
	Trending ▼ ICSE CBSE 10th ISC CBSE 12th CTET GATE UGC NET Vestibulares ResFinder

8.%20Condensed Matter Physics NET-JRF VKS

18 pages, 0 questions, 0 questions with responses, 0 total responses,

Brijmohan
Banaras Hindu University (BHU), Varanasi
PhD Condensed matter Physics

+Fave Message

Profile Timeline Uploads

Home > brijupc >

Formatting page ...

fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES CONDENSED MATTER PHYSICS NET/JRF (JUNE-2011) Q1. A narrow beam of X-rays with wavelength 1.5 is reflected from an ionic crystal with an fcc lattice structure with a density of 3.32 gcm-3. The molecular weight is 108 AMU (1AMU = 1.66 10-24 g) A. The lattice constant is (a) 6.00 Ans: (b) 4.56 (c) 4.00 (d) 2.56 (b) Solution: Given ne f f 4 , M = 108 kg, 3.32 gm cm -3 = 3320 kgm-3, N A 6.023 10 26 atoms kmd a3 ne f f M NA 4 108 6.00 10 30 m 3 6.00 10 10 6.00 A0 6.023 10 26 3320 B. The sine of the angle corresponding to (111) reflection is (a) Ans: 3 4 (b) 3 8 (c) 1 4 (d) 1 8 (b) Solution: According to Bragg s law 2d sin , sin sin 3 2a 2d where d a h2 k 2 l 2 a 3 for (111) plane 3 1.5 A 0 3 3 3 . 0 2 62 8 2 6A Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 1 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q2. A flux quantum (fluxoid) is approximately equal to 2 10-7 gauss-cm2. A type II superconductor is placed in a small magnetic field, which is then slowly increased till the field starts penetrating the superconductor. The strength of the field at this point is 2 105 gausss. A. The penetrating depth of this superconductor is (a) 100 Ans: (b) 10 (c) 1000 (d) 314 (a) Solution: Given Fluxoid 0 2 10 7 gauss cm2 First Critical field H c1 2 10 5 gauss The relation between first critical field and penetration depth is H c1 0 0 2.10 7 2 10 12 cm 2 10 6 cm 100 A0 H c1 2 10 5 2 B. The applied field is further increased till superconductivity is completely destroyed. The strength of the field is now 8 105 gauss. The correlation length of the superconductor is (a) 20 (b) 200 (c) 628 (d) 2000 Ans: Solution: Given second critical field H c 2 field and correlation length is H c 2 2 0 H c 2 8 105 gauss. The relation between second critical 0 . 2 2 10 7 1 10 12 cm 2 8 10 5 4 1 1 100 10 6 cm 10 6 cm 10 10 m 50A 0 2 2 2 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 2 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q3. The two dimensional lattice of graphene is an arrangement of Carbon atoms forming a honeycomb lattice of lattice spacing a, as shown below. The Carbon atoms occupy the 1 a1 d1 1 a2 1 1 3 2 a 2 1 (b) c2 1 (a) 2a 2 c1 d2 (A). The Wigner-Seitz cell has an area of (c) 6 3a 1 1 vertices. b1 b2 a 3 3 2 a (d) 2 2 Ans: Solution: Area of Wigner-Seitz cell Area of normal cell Ne f f Where Neff = effective number of lattice paints 6 Area of normal cell 1 2 3 3 3 2 3 3 2 3 3 2 a /2 a a Area of wigner-Seitz cell 2 4 2 (B). The Bravais lattice for this array is a (a) rectangular lattice with basis vectors d 1 and d 2 (b) rectangular lattice with basis vectors c1 and c 2 (c) hexagonal lattice with basis vectors a1 and a 2 (d) hexagonal lattice with basis vectors b1 and b2 Ans: (c) Solution: The Bravaiss lattice for this array is the Hexagonal lattice with basis vectors a1 and a 2 NET/JRF (DEC-2011) Q4. The potential of a diatomic molecule as a function of the distance r between the atoms is given by V r a b 12 . The value of the potential at equilibrium separation between 6 r r the atoms is: (a) 4a 2 / b (b) 2a 2 / b (c) a 2 / 2b Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com (d) a 2 / 4b Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 3 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Ans: (d) Solution: Given V r a b dV r 12 . At equilibrium radius, 0 6 dr r r0 r r r 13 12b 2b dV r 6a 12 b 2b 7 13 0 07 r06 dr r0 r0 a 6a a r0 The value of potential at equilibrium is V r0 Q5. a b a2 a2 a 2 . 