UPKAR PRAKASHAN, AGRA-2

ByAnshul Gupta

&Dr. Surekha Tomar

© Publishers

Publishers

UPKAR PRAKASHAN2/11A, Swadeshi Bima Nagar, AGRA–282 002Phone : 4053333, 2530966, 2531101Fax : (0562) 4053330E-mail : care@upkar.in, Website : www.upkar.in

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ISBN : 978-93-5013-269-2

Price : 499·00(Rs. Four Hundred Ninety Nine Only)

Code No. 1551

Printed at : UPKAR PRAKASHAN (Printing Unit) Bye-pass, AGRA

Preface of the Revised Edition

This revised version of the book consists of material covering the latest syllabusprescribed by CSIR–UGC/GATE as well as other competitive examinations ofnational level. This book is remarkable for its comprehensive coverage.

One aspect in each area of the problems spans a wide spectrum of topics. Theproblems themselves are remarkable for their versatility in applying the physical lawsand principles, their up-to-date realistic situations and their scanty demand onmathematical skills.

The solutions presented generally just provide a guidance to solving the problems,rather than step by step manipulation, and leave much to the students to work out forthemselves, of which much is demanded of the basic knowledge in physics. Thus, thebook would provide an invaluable complement to the text books. International unitsare used whenever possible, but in order to conform to some of the problems,Gaussian units are also used. This in fact would give the student broader training andwider experience. Great pains have been taken to trace the logical steps from the firstprinciples to the final solutions. These efforts hopefully will enhance the value of thebook to students and teachers alike.

—Dr. Surekha Tomar

CCCCoooonnnntttteeeennnnttttssss

● Previous Year’s Solved Paper

Part–A● General Aptitude………………………………………………………………… 1–64

Part–B & CUnit-1

Basic Mathematical Methods……………………………………………….…… 65–150Unit-2

Classical Dynamics……………………………………………………………… 151–222Unit-3

Electromagnetics………………………………………………………………… 223–297Unit-4

Quantum Physics and Applications………………………………………...…… 298–369Unit-5

Thermodynamic and Statistical Physics……………………………………..… 370–445Unit-6

Electronics…………………………………………………………,…………… 446–522Unit-7

Experimental Methods………………………………….……………,………… 523–558Unit-8

Atomic and Molecular Physics…………………………………………….…… 559–626Unit-9

Condensed Matter Physics……………………………………………………… 627–708Unit-10

Nuclear and Particle Physics…………………………………………………… 709–754Unit-11

Nature of Nuclear Forces………………………………………………..……… 755–770● Optics (Additional Reading),…………………………………………………… 771–776● Model Paper-I…...……………………………………………………………… 777–784● Model Paper-II…..……………………………………………………………… 785–792

GENERAL INFORMATION

EXAM SCHEMETime : 3 Hours Max. Marks : 200

Single Paper Test having Multiple ChoiceQuestions (MCQs) is divided in three parts.

Part 'A' This part shall carry 20 questions pertaining

to General Science Quantitative Reasoning &Analysis and Research Aptitude. The candidatesshall be required to answer any 15 questions. Eachquestion shall be of two marks. The total marksallocated to this section shall be 30 out of 200.

Part 'B'This part shall contain 25 Multiple Choice

Questions (MCQs) generally covering the topicsgiven in the Part ‘A’ (CORE) of syllabus. Eachquestion shall be of 3·5 marks. The total marksallocated to this section shall be 70 out of 200.Candidates are required to answer any 20questions.

Part 'C'This part shall contain 30 questions from Part

‘B’ (Advanced) and Part ‘A’ of the syllabus thatare designed to test a candidate's knowledge ofscientific concepts and/or application of thescientific concepts. The questions shall be ofanalytical nature where a candidate is expected toapply the scientific knowledge to arrive at thesolution to the given scientific problem. Acandidate shall be required to answer any 20questions. Each question shall be of 5 marks. Thetotal marks allocated to this section shall be 100out of 200.● There will be negative marking @25% for

each wrong answer.

● To enable the candidates to go through thequestions, the question paper booklet shall bedistributed 15 minute before the scheduledtime of the Exam. The answer sheet (OMR

sheet) shall be distributed at the scheduledtime of the Exam.

