. The Bragg reflection is observed due to the change in the wave vector between the incident and the scattered beam as given by

, where

, and

are primitive reciprocal lattice vectors. For

and

, the geometrical structure factor is _____.

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The relative magnetic permeability of a type-I superconductor is

Your answerChoose one option.

−1

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In order to estimate the specific heat of phonons, the appropriate method to apply would be

Your answerChoose one option.

Einstein model for acoustic phonons and Debye model for optical phonons

Einstein model for optical phonons and Debye model for acoustic phonons

Einstein model for both optical and acoustic phonons

Debye model for both optical and acoustic phonons

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Consider a three-dimensional crystal of

inert gas atoms. The total energy is given by

, where

, and

is the nearest neighbor distance between two atoms. The two constants,

and

, have the dimensions of energy and length, respectively. The equilibrium separation between two nearest neighbor atoms in units of

(rounded off to two decimal places) is

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The energy-vector (

) dispersion relation for a particle in two dimensions is

, where

is a constant. If its density of states

is proportional to

then the value of

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GATE PH topic:solid-state-physics PYQs

Question 41

Question 52

Question 19

Question 35

Question 37

Question 44

Question 1

Question 11

Question 17

Question 18