4b 2b 4b r06 r012 If the number density of a free electron gas in three dimensions is increased eight times, its Fermi temperature will (a) increase by a factor of 4 (c) increase by a factor of 8 Ans: (b) decrease by a factor of 4 (d) decrease by a factor of 8 (a) 2/3 2 3 2 n . Solution: The relation between Fermi energy and electron density is E F 2m Q6. 2/3 2 E 3 2 8n 4E F . 2m The excitations of a three-dimensional solid are bosonic in nature with their frequency ' F and wave-number k are related by k2 in the large wavelength limit. If the chemical potential is zero, the behaviour of the specific heat of the system at low temperature is proportional to (a) T1/2 Ans: (b) T (c) T3/2 (d) T3 (c) Solution: If the dispersion relation is k s in large wavelength. Than the specific heat is C v T 3 / s . Given k 2 C v T 3 / 2 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 4 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES NET/JRF (JUNE-2012) Q7. Consider a system of non-interacting particles in d dimensional obeying the dispersion relation Ak s , where is the energy k is the wavevector, s is an integer and A constant. The density of states, N( ), is proportional to s (a) d 1 (b) d 1 s (c) d 1 s s (d) d 1 Ans: (b) Q8. The experimentally measured transmission spectra of metal, insulator and semiconductor thin films are shown in the figure. It can be inferred that I, II and III correspond, respectively, to Transmission (%) (a) insulator, semiconductor and metal (b) semiconductor, metal and insulator (c) metal, semiconductor and insulator (d) insulator, metal and semiconductor Ans: 300 (a) 1000 Wavelength (nm) Q9. The energy required to create a lattice vacancy in a crystal is equal to 1 eV. The ratio of the number densities of vacancies n(1200 K)/n(300 K) when the crystal is at equilibrium at 1200 K and 300 K, respectively, is approximately (a) exp 30 Ans: (b) exp 15 (c) exp 15 (d) exp 30 (d) Solution: The equation for number density of vacancies n Ne E / 2 k BT where E: Energy required to form vacancies, N: density of lattice sites E 1 1 n n1 e E / 2 k BT1 1200K 2k T T E / 2 k BT2 e B 2 1 e 2 k B 300 1200 e 2 k B 400 e 30 n2 e n 300K E 1 1 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com E 1 Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 5 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q10. The dispersion relation of phonons in a solid is given by 2 3 cosk x a cosk y a cosk z a 2 k 0 The velocity of the phonons at large wavelength is (a) 0 a / 3 Ans: (b) 0 a (c) (d) 0 a / 2 3 0 a (d) Solution: For large , k x a, k y a, k z a are small. 2 2 2 2 k 2a2 k y a k z2 a 2 0 a 2 2 x k 3 1 1 1 kx ky k z2 2 2 2 2 2 2 k 2 0 02 a 2 2 k2 0 a 2 d 0 a . dk 2 k vg NET/JRF (DEC-2012) Q11. The free energy difference between the superconducting and the normal states of a material is given by F FS FN 2 2 , where is an order parameter and 4 and are constants such that 0 in the normal and 0 in the superconducting state, while 0 always. The minimum value of F is (a) 2 / (c) 3 2 / 2 Ans: (b) 2 / 2 (d) 5 2 / 2 (b) Solution: F 2 2 4 x 2 2 x 4 where x . F 2 x 2 x 3 0 2 x 2 x 3 0 x 2 since x 0 is trivial. x Thus F min x 2 x 4 . 2 x 2 2 2 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 6 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q12. Consider a one-dimensional Ising model with N spins, at very low temperatures when almost all spins are aligned parallel to each other. There will be a few spin flips with each flip costing an energy 2J. In a configuration with r spin flips, the energy of the system is E = - NJ + 2rJ and the number of configuration is N C r ; r varies from 0 to N. The partition function is J (a) k T B N (b) e NJ / k BT J (c) sinh k T B Ans: N J (d) cosh k T B N (d) Solution: Let us consider only three energy levels, Er 2 J 2rJ i.e. E0 2 J , E1 0 and E2 2 J . Q2 Ce 2 0 E0 2C1e E1 2C 2 e E2 2 r 0 e J e J Q2 2 Q13. 