SYLLABUS

PART 'A' (CORE)I. Mathematical Methods of Physics

Dimensional analysis. Vector algebra andvector calculus. Linear algebra, matrices, Cayley-Hamilton Theorem. Eigenvalues and eigenvectors.Linear ordinary differential equations of first &second order, Special functions (Hermite, Bessel,Laguerre and Legendre functions). Fourier series,Fourier and Laplace transforms. Elements ofcomplex analysis, analytic functions; Taylor &Laurent series; poles, residues and evaluation ofintegrals. Elementary probability theory, randomvariables, binomial, Poisson and normal distri-butions. Central limit theorem.

II. Classical MechanicsNewton’s laws. Dynamical systems, Phase

space dynamics, stability analysis. Central forcemotions. Two body Collisions—scattering inlaboratory and Centre of mass frames. Rigid bodydynamics—moment of inertia tensor. Non-inertialframes and pseudoforces. Variational principle.Generalized co-ordinates. Lagrangian andHamiltonian formalism and equations of motion.Conservation laws and cyclic co-ordinates.Periodic motion: small oscillations, normalmodes. Special theory of relativity—Lorentztransformations, relativistic kinematics and mass–energy equivalence.

III. Electromagnetic Theory

Electrostatics : Gauss’s law and itsapplications, Laplace and Poisson equations,boundary value problems. Magnetostatics: Biot-Savart law, Ampere's theorem. Electromagnetic

( vii )

induction. Maxwell's equations in free space andlinear isotropic media; boundary conditions on thefields at interfaces. Scalar and vector potentials,gauge invariance. Electromagnetic waves in freespace. Dielectrics and conductors. Reflection andrefraction, polarization, Fresnel’s law, inter-ference, coherence and diffraction. Dynamics ofcharged particles in static and uniformelectromagnetic fields.

IV. Quantum Mechanics

Wave-particle duality. Schrödinger equation(time-dependent and time-independent).Eigenvalue problems (particle in a box, harmonicoscillator, etc.). Tunneling through a barrier.Wave-function in co-ordinate and momentumrepresentations. Commutators and Heisenberguncertainty principle. Dirac notation for statevectors. Motion in a central potential: orbitalangular momentum, angular momentum algebra,spin, addition of angular momenta; Hydrogenatom. Stern-Gerlach experiment. Time-inde-pendent perturbation theory and applications.Variational method. Time dependent perturbationtheory and Fermi's golden rule, selection rules.Identical particles, Pauli exclusion principle, spin-statistics connection.

V. Thermodynamic and Statistical Physics

Laws of thermodynamics and their con-sequences. Thermodynamic potentials, Maxwellrelations, chemical potential, phase equilibria.Phase space, micro and macro-states. Micro-canonical, canonical and grand-canonicalensembles and partition functions. Free energyand its connection with thermodynamic quantities.Classical and quantum statistics. Ideal Bose andFermi gases. Principle of detailed balance.Blackbody radiation and Planck's distribution law.VI. Electronics and Experimental Methods

Semi-conductor devices (diodes, junctions,transistors, field effect devices, homo and hetero-junction devices), device structure, devicecharacteristics, frequency dependence andapplications. Opto-electronic devices (solar cells,photo-detectors, LEDs). Operational amplifiersand their applications. Digital techniques andapplications (registers, counters, comparators andsimilar circuits). A/D and D/A converters.Microprocessor and microcontroller basics. Data

interpretation and analysis. Precision andaccuracy. Error analysis, propagation of errors.Least squares fitting.

PART 'C' ADVANCED

I. Mathematical Methods of PhysicsGreen’s function. Partial differential

equations (Laplace, wave and heat equations intwo and three dimensions). Elements ofcomputational techniques: root of functions,interpolation, extrapolation, integration bytrapezoid and Simpson’s rule, Solution of firstorder differential equation using Runge-Kuttamethod. Finite difference methods. Tensors.Introductory group theory : SU(2), O(3).

II. Classical MechanicsDynamical systems, Phase space dynamics,

stability analysis. Poisson brackets and canonicaltransformations. Symmetry, invariance andNoether’s theorem. Hamilton-Jacobi theory.

III. Electromagnetic TheoryDispersion relations in plasma. Lorentz

invariance of Maxwell’s equation. Transmissionlines and wave guides. Radiation from movingcharges and dipoles and retarded potentials.

IV. Quantum Mechanics

Spin-orbit coupling, fine structure. WKBapproximation. Elementary theory of scattering :phase shifts, partial waves, Born approximation.Relativistic quantum mechanics : Klein-Gordonand Dirac equations. Semi-classical theory ofradiation.

