R>mog Ad鎛m ^m¡{VH$s

(1)

MPH-07

June - Examination 2017

M.Sc. Physics (Final) Examination Solid State Physics

R>mog AdñWm ^m¡{VH$s

Paper - MPH-07

Time : 3 Hours ] [ Max. Marks :- 80

Note: The question paper is divided into three sections. A, B and C. Write answer as per the given instructions. Check your paper code and paper title before starting the paper. In case of any discrepancy English version will be final for all purposes.

{ZX}e : ¶h àíZ nÌ "A', "~' Am¡a "g' VrZ IÊS>m| ‘| {d^m{OV h¡& àË¶oH$

IÊS> Ho$ {ZX}emZwgma àíZm| Ho$ CÎma Xr{OE& àíZnÌ ewê$ H$aZo go nyd©

àýnÌ H$moS> d àýnÌ erf©H$ Om±M b|& {H$gr ^r {dg§JVVm H$s pñW{V

‘o A§J«oOr ê$n hr A§{V‘ ‘mZm Om¶oJm&

Section - A 8

×

2 = 16

(Very Short Answer Type Questions) (Compulsory)

Note: Answer all questions. As per the nature of the question delimit your answer in one word, one sentence or maximum upto 30 words. Each question carries 2 marks.

855

(2)

MPH-07 /700 / 5 (2) (Contd.)

IÊS> - "A' (A{V bKw CÎmar¶ àíZ)

{ZX}e : g^r àíZm| Ho$ CÎma Xr{OE& Amn AnZo CÎma H$mo àíZmZwgma EH$ eãX, EH$ dm³¶ ¶m A{YH$V‘

³⁰

eãXm| ‘| n[agr{‘V H$s{O¶o& àË¶oH$ àíZ

2

A§H$m| H$m h¡&

1) (i) What is value of packing fraction of B.C.C. crystal?

B.C.C.

{H«$ñQ>b H$m g§Hw$bZ JwUmS²>H$ {H$VZm h¡?

(ii) What ate Burger vectors in crystal?

~O©a g{Xe {H«$ñQ>b ‘| ³¶m hmoVo h¢?

(iii) What is Umklapp process?

C‘³bm°n à{H«$¶m ³¶m h¡?

(iv) Write the mathematical form of Weidman-Franz Law.

dmBS>‘oZ ’«o$ÝO {Z¶‘ H$m J{UVr¶ ê$n [bImo&

(v) What is Bloch function?

ãbm°M ’$bZ ³¶m h¡?

(vi) Suppose energy E of an electron in a one dimensional lattice varies with wavenumber K as E= 2k+bh k^{2 2} where b is constant. Find the effective mass of the electron.

‘mZm {H$ R>mog ‘o EH$ {d‘r¶ OmbH$ ‘| Bbo³Q´>mZ H$s D$Om©

^E

, Va§J g§»¶m

^K

Ho$ gmW

^E⁼ ²^k⁺ ^b^{h k}^{2 2}

H$s Vah n[ad{V©V hmo ahr h¡

Ohm±

^b

AMa h¡& Bbo³Q´>mZ H$m à^mdr Ðì¶‘mZ kmV H$amo&

(vii) If dielectric constant of the solid medium is 1.05, then what is the value of the electric susceptibility of the medium?

¶{X EH$ R>mog ‘mÜ¶‘ H$m nam d¡ÚwVm§H$

^1.05

h¡¡ Vmo ‘mÜ¶‘ H$s {dÚwV

àd¥{Îm H$m ‘mZ ³¶m hmoJm?

(3)

(viii) What is Cooper pair? Explain.

Hy$na nw½‘ ³¶m hmoVm h¡? g‘PmAmo&

Section - B 4

×

8 = 32

(Short Answer Type Questions)

Note: Answer any four questions. Each answer should not exceed 200 words. Each question carries 08 marks.

(IÊS> - ~) (bKw CÎmar¶ àíZ)

{ZX}e : {H$Ýht Mma àíZm| Ho$ CÎma Xr{O¶o& AmnH$mo AnZo CÎma H$mo A{YH$V‘

200

eãXm| ‘| n[agr{‘V H$aZm h¡& àË¶oH$ àíZ

⁰⁸

A§H$m| H$m h¡&

2) What do you mean by Space lattice, primitive cell and unit cell.

AmH$mer OmbH$, A^mÁ¶ H$mo{ð>H$m Ed§ EH$H$ H$mo{ð>H$m go AmnH$m ³¶m VmËn¶© h¡&

3) With diagrams explain the classification of the Schottky and Frenkel defect in Crystal.

{H«$ñQ>b ‘| em°Q>H$s VWm ’«o$ÝH$b Xmofm| Ho$ dJuH$aU H$mo {MÌ g{hV g‘PmAmo&

4) Explain the electronic polarisation of the material.

nXmW© Ho$ Bbo³Q´>mo{ZH$ Y«wdU H$mo g‘PmAmo&

5) Describe the Einstein model of specific heat of solid.

R>mogm| Ho$ {d{eï> Cî‘m Ho$ AmBÝgQ>rZ ‘m°S>b H$m dU©Z H$amo&

6) Explain the entropy phenomena and Isotope Effect in super conductor.

A{V MmbH$ Ho$ {bE E§Q´>monr n[aKQ>Zm Ed§ g‘ñWm{ZH$ à^md H$mo g‘PmAmo&

(4)

MPH-07 /700 / 5 (4) (Contd.)

7) What is Ferro electrics and describe the main characteristics of Ferro electrics?

’o$amo Bbop³Q´>³g ³¶m h¡ Am¡a ’o$amo Bbop³Q´>³g Ho$ ‘w»¶ JwUY‘m} H$m dU©Z H$amo&

8) Prove that F.C.C. lattice is the reciprocal lattice of the B.C.C. and B.C.C. lattice is a reciprocal lattice of F.C.C. lattice.

{gÕ H$amo {H$

^B.C.C.

OmbH$ H$m ì¶wËH«$‘ OmbH$

^F.C.C.

Ed§

^F.C.C.

OmbH$ H$m ì¶wËH«$‘ OmbH$

^B.C.C.

hmoVm h¡&

9) Explain Fermi-Dirac distribution function. Plot this function for various temperature including zero kelvin.

’$‘u-{S>amH$ ’$bZ H$s ì¶m»¶m H$s{OE& Bg ’$bZ H$m {d{^Þ Vmnm|

(na‘eyÝ¶ Vmn na ^r) Ho$ gmW J«m’$ ~ZmB¶o&

Section - C 2

×

16 = 32 (Long Answer Type Questions)

Note: Answer any two questions. You have to delimit your each answer maximum 500 words. Each question carries 16 marks.

{ZX}e : {H$Ýht Xmo àíZm| Ho$ CÎma Xr{O¶o& Amn AnZo CÎma H$mo A{YH$V‘

500

eãXm| ‘| n[agr{‘V H$s{O¶o& àË¶oH$ àíZ

¹⁶

A§H$m| H$m h¡&

10) Describe the vibrational modes of a diatomic linear lattice. Name the different branches of the dispersion relation curve. Show that the group velocity vanishes at the zone boundary.

(5)

EH$ {Ûna‘mUwH$ aoIr¶ OmbH$ Ho$ H$ånZ {dYm H$m dU©Z H$amo& n{djonU gå~ÝY dH«$ H$s {d{^Þ emImAm| H$m Zm‘H$aU H$s{OE& àX{e©V H$amo {H$

OmoZ gr‘m na g‘yh doJ g‘má hmo OmVm h¡&

11) What is periodic potential? State and derive the Bloch theorem.

AmdVu {d^d ³¶m h¡? ãbm°H$ à‘o¶ H$m H$WZ H$amo Ed Bgo ì¶wËnÞ H$s{OE&

12) Derive London equations. Hence discuss the Merssner effect and London penetrations depth in super conductor.

13) (i) Discuss Lave equations and Bagg's law.

(ii) Explain the term phonon. Write all characteristics of phonons.

(i)

bdo g‘rH$aUm| d ~«oJ {Z¶‘ H$s {ddoMZm H$ao&

(ii)

’$moZm±Z nX H$mo g‘PmAmo& ’$moZm±Z Ho$ g‘ñV A{^bmj{UH$ JwU

{b{IE&