2 Cr e 2J 2e 0 e 2 J e J e J 4 4 2 2 2 2 N cosh J cosh J QN cosh J . A magnetic field sensor based on the Hall Effect is to be fabricated by implanting As into a Si film of thickness 1 m. The specifications require a magnetic field sensitivity of 500 mV/Tesla at an excitation current of 1 mA. The implantation dose is to be adjusted such that the average carrier density, after activation, is (a) 1.25 1026 m-3 (c) 4.1 1021 m-3 Ans: (b) 1.25 1022 m-3 (d) 4.1 1020 m-3 (b) Solution: n V IB 103 1 6 1.25 10 22 m 3 where H 500 10 3 V / T . 19 3 B teVH 10 1.6 10 500 10 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 7 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q14. In a band structure calculation, the dispersion relation for electrons is found to be k cos k x a cos k y a cos k z a , where is a constant and a is the lattice constant. The effective mass at the boundary of the first Brillouin zone is (a) Ans: 2 2 5 a 2 (b) 4 2 5 a 2 (c) 2 2 a 2 (d) 2 3 a 2 (d) Solution: k cos k x a cos k y a cos k z a , Effective mass m Brilliouin zone boundary is at k x d 2 k Hence d 2k a ,ky a , kz 2 d 2 k d 2k a . 2 2 . 3 a m 3 a 2 , , a a a Q15. The radius of the Fermi sphere of free electrons in a monovalent metal with an fcc structure, in which the volume of the unit cell is a3, is 12 2 (a) a3 Ans: 1/ 3 3 2 (b) a3 1/ 3 2 (c) a3 1/ 3 (d) 1 a (a) 3 2 N Solution: Radius of Fermi sphere is k F V 12 2 N 4 For fcc solid 3 kF a3 V a 1/ 3 . 1/ 3 . Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 8 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES NET/JRF (JUNE-2013) Q16. Using the frequency-dependent Drude formula, what is the effective kinetic inductance of a metallic wire that is to be used as a transmission line? [In the following, the electron mass is m , density of electrons is n , and the length and cross-sectional area of the wire and A respectively.] (a) mA / ne 2 (b) zero (c) m / ne 2 A (d) m A / ne 2 2 Ans: (c) Q17. The phonon dispersion for the following one-dimensional diatomic lattice with masses M 1 and M 2 (as shown in the figure) K is given by M1 M2 M1 M2 1 4M 1 M 2 1 2 qa 1 1 sin 2 2 M M M 1 M 2 1 2 2 q K where a is the lattice parameter and K is the spring constant. The velocity of sound is (a) (b) (c) Ans: K M 1 M 2 a 2M 1 M 2 K M 1 M 2 a M 1M 2 (d) K a 2 M 1 M 2 KM 1 M 2 2 M 1 M 2 3 a (b) Solution: For small value of q (i.e. long wavelength approximation limit), we have qa qa sin 2 2 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 9 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES 1 4M 1 M 2 1 2 qa 1 1 sin 2 q 2 M 2 M M 1 M 2 1 2 2 1 4M 1 M 2 qa 1 2 q 1 1 2 M M1 M 2 2 1 M 2 1 4 M 1 M 2 q 2 a 2 1 1 q 1 1 2 M M 2 4 M M 2 1 1 2 2 1 M 1M 2 1 q2a2 1 2 q 1 2 M 1 M 2 M 1 M 2 2 1 M 1M 2 1 q 2a 2 1 1 For Acoustical branch: 2 q 2 M 1 M 2 M 1 M 2 2 M1 M 2 2 q M M 1 2 q M 1 M 2 q 2 a 2 a 2 2 M M 2 2 2 M M q 1 1 2 2 aq 2 M 1 M 2 Velocity of sound is v g Q18. q a 2 M 1 M 2 The electron dispersion relation for a one-dimensional metal is given by k 2 0 sin 2 ka 1 2 sin ka 2 6 where k is the momentum, a is the lattice constant, 0 is a constant having dimensions of energy and ka . If the average number of electrons per atom in the conduction band is 1/3, then the Fermi energy is (a) 0 / 4 Ans: (b) 0 (c) 2 0 / 3 (d) 5 0 / 3 (a) Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 10 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q19. If the energy dispersion of a two-dimensional electron system is E u k where u is the velocity and k is the momentum, then the density of states D E depends on the energy as (a) 1 / E Ans: (b) E (c) E (d) constant (c) Solution: In two dimensional system, the number of allowed k-states in range k and k dk is 2 L g k dk 2 kdk . 