V. Thermodynamic and Statistical PhysicsFirst and second-order phase transitions.

Diamagnetism, paramagnetism and ferromag-netism. Ising model. Bose-Einstein condensation.Diffusion equation. Random walk and Brownianmotion. Introduction to non-equilibrium processes.

VI. Electronics and Experimental MethodsLinear and non-linear curve fitting, chi-square

test. Transducers (temperature, pressure/ vacuum,magnetic fields, vibration, optical and particledetectors). Measurement and control. Signalconditioning and recovery. Impedance matching,amplification (Op-amp based, instrumentationamp, feedback), filtering and noise reduction,

( viii )

shielding and grounding. Fourier transforms, lock-in detector, box-car integrator, modulationtechniques.

High frequency devices (including generatorsand detectors).

VII. Atomic & Molecular PhysicsQuantum states of an electron in an atom.

Electron spin. Spectrum of helium and alkaliatom. Relativistic corrections for energy levels ofhydrogen atom, hyperfine structure and isotopicshift, width of spectrum lines, LS & JJ couplings.Zeeman, Paschen-Bach & Stark effects. Electronspin resonance. Nuclear magnetic resonance,chemical shift. Frank-Condon principle. Born-Oppenheimer approximation. Electronic,rotational, vibrational and Raman spectra ofdiatomic molecules, selection rules. Lasers :spontaneous and stimulated emission, Einstein A& B coefficients. Optical pumping, populationinversion, rate equation. Modes of resonators andcoherence length.

VIII. Condensed Matter PhysicsBravais lattices. Reciprocal lattice. Diffraction

and the structure factor. Bonding of solids. Elasticproperties, phonons, lattice specific heat. Freeelectron theory and electronic specific heat.Response and relaxation phenomena. Drudemodel of electrical and thermal conductivity. Halleffect and thermo-electric power. Electron motion

in a periodic potential, band theory of solids :metals, insulators and semi-conductors.Superconductivity : type-I and type-II super-conductors. Josephson junctions. Superfluidity.Defects and dislocations. Ordered phases ofmatter : translational and orientational order,kinds of liquid crystalline order. Quasi crystals.

IX. Nuclear and Particle Physics

Basic nuclear properties : size, shape andcharge distribution, spin and parity. Bindingenergy, semi-empirical mass formula, liquid dropmodel. Nature of the nuclear force, form ofnucleon-nucleon potential, charge-independenceand charge-symmetry of nuclear forces. Deuteronproblem. Evidence of shell structure, single-particle shell model, its validity and limitations.Rotational spectra. Elementary ideas of alpha, betaand gamma decays and their selection rules.Fission and fusion. Nuclear reactions, reactionmechanism, compound nuclei and direct reactions.

Classification of fundamental forces.Elementary particles and their quantum numbers(charge, spin, parity, isospin, strangeness, etc.).Gellmann-Nishijima formula. Quark model,baryons and mesons. C, P, and T invariance.Application of symmetry arguments to particlereactions. Parity non-conservation in weakinteraction. Relativistic kinematics.

Physical SciencesCSIR-UGC-NET/JRF Exam.

(December 2016)Solved Paper

December 2016Physical Sciences

PART A

1. Find out the missing pattern—

(A) (B)

(C) (D)

2. Seeds when soaked in water gain about 20%by weight and 10% by volume. By what fac-tor does the density increase ?

(A) 1·20 (B) 1·10

(C) 1·11 (D) 1·09

3. Retarding frictional force, f, on a moving ball,is proportional to its velocity, V. Two iden-tical balls roll down on two identical slopes(A & B) from different heights. Compare theretarding forces and the velocities of the ballsat the bases of the slopes.

(A) fA > fB; VA > VB

(B) fA > fB; VB > VA

(C) fB > fA; VB > VA

(D) fB > fA; VA > VB

4. Two cockroaches of the same species havethe same thickness but different lengths andwidths. Their ability to survive in oxygen

deficient environments will be compromised.if—(A) their thickness increases, and the rest of

the size remains the same(B) their thickness remains unchanged, but

their length increases(C) their thickness remains unchanged, but

their width decreases(D) their thickness decreases, but the rest of

the size remains unchanged

5. The bar chart shows number of seats won byfour political parties in a state legislativeassembly—

Which of the following pie-charts correctlydepicts this information ?

