# Awadhesh Pratap Singh University 2010-4th Sem M.Sc Physics Condensed matter , - Question Paper

M.S

**c.**(Physics)

Condensed Matter Physics

Semester:-4th

Year: - June 2010

Maximum marks:-35

Minimum marks:-12

part A

**Q.1**select the accurate ans. every carry's ½ marks each: -

**(**To explore crystal structure using X-ray diffraction, X-ray energy should be of the order of:-

**I)****(**1.24*104 eV

**a)****(**150 eV

**b)****(**0.08 eV

**c)****(**None of these.

**d)**(II)Volume of a unit cell of the reciprocal lattice is provided by :-

**(**a.b.c

**a)****(**(2p)3/ (a.b*c)

**b)****(**(2p)3 (a.b*c)

**c)****(**two p/ (a.b*c)

**d)****(**Reciprocal lattice of a BCC lattice is :-

**I****I****I)**(a)FCC lattice

(b)SC lattice

(c)HCP lattice

(c)BCC lattice

**(**In a binary ionic crystal (A

**I****V)****B)**if a cation-anion pair (A+ and B-) is missing from a lattice position, then it Is called:-

**(**Vacancy defect

**a)****(**Frenkael defect

**b)****(**Schottky defect

**c)****(**Substitutional defect

**d)****(**A planer defect due to boundary ranging from 2 crystallites in a polycrystalline solid is termed as:-

**V)**(a)Stacking fault

(b)Tilt boundary

(c)Gain boundary

(d)None of these

**(**Somerfield's free electron theory is based on:-

**V****I)****(**Maxwell Boltzmann Statistics

**a)****(**Fermi Dirac Statistics

**b)****(**Bose-Einstein Statistics

**c)****(**None of these.

**d)****(**According to Bloch theorem, the electron motion is not free ; is this Correct:-

**V****I****I)****(**Yes.

**a)****(**No.

**b)****(**Electrons motion is free but not according to Bloch.

**c)****(**It depends on Temperature.

**d)****(**The ferromagnetic Curie temperature (T

**V****I****I****I)****f)**separates:-

**(**The ordered ferromagnetic phase at T

**a)****(**The ordered ferromagnetic phase at T>Tf from the disordered paramagnetic phase at T< Tf.

**b)****(**Both

**c)****(**& (b)

**a)****(**None of These.

**d)****(**In Hall Effect, the Hall constant for electron is provided by:-

**I****X)****(**RH= -1/Ne

**a)****(**RH =Ne

**b)****(**RH= 1/Ne

**c)****(**RH =-Ne

**d)****(**In transverse magneto resistance, the effect of a transverse weak magnetic field H is to increase the resistance by a term proportional to:-

**X)**(a)H

**(**1/H

**b)**(c)H2

**(**1/H2

**d)**part B

ans any 5 of the subsequent ques.. every carry two Marks every.

**Q.2**Prove that every vector of the reciprocal lattice is normal to set of lattice planes of the direct lattice.

Or

Prove that reciprocal lattice of an FCC lattice is a BCC lattice.

**Q.3**For a 1 dimensional crystal of N unit cells, show that number of states possible in a band is equal

to N, the number of unit cells.

Or

For 1 dimensional case draw diagram for energy bands in

Reduced zone scheme and

Repeated zone scheme.

**Q.4**Show that Bulk polarization P of a dielectric material is provided by:-

P=N.F.E

Where N=Number of molecules per unit volume, F is Polarizability and E is the electric

fieldIntensity.

Or

describe Hall Effect and what is Quantum Hall effect?

**Q.5**discuss Meissner effect in superconductors.

Or

discuss flux quantization in superconductors.

part C

ans the subsequent ques. in 300-500 words. every carry 10 marks every.

**Q.6**define and explain rotating crystal method for structure determination of a crystal.

**Q.7**Derive 1st and 2nd London formula for fields inside a superconductor . What is London

Penetration depth? How does it discuss the Meissner Effect?

**Q.8**State and Prove Bloch theorem for motion in a crystal. What is the physical significance of

real Roots?

**Q.9**define the Weiss molecular field theory for ferromagnetism. Derive an expression for

Paramagnetic Susceptibility.