2 Given dispersion relation is E u k k E dE dk u u E dE L 2 L EdE g E dE 2 2 u u 2 u 2 2 2 E g E dE 1 L2 E. dE u 2 2 NET/JRF (DEC-2013) Q20. The physical phenomenon that cannot be used for memory storage applications is (a) large variation in magnetoresistance as a function of applied magnetic field (b) variation in magnetization of a ferromagnet as a function of applied magnetic field (c) variation in polarization of a ferroelectric as a function of applied electric field (d) variation in resistance of a metal as a function of applied electric field Ans: (d) Q21. The energy of an electron in a band as a function of its wave vector k is given by E k E 0 B cos k x a cos k y a cos k z a , where E 0 B and a are constants. The effective mass of the electron near the bottom of the band is 2 2 (a) 3Ba 2 2 (b) 3Ba 2 2 (c) 2Ba 2 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com 2 (d) Ba 2 Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 11 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Ans: (d) Solution: Near the bottom of the band the k 0 1 k x a 2 , 2 1 k y a 2 , 2 1 k z a 2 2 2 1 1 2 2 1 E k E0 B cos k x a cos k y a cos k z a E0 B 1 k x a 1 k y a 1 k z a 2 2 2 1 1 2 E0 B 3 a 2 k x k x k x E0 3B Ba 2k 2 2 2 cos k x a 1 cos k y a 1 Effective mass of the electron is m * Q22. cos k z a 1 2 2 d 2 E / dk 2 Ba 2 A DC voltage V is applied across a Josephson junction between two superconductors with a phase difference 0 . If l 0 and k are constants that depend on the properties of the junction, the current flowing through it has the form 2eVt 0 (a) I 0 sin (c) kV sin 0 Ans: 2eVt 0 (b) kV sin (d) I 0 sin 0 kV (a) Q23. A uniform linear monoatomic chain is modeled by a spring-mass system of masses m 2 separated by nearest neighbour distance a and spring constant m 0 . The dispersion relation for this system is ka (a) k 2 0 1 cos 2 ka (c) k 2 0 sin 2 Ans: ka (b) k 2 0 sin 2 2 ka (d) k 2 0 tan 2 (c) Solution: The dispersion relation for uniform linear mono-atomic chain of atoms is ka 2 k 2 0 sin Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 12 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES NET/JRF (JUNE-2014) Q24. The pressure of a nonrelativistic free Fermi gas in three-dimensions depends, at T 0 , on the density of fermions n as (a) n 5 / 3 (c) n 2 / 3 (b) n1 / 3 (d) n 4 / 3 Ans: (a) Solution: The Fermi energy in three dimension is defined as 2 3 2 N EF 2m V 2/3 2 3 2 n 2m 2/3 Where, n is the electron concentration or density of free Fermi gas. The total energy of free Fermi gas in 3D is 3 3 2 3 2 N E NE F N 5 5 2m V 2/3 The pressure of a nonrelativistic free Fermi gas is defined as 3 2 E p F 3 2 N N V 5 2 m N 2 2 2 nEF n 3 2 n 5 5 2m Q25. 2/3 2/3 2 V 5 / 3 3 2 2 3 2 5 2m 2/3 n5 / 3 Consider an electron in b.c.c. lattice with lattice constant a . A single particle wavefunction that satisfies the Bloch theorem will have the form f r exp ik .r , with f r being 2 2 2 (a) 1 cos x y z cos x y z cos x y z a a a 2 2 2 (b) 1 cos x y cos y z cos z x a a a (c) 1 cos x y cos y z cos z x a a a (d) 1 cos x y z cos x y z cos x y z a a a Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 13 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Ans: (b) Solution: The primitive translational vector for BCC is a a , b' a i a' i j k , b' i j k j k 2 2 2 Bloch function defined as k r uk r eik .r f r e ik .r Here f r is atomic wavefunction, which has the periodicity of the lattice i.e. u k r a u k r Given Bloch function 2 2 2 f (r ) 1 cos x y cos y z cos x z a a a 2 2 2 a a a a a a f (r a ' ) 1 cos x y cos y z cos z x 2 2 2 2 2 2 a a a 2 2 2 f (r a ' ) 1 cos x y cos y z 2 cos z x a a a 2 2 2 f (r a ' ) 1 cos x y cos y z cos z x f (r ) a a a f (r a ' ) f (r ) Similarly f (r b ' ) f (r ) and f (r c ' ) f (r ) Other functions do not satisfy the periodicity Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 14 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q26. The dispersion relation for electrons in an f.c.c. crystal is given, in the tight binding approximation, by k 4 0 cos kya kya kxa k a k a k a cos cos cos z cos z cos x 2 2 2 2 2 2 where a is the lattice constant and 0 is a constant with the dimension of energy. The x component of the velocity of the electron at , 0, 0 is a (a) 2 0 a / Ans: (c) 4 0 a / (b) 2 0 a / (d) 4 0 a / (d) Solution: Group velocity of electron in dispersive medium is expressed as 1 d 1 d d d v i j dk dk y dk z dk x v k xi v y j vz k k x a