(A) (B)

(C) (D)

6. The random errors associated with the mea-surement of P and Q are 10% and 2%, respec-tively. What is the percentage random error inP/Q ?(A) 12·0 (B) 9·8(C) 8·0 (D) 10·2

4 | Phy. Sciences CSIR-UGC (Dec. 16)

7. In how many distinguishable ways can theletters of the word CHANCE be arranged ?(A) 120 (B) 720(C) 360 (D) 240

8. Which of the following graphs correctly showsthe speed and the corresponding distance cov-ered by an object moving along a straight line ?

(A)

(B)

(C)

(D)

9. A normal TV screen has a width to heightratio of 4 : 3, while a high definition TV screenhas a ratio of 16 : 9. What is the approximateratio of their diagonals, if the heights of thetwo types of screens are the same ?(A) 5 : 9 (B) 5 : 18(C) 5 : 15 (D) 5 : 6

10. Comparing numerical values, which of thefollowing is different from the rest ?(A) The ratio of the circumference of a circle

of its diameter(B) The sum of the three angles of a plane

triangle expressed in radians

(C)227

(D) The net volume of a hemisphere of unitradius and a cone of unit radius and unitheight

11. A river is 4·1 km wide. A bridge built across

it has 17 of its length on one bank and

18 of its

length on the other bank. What is the totallength of the bridge ?(A) 5·1 km (B) 4·9 km(C) 5·6 km (D) 5·4 km

12. OA, OB and OC are radii of the quarter circleshown in the figure. AB is also equal to theradius.

What is angle OCB ?(A) 60° (B) 75°(C) 55° (D) 65°

13. Intravenous (IV) fluid has to be administeredto a child of 12 kg with dehydration, at a doseof 20 mg of fluid per kg of body weight, in1 hour. What should be the drip rate (in drops/min) of IV fluid ? (1 mg = 20 drops)(A) 7 (B) 80(C) 120 (D) 4

14. A hall with a high roof is supported by an arrayof identical columns such that, to a personlying on the floor and looking at the ceiling,the columns appear parallel to each other.Which of the following designs conforms tothis ?

(A)

(B)

(C)

(D)

Phy. Sciences CSIR-UGC (Dec. 16) | 5

15. The sum of digits of a two-digit number is 9.If the fraction formed by taking 9 less thanthe number as numerator and 9 more than the

number as denominator is 34, what is the

number ?(A) 36 (B) 63(C) 45 (D) 54

16. The distance between X and Y is 1000 km. Aperson flies from X at 8 AM local time andreaches Y at 10 AM local time. He flies backafter a halt of 4 hours at Y and reaches X at 4PM local time on the same day. What is hisaverage speed for the duration he is in the air ?

(A) 500 km/hour

(B) 250 km/hour

(C) 750 km/hour

(D) cannot be calculated with the given infor-mation

17. If a person travels x% faster than normal, hereaches y minutes earlier than normal. What ishis normal time of travel ?

(A) ( )100x

+ 1 y minutes

(B) ( )x100

+ 1 y minutes

(C) ( )y100

+ 1 x minutes

(D) ( )100y

+ 1 x minutes

18. A and B walk up an escalator one step at atime, while the escalator itself moves up at aconstant speed. A walks twice as fast as B. Areaches the top in 40 steps and B in 30 steps.How many steps of the escalator can be seenwhen it is not moving ?(A) 30 (B) 40(C) 50 (D) 60

19. Two iron spheres of radii 12 cm and 1 cm aremelted and fused. Two new spheres are madewithout any loss of iron. Their possible radiicould be—(A) 9 and 4 cm(B) 9 and 10 cm(C) 8 and 5 cm(D) 2 and 11 cm

20. A man buys alcohol at R 75/cL, adds waterand sells it at R 75/cL making a profit of 50%.What is the ratio of alcohol to water ?(A) 2 : 1 (B) 1 : 2(C) 3 : 2 (D) 2 : 3

PART B

21. A ball of mass m is dropped from a tallbuilding with zero initial velocity. In additionto gravity, the ball experiences a dampingforce of the form –γv, where v is its instanta-neous velocity and γ is a constant. Given thevalues m = 10 kg, γ = 10 kg/s and g ≈ 10 m/s2,the distance travelled (in metres) in time t inseconds, is—(A) 10(t + 1 – e–t) (B) 10(t – 1 + e–t)(C) 5t2 – (1 – et) (D) 5t2

22. The matrix M =

⎝⎜⎜⎜⎛

⎠⎟⎟⎟⎞1 3 2

3 –1 0

0 0 1

satisfies the

equation—(A) M3 – M2 – 10M + 12I = 0(B) M3 + M2 – 12M + 10I = 0(C) M3 – M2 – 10M + 10I = 0(D) M3 + M2 – 10M + 10I = 0

23. The Laplace transform of

f (t) = ⎩⎪⎨⎪⎧ t

T‚ 0 < t < T

1‚ t > Tis—

(A) – (1 – e–sT)

s2T(B)

(1 – e–sT)s2T

(C)(1 + e–sT)

s2T(D)

(1 – esT)s2T

24. A relativistic particle moves with a constantvelocity v with respect to the laboratory frame.In time t, measured in the rest frame of theparticle, the distance that it travels in the labo-ratory frame is—

(A) vt (B)ct

1 – v2

c2

(C) vt 1 – v2

c2 (D)vt

1 – v2

c2

6 | Phy. Sciences CSIR-UGC (Dec. 16)

25. A particle in two dimensions is in a potentialV(x, y) = x + 2y. Which of the following (apartfrom the total energy of the particle) is also aconstant of motion ?(A) py – 2px (B) px – 2py

(C) px + 2py (D) py + 2px

26. The dynamics of a particle governed by the

Lagrangian L = 12 m

.x2 – 1

2 kx2 – kx

.xt

describes—(A) an undamped simple harmonic oscillator(B) a damped harmonic oscillator with a time

varying damping factor(C) an undamped harmonic oscillator with a

time dependent frequency(D) a free particle

27. The parabolic co-ordinates (ξ, η) are related tothe Cartesian co-ordinates (x, y) by x = ξη and

y = 12 (ξ2 – η2). The Lagrangian of a two-

dimensional simple harmonic oscillator ofmass m and angular frequency ω is—

(A)12

m [ ].ξ2 +

.η2 – ω2 (ξ2 + η2)

(B)12 m (ξ2 + η2) ⎣⎢

⎢⎡

⎦⎥⎥⎤

(.ξ2 +

.η2) –

14

ω2 (ξ2 + η2)

(C)12 m (ξ2 + η2) ⎝

⎜⎛

⎠⎟⎞.

ξ2 + .η2 –

12 ω2ξη

(D)12 m (ξ2 + η2) ⎝

⎜⎛

⎠⎟⎞.

ξ2 + .η2 –

14 ω2

28. Consider two radioactive atoms, each of whichhas a decay rate of 1 per year. The probabilitythat at least one of them decays in the first twoyears is—

(A)14

(B)34

(C) 1 – e–4 (D) (1 – e–2)2

29. The Fourier transform ∫∞

–∞ dx f(x)eikx of the

function f(x) = 1

x2 + 2 is—

(A) √⎯ 2π e–√⎯⎯2|k | (B) √⎯ 2π e–√⎯⎯2k

(C)π

√⎯ 2 e–√⎯⎯2k (D)

π

√⎯ 2 e–√⎯⎯2|k |

30. A screen has two slits, each of width w withtheir centres at a distance 2w apart. It is illu-minated by a monochromatic plane wave trav-elling along the x-axis—

w

w

w

x

The intensity of the interference pattern, mea-sured on a distant screen, at an angle θ = nλ/wto the x-axis is—(A) zero for n = 1, 2, 3 …(B) maximum for n = 1, 2, 3 …

(C) maximum for n = 12,

32,

52 …

(D) zero for n = 0 only

31. The electric field of an electromagnetic wave is→E (z, t) = E0cos (kz + ωt) i + 3E0sin (kz + ωt) j ,where ω and k are positive constants. Thisrepresents—(A) a linearly polarised wave travelling in

the positive z-direction(B) a circularly polarised wave travelling in

the negative z-direction(C) an elliptically polarised wave travelling

in the negative z-direction(D) an unpolarised wave travelling in the

positive z-direction

32. Consider the two lowest normalized energyeigenfunctions ψ0(x) and ψ1(x) of a one dimen-sional system. They satisfy ψ0(x) = ψ*

0(x) and

ψ1(x) = αdψ0

dx, where α is a real constant. The

expectation value of the momentum operatorin the state ψ1 is—

(A) – h

α2 (B) 0

(C)h

α2 (D)2h

α2

33. Consider the operator a = x + ddx

acting on

smooth functions of x. The commutator[a, cos x] is—(A) – sin x (B) cos x(C) – cos x (D) 0

Phy. Sciences CSIR-UGC (Dec. 16) | 7

34. Let a = 1

√⎯ 2 (x + ip) and a† =

1

√⎯ 2 (x – ip) be

the lowering and raising operators of a simpleharmonic oscillator in units where the mass,angular frequency and h have been set to unity.

If |0⟩ is the ground state of the oscillator andλ is a complex constant, the expectation valueof (ψ| x |ψ⟩ in the state |ψ) = exp(λa† – λ*a)|0⟩,is—

(A) | λ | (B) | λ |2 + 1

| λ |2

(C)1

√⎯⎯2i (λ – λ*) (D)

1

√⎯ 2 (λ + λ*)

35. Consider the operator →π =

→p – q

→A , where

→p

is the momentum operator, →A = (Ax, Ay, Az)

is the vector potential and q denotes the elec-

tric charge. If →B = (Bx, By, Bz) denotes the

magnetic field, the z-component of the vector

operator →π ×

→π is—

(A) iqhBz + q(Axpy – Aypx)

(B) –iqhBz – q(Axpy – Aypx)

(C) –iqhBz

(D) iqhBz

36. A conducting circular disc of radius r andresistivity ρ rotates with an angular velocityω in a magnetic field B perpendicular to it. Avoltmeter is connected as shown in the figurebelow—

Assuming its internal resistance to be infinite,the reading on the voltmeter—(A) depends on ω, B, r and ρ(B) depends on ω, B and r, but not on ρ(C) is zero because the flux through the loop

is not changing(D) is zero because a current flows in the

direction of B

37. The charge per unit length of a circular wireof radius a in the xy-plane, with its centre atthe origin, is λ = λ0cos θ, where λ0 is a con-stant and the angle θ is measured from thepositive x-axis. The electric field at the centreof the circle is—

(A)→E = –

λ0

4ε0a i (B)

→E =

λ0

4ε0a i

(C)→E = –

λ0

4ε0a j (D)

→E =

λ0

4πε0a k

38. The partition function of a two-level system

governed by the Hamiltonian H = ⎣⎢⎢⎡

⎦⎥⎥⎤γ –δ

–δ –γis—

(A) 2sinh ( )β√⎯⎯⎯⎯⎯γ2 + δ2

(B) 2cosh ( )β√⎯⎯⎯⎯⎯γ2 + δ2

(C)12 [ ]cosh ( )β√⎯⎯⎯γ2

+ δ2 + sinh ( )β√⎯⎯⎯γ2

+ δ2

(D)12 [ ]cosh ( )β√⎯⎯⎯γ2

+ δ2 – sinh ( )β√⎯⎯⎯γ2

+ δ2

39. A silica particle of radius 0·1 μm is put in acontainer of water at T = 300 K. The densitiesof silica and water are 2000 kg/m3 and 1000kg/m3, respectively. Due to thermal fluctua-tions, the particle is not always at the bottomof the container. The average height of theparticle above the base of the container isapproximately—

(A) 10–3 m (B) 3 × 10–4 m

(C) 10–4 m (D) 5 × 10–5 m

40. Which of the following circuits implementsthe Boolean function F(A, B, C) = Σ(1, 2, 4, 6)?

(A)

(B)

8 | Phy. Sciences CSIR-UGC (Dec. 16)

(C)

(D)

41. A pair of parallel glass plates separated by adistance d is illuminated by white light asshown in the figure below. Also shown is thegraph of the intensity of the reflected light Ias a function of the wavelength λ recorded bya spectrometer—

Assuming that the interference takes placeonly between light reflected by the bottomsurface of the top plate and the top surface ofbottom plate, the distance d is closest to—(A) 12 μm (B) 24 μm(C) 60 μm (D) 120 μm

42. The I-V characteristics of a device can be

expressed as I = Is[ ]exp( )aVT

– 1 , where T

is the temperature and a and IS are constantsindependent of T and V. Which one of the

following plots is correct for a fixed appliedvoltage V ?

(A)

a

(B)

a

(C)

a

(D)

a

43. The active medium in a blue LED (light emit-ting diode) is a GaxIn1–xN alloy. The band gapsof GaN and InN are 3·5 eV and 1·5 eV respe-ctively. If the band gap of GaxIn1–xN variesapproximately linearly with x, the value ofx required for the emission of blue light ofwavelength 400 nm is—

(take hc ≈ 1200 eV-nm)(A) 0·95 (B) 0·75(C) 0·50 (D) 0·33

CSIR-UGC NET/JRF/SET PhysicalSciences

Publisher : Upkar Prakashan ISBN : 9789350132692Author : Anshul Gupta & Dr.Surekha Tomar

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