**Q.10**Derive an expression for dipole polarizability for molecular polarization of a dielectri

**c.**

What is Langevin Function?

__M.Sc. (Physics)__

**Condensed Matter
Physics**

**Semester:-4 ^{th}**

**Year: -
June 2010**

**Maximum
marks:-35**

**Minimum
marks:-12**

__Section A__

## Q.1 Choose the correct answer. Each carrys marks each: -

(I) To explore crystal structure using X-ray diffraction, X-ray energy should be of the order of:-

(a) 1.24*104 eV

(b) 150 eV

(c) 0.08 eV

(d) None of these.

(II)Volume of a unit cell of the reciprocal lattice is given by :-

(a) a.b.c

(b) (2)^{3}/
(a.b*c)

(c) (2)^{3}
(a.b*c)

(d) 2/ (a.b*c)

(III) Reciprocal lattice of a BCC lattice is :-

(a) FCC lattice

(b) SC lattice

(c) HCP lattice

(d) BCC lattice

(IV) In a binary ionic crystal (AB) if a cation-anion pair (A+ and B-) is missing from a lattice position, then it Is called:-

(a) Vacancy defect

(b) Frenkael defect

(c) Schottky defect

(d) Substitutional defect

(V) A planer defect due to boundary between two crystallites in a polycrystalline solid is termed as:-

(a)Stacking fault

(b)Tilt boundary

(c)Gain boundary

(d)None of these

(VI) Somerfields free electron theory is based on:-

(a) Maxwell Boltzmann Statistics

(b) Fermi Dirac Statistics

(c) Bose-Einstein Statistics

(d) None of these.

(VII) According to Bloch theorem, the electron motion is not free ; is this Correct:-

(a) Yes.

(b) No.

(c) Electrons motion is free but not according to Bloch.

(d) It depends on Temperature.

(VIII) The ferromagnetic Curie temperature (T_{f})
separates:-

(a) The ordered ferromagnetic phase at T<T_{f }from
the disordered paramagnetic phase at T>T_{f}.

(b) The ordered ferromagnetic phase at T>T_{f }from
the disordered paramagnetic phase at T< T_{f}.

(c) Both (a) & (b)

(d) None of These.

(IX) In Hall Effect, the Hall constant for electron is given by:-

(a) R_{H}= -1/Ne

(b) R_{H} =Ne

(c) R_{H}= 1/Ne

(d) R_{H }=-Ne

(X) In transverse magneto resistance, the effect of a transverse weak magnetic field H is to increase the resistance by a term proportional to:-

(a)H

(b) 1/H

(c)H^{2}

(d) 1/H^{2}

__Section B__

## Answer any five of the following question. Each carry 2 Marks each.

Q.2 Prove that every vector of the reciprocal lattice is normal to set of lattice planes of the direct lattice.

**Or**

Prove that reciprocal lattice of an FCC lattice is a BCC lattice.

Q.3 For a one dimensional crystal of N unit cells, show that number of states possible in a band is equal

to N, the number of unit cells.

** Or**

For one dimensional case draw diagram for energy bands in

(a) Reduced zone scheme and

(b) Repeated zone scheme.

Q.4 Show that Bulk polarization P of a dielectric material is given by:-

P=N.Φ.E

Where N=Number of molecules per unit volume, Φ is Polarizability and E is the electric field

Intensity.

**Or**

Define Hall Effect and what is Quantum Hall effect?

Q.5 Explain Meissner effect in superconductors.

**Or**

Explain flux quantization in superconductors.

__Section C__

## Answer the following question in 300-500 words. Each carry 10 marks each.

Q.6 Describe and discuss rotating crystal method for structure determination of a crystal.

Q.7 Derive First and Second London equation for fields inside a superconductor . What is London

Penetration depth? How does it explain the Meissner Effect?

Q.8 State and Prove Bloch theorem for motion in a crystal. What is the physical significance of real

Roots?

Q.9 Describe the Weiss molecular field theory for ferromagnetism. Derive an expression for

Paramagnetic Susceptibility.

Q.10 Derive an expression for dipole polarizability for molecular polarization of a dielectric. What is

Langevin Function?

__M.Sc. (Physics)__

**Condensed Matter
Physics**

**Semester:-4 ^{th}**

**Year: -
June 2010**

**Maximum
marks:-35**

**Minimum
marks:-12**

__Section A__

## Q.1 Choose the correct answer. Each carrys marks each: -

(I) To explore crystal structure using X-ray diffraction, X-ray energy should be of the order of:-

(a) 1.24*104 eV

(b) 150 eV

(c) 0.08 eV

(d) None of these.

(II)Volume of a unit cell of the reciprocal lattice is given by :-

(a) a.b.c

(b) (2)^{3}/
(a.b*c)

(c) (2)^{3}
(a.b*c)

(d) 2/ (a.b*c)

(III) Reciprocal lattice of a BCC lattice is :-

(a) FCC lattice

(b) SC lattice

(c) HCP lattice

(d) BCC lattice

(IV) In a binary ionic crystal (AB) if a cation-anion pair (A+ and B-) is missing from a lattice position, then it Is called:-

(a) Vacancy defect

(b) Frenkael defect

(c) Schottky defect

(d) Substitutional defect

(V) A planer defect due to boundary between two crystallites in a polycrystalline solid is termed as:-

(a)Stacking fault

(b)Tilt boundary

(c)Gain boundary

(d)None of these

(VI) Somerfields free electron theory is based on:-

(a) Maxwell Boltzmann Statistics

(b) Fermi Dirac Statistics

(c) Bose-Einstein Statistics

(d) None of these.

(VII) According to Bloch theorem, the electron motion is not free ; is this Correct:-

(a) Yes.

(b) No.

(c) Electrons motion is free but not according to Bloch.

(d) It depends on Temperature.

(VIII) The ferromagnetic Curie temperature (T_{f})
separates:-

(a) The ordered ferromagnetic phase at T<T_{f }from
the disordered paramagnetic phase at T>T_{f}.

(b) The ordered ferromagnetic phase at T>T_{f }from
the disordered paramagnetic phase at T< T_{f}.

(c) Both (a) & (b)

(d) None of These.

(IX) In Hall Effect, the Hall constant for electron is given by:-

(a) R_{H}= -1/Ne

(b) R_{H} =Ne

(c) R_{H}= 1/Ne

(d) R_{H }=-Ne

(X) In transverse magneto resistance, the effect of a transverse weak magnetic field H is to increase the resistance by a term proportional to:-

(a)H

(b) 1/H

(c)H^{2}

(d) 1/H^{2}

__Section B__

## Answer any five of the following question. Each carry 2 Marks each.

Q.2 Prove that every vector of the reciprocal lattice is normal to set of lattice planes of the direct lattice.

**Or**

Prove that reciprocal lattice of an FCC lattice is a BCC lattice.

Q.3 For a one dimensional crystal of N unit cells, show that number of states possible in a band is equal

to N, the number of unit cells.

** Or**

For one dimensional case draw diagram for energy bands in

(a) Reduced zone scheme and

(b) Repeated zone scheme.

Q.4 Show that Bulk polarization P of a dielectric material is given by:-

P=N.Φ.E

Where N=Number of molecules per unit volume, Φ is Polarizability and E is the electric field

Intensity.

**Or**

Define Hall Effect and what is Quantum Hall effect?

Q.5 Explain Meissner effect in superconductors.

**Or**

Explain flux quantization in superconductors.

__Section C__

## Answer the following question in 300-500 words. Each carry 10 marks each.

Q.6 Describe and discuss rotating crystal method for structure determination of a crystal.

Q.7 Derive First and Second London equation for fields inside a superconductor . What is London

Penetration depth? How does it explain the Meissner Effect?

Q.8 State and Prove Bloch theorem for motion in a crystal. What is the physical significance of real

Roots?

Q.9 Describe the Weiss molecular field theory for ferromagnetism. Derive an expression for

Paramagnetic Susceptibility.

Q.10 Derive an expression for dipole polarizability for molecular polarization of a dielectric. What is

Langevin Function?

Earning: Approval pending. |