kya kya kya k x a kxa kza kza sin cos cos sin i cos sin sin cos j 2 2 2 2 2 2 2 2 2 a v kya kza kxa kza sin cos cos sin k 2 2 2 2 , 0, 0 a At 2 a v cos sin 0 sin 0 cos0 j cos0 sin 0 sin 0 cos k sin cos0 cos0 sin i 2 2 2 2 4 a 0i v 0 v i 0 j 0k j 0k xi v y j vz k 4 a vx , v y 0, vz 0 The x - component of velocity is v x 4 a Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 15 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES NET/JRF (JUNE-2014) Q27. When laser light of wavelength falls on a metal scale with 1 mm engravings at a grazing angle of incidence, it is diffracted to form a vertical chain of diffraction spots on a screen kept perpendicular to the scale. If the wavelength of the laser is increased by 200 nm, the angle of the first-order diffraction spot changes from 5 0 to (a) 6.60 0 Ans: (b) 5.14 0 (c) 5.0180 (d) 5.210 (c) Solution: The condition of maxima peak in grating is b sin m ; m 0,1, 2,3,.... where b is the width of slit or width of engraving, whereas m is the order of diffraction and is the angle of diffraction b sin For 1st order diffraction: (i) When wavelength of incident light increased to 200 nm , let s assume the 1st order b sin 200 peak appears at (ii) Subtracting equation (i) from equation (ii), we get b sin b sin 200 sin sin 200 200 10 9 sin sin b 10 3 sin 2 10 4 sin 2 10 4 sin 50 2 10 4 0.087196 0.08736 sin 1 0.08736 5.010 Q28. Consider the crystal structure of sodium chloride which is modeled as a set of touching spheres. Each sodium atom has a radius r1 and each chlorine atom has a radius r2 . The centres of the spheres from a simple cubic lattice. The packing fraction of this system is r 3 r 3 1 2 (a) r r r r 1 2 1 2 (c) r13 r23 (b) 2 r13 r23 3 r1 r2 3 (d) r1 r2 3 r13 r23 2 r1 r2 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com 3 Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 16 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Ans: (b) Solution: This question can only be solved by solving each option by assuming r1 r2 and comparing result with the packing fraction of simple cubic which is . 6 3 3 3 3 r r 1 1 Option (a): 1 2 r r r r 2 2 4 1 2 1 2 2 r13 r23 2 2r 3 2 1 Option (b): 3 r1 r2 3 3 8r 3 3 4 6 Option (c): Option (d): r13 r23 r1 r2 3 r13 r23 2r 3 1 8r 3 4 2 r1 r2 3 2r 3 3 2 8r 8 Thus, correct option is (b) Q29. Consider two crystalline solids, one of which has a simple cubic structure, and the other has a tetragonal structure. The effective spring constant between atoms in the c -direction is half the effective spring constant between atoms in the a and b directions. At low temperatures, the behaviour of the lattice contribution to the specific heat will depend as a function of temperature T as (a) T 2 for the tetragonal solid, but as T 3 for the simple cubic solid (b) T for the tetragonal solid, and as T 3 for the simple cubic solid (c) T for both solids (d) T 3 for both solids Ans: (d) Solution: The specific heat of solid in three dimensions is proportional to T 3 and it is independent of crystal structure. In 3D : CV T 3 In 2D : CV T 2 In 1D : CV T Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 17 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q30. A superconducting ring carries a steady current in the presence of a magnetic field B normal to the plane of the ring. Identify the incorrect statement. (a) The flux passing through the superconductor is quantized in units of hc / e (b) The current and the magnetic field in the superconductor are time independent. (c) The current density j and B are related by the equation j 2 B 0 , where is a constant (d) The superconductor shows an energy gap which is proportional to the transition temperature of the superconductor Ans: (a) Solution: The flux quantization in superconducting ring is n o where o hc h in CGS units and o in MKS units. 2e 2e Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 18

Formatting page ...

brijupc chat

Horizontal lines at:
Guest Horizontal lines at:
AutoRM Data:
Box geometries: