CSIR-NET DEC 2012 Physics Previous Year Question Paper

Q.1) Three charges are located on the circumference of a circle of radius ‘R’ as shown in the figure below. The two charges Q subtend an angle 90˚ at the centre of the circle. The charge ‘q’ is symmetrically placed with respect to the charges Q. If the electric field at the centre of the circle is zero, what is the magnitude of Q?

1. a) q2
2. b) 2 q
3. c) 2q
4. d) 4q

Ans: A

Q.2) Consider a hollow charged shell of inner radius a and outer radius b. The volume charge density is ρ(r)=kr2 (k is constant) in the region a<r<b. The magnitude of the electric field produced at distance r>a is

1. a) k(b-a)ε0r2for all r>a
2. b) kb-aε0r2for all a<r<b and k(b-a)ε0r2for r>b
3. c) k(r-a)ε0r2for all a<r<b and k(b-a)ε0r2for r>b
4. d) k(r-a)ε0r2for all a<r<b andk(b-a)ε0r2for r>b

Ans: C

Q.3) A point charges q of mass m is kept at a distance d below a grounded infinite conducting sheet which lies in the xy-plane. For what value of d will the charge remains stationary?

1. a) q/4mgπε0
2. b) q/mgπε0
3. c) There is no finite value of d
4. d) mgπε0/q

Ans: A

Q.4) Four charges (two + q and two – q) are kept fixed at the four vertices of a square of side a as shown. At the point P which is at distance R from the centre (R≫a), the potential is proportional to

1. a) 1/R
2. b) 1/R2
3. c) 1/R3
4. d) 1/R4

Ans: C

Q.5) Consider an infinite conducting sheet in the xy- plane with a time dependent current density Kti^ , where K is a constant. The vector potential at (x,y,z) is given by A→=μ0K4c(ct-z)2 i^.The magnetic field B→ is

1. a) μ0Ktcj^
2. b) -μ0Kz2cj^
3. c) -μ0K2c(ct-z)i^
4. d) -μ0Kt2c(ct-z)j^

Ans: D

Q.6) Consider the interference of two coherent electromagnetic waves whose electric field vectors are given by E→1=i^E0 cosωt and E→2=j^E0 cos⁡(ωt+φ) where φ is the phase difference. The intensity of the resulting wave is given by ε02⟨E2⟩, where E2 is the time average of E2. The total intensity is

1. a) 0
2. b) ε0E02
3. c) ε0E02sin2φ
4. d) ε0E02cos2φ

Ans: A

Q.7) When a charged particle emits electromagnetic radiation, the electric field E→ and the Poynting vector S→=1μ0E→x B→ at a larger distance r from emitter vary as 1rnand1rm respectively. Which of the following choices for n and m are correct?

1. a) n=1 and m=1
2. b) n=2 and m=2
3. c) n=1 and m=2
4. d) n=2 and m=4

Ans: C

Q.8) The unit normal vector of the point a3,b3,c3 on the surface of the ellipsoid x2a2+y2b2+z2c2=1 is

1. a) bci^+caj^+abk^a2+b2+c2
2. b) ai^+bj^+ck^a2+b2+c2
3. c) bi^+cj^+ak^a2+b2+c2
4. d) i^+j^+k^3

Ans: D

Q.9) Given a 2×2 unitary matrix U satisfying U†U=UU†=1 with detU=eiφ one can construct a unitary matrix V(V†V=VV†=1) with detV=1from it by

1. a) multiplying U by e-iφ/2
2. b) multiplying any single element of U by eiφ
3. c) multiplying any row or column of U by e-iφ/2
4. d) multiplying U by eiφ

Ans: A

Q.10) The eigenvalues of the antisymmetric matrix,A=0-n3n2n30-n1-n2n10 where n1,n2 and n3 are the components of a unit vector, are

1. a) 0,i,-i
2. b) 0,1,-1
3. c) 0,1+i,-1,-i
4. d) 0,0,0

Ans: A

Q.11) Let ∆W be the work done in a quasistatic reversible thermodynamic process. Which of the following statements about ∆W is correct?

1. a) ∆W is a perfect differential if the process is isothermal
2. b) ∆W is a perfect differential if the process is adiabatic
3. c) ∆W is always a perfect differential
4. d) ∆W Cannot be a perfect differential

Ans: B

Q.12) A given quantity of gas is taken from the state A→C reversibly, by two paths, A→C directly and A→B→C as shown in the figure. During the process A→C the work done by the gas is 100 J and the heat absorbed is 150 J . If during the process A→B→C the work done by the gas is 30 J , the heat absorbed is.

1. a) 20 J
2. b) 80 J
3. c) 220 J
4. d) 280 J

Ans: B

Q.13) Consider a sinusoidal waveform of amplitude 1V and frequency f0. Starting from an arbitrary intial time, the waveform is sampled at intervals of 12f0.If the corresponding Fourier spectrum peaks at a frequency and an amplitude A-, them

1. a) f-=2f0 and A-=1V
2. b) f-=2f0and 0≤A- ≤1 V
3. c) f-=0 and A-=1V
4. d) f-=f02 and A-=12v

Ans: B

Q.14) The Taylor expansion of the function ln⁡ (cosh⁡x) where x is real, about the point x=0 starts with the following terms: f'(x)x-0=1ex+e-x2∙ex-e-x2=ex-e-xex+e-xex=tanhx=0

1. a) -12×2+112×4+⋯
2. b) 12×2-112×4+⋯
3. c) -12×2+16×4+⋯
4. d) 12×2+16×4+⋯

Ans: B

Q.15) In a series of five Cricket matches, one of the captains calls “Heads” every time when the toss is taken. The probability that he will win 3 times and lost 2 times is

1. a) 1/8
2. b) 5/8
3. c) 3/16
4. d) 5/16

Ans: D

Q.16) A ball is picked at random from one of two boxes that contain 2 black and 3 white and 3 black and 4 white balls respectively. What is the probability that it is white?

1. a) 34/70
2. b) 41/70
3. c) 36/70
4. d) 29/70

Ans: B

Q.17) A diode D as shown in the circuit has a i-v relation that can be approximated by iD=vD2+2vD,for vD>00forvD≤0

The value of vD in the circuit is

1. a) (-1+11)V
2. b) 8 V
3. c) 5V
4. d) 2V

Ans: D

Q.18) The free energy difference between the superconducting and the normal states of a material is given by ∆F=fs-fN=αΨ2+β2Ψ4 where Ψ is an order parameter and α and β are constants s.t.α>0Normal and α<0 in the super conducting state, while β>0 always, minimum value of ∆F is.

1. a) -α2β
2. b) -α22β
3. c) -3α22β
4. d) -5α22β

Ans: B

Q.19) Band-pass and band-reject filters can be implemented by combining a low pass and a high pass filter in series and in parallel, respectively. If the cut-off frequencies of the low pass and high pass filters areω0LP and ω0HP, respectively, the condition required to implement the band-pass and band-reject filters are, respectively,

1. a) ω0HP<ω0LP And ω0HP<ω0LP
2. b) ω0HP<ω0LP And ω0HP>ω0LP
3. c) ω0HP>ω0LP And ω0HP<ω0LP
4. d) ω0HP>ω0LP And ω0HP>ω0LP

Ans: B

Q.20) In the op-amp circuit shown in the figure, Vi is a sinusoidal input signal of frequency 10 Hz and V0 is the output signal. The magnitude of the gain and the phase shift, respectively, close to the values

1. a) 52 And π/2
2. b) 52 And -π/2
3. c) 10 and zero
4. d) 10 and π

Ans: D

Q.21) The entropy of a system, (S), is related to the accessible phase space volume ΓbyS=kBInΓE,N,V where E, N and V are the energy, number of particles and volume respectively. From this one can conclude that

1. a) Does not change during evolution to equilibrium
2. b) Oscillates during evolution to equilibrium
3. c) Is a maximum at equilibrium
4. d) Is a minimum at equilibrium

Ans: C

Q.22) 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 energy2J. In a configuration with r spin flips, the energy of the system is E=-NJ+2rJ and the number of configuration is Cr N: r varies from 0 to N. The partition function is.

1. a) JkBTN
2. b) e-NJ/kBT
3. c) sinhJkBTN
4. d) coshJkBTN

Ans: D

Q.23) Consider a system of three spins S1,S2 each of which can take values +1 and -1. The energy of the system is given by E=-JS1S2+S2S3+S3S1 where J is a positive constant. The minimum energy and the corresponding number of spin configuration are respectively,

1. a) J and 1
2. b) -3J and 1
3. c) -3J and 2
4. d) -6J and 2

Ans: C

Q.24) The logic circuit shown in the figure below Implements the Boolean expression

1. a) y=A∙B
2. b) y=A ∙B̅
3. c) y=A∙B
4. d) y=A+B

Ans: A

Q.25) A live music broadcast consists of a radio-wave of frequency 7 MHz, amplitude-modulated by a microphone output consisting of signals with a maximum frequency of 10 kHz. The spectrum of modulated output will be zero outside the frequency band

7. a) 00 MHz to 7.01 MHz
8. b) 99 MHz to 7.01 MHz
9. c) 99 MHz to 7.00 MHz
10. d) 995 MHz to 7.005 MHz

Ans: B

Q.26) Three particles of equal mass (m) are connected by two identical massless springs of stiffness constant (K) as shown in the figure

1. a) 12K[x12+x22+x32]
2. b) 12K[x12+x22+x32-x2(x1+x3)]
3. c) 12K[x12+2×22+x32-2×2(x1+x3)]
4. d) 12K[x12+2×22+2×2(x1+x3)]

Ans: C

Q.27) A planet of mass m moves in the gravitational field of the Sum (mass M). If the semi-major and semi-minor axes of the orbit are a and b respectively, the angular momentum of the planet is

1. a) 2GMm2(a+b)
2. b) 2GMm2(a-b)
3. c) 2GMm2aba-b
4. d) 2GMm2aba+b

Ans: D

Q.28) Two bodies of equal mass m are connected by a massless rigid rod of length l lying in the xy- plane with the centre of the rod at the origin. If this system is rotating about the z-axis with a frequency ω, its angular momentum is

1. a) ml2ω/4
2. b) ml2ω/2
3. c) ml2ω
4. d) 2ml2ω

Ans: B

Q.29) If a particle is represented by the normalized wave function Ψ(x)={15(a2-x2)4a5/2,for-a<x<a0,otherwise the uncertainty ∆p in its momentum is

1. a) 2ℏ/5a
2. b) 5ℏ/2a
3. c) 10ℏ/a
4. d) 5ℏ/2a

Ans: D

Q.30) The energy eigenvalue of a particle in the potential V(x)=12mω2×2-ax are

1. a) En=(n+12)ℏω-a22mω2
2. b) En=(n+12)ℏω+a22mω2
3. c) En=(n+12)ℏω-a2mω2
4. d) En=(n+12)ℏω

Ans: A

Q.31) The Hamiltonian of a simple pendulum consisting of a mass m attached to a massless string of length l is H=pe22ml2+mgl(1-cos θ). If L denotes the Ligrangian, the value of dLdt is:

1. a) -2glpθ sin θ
2. b) –glpθ sin 2θ
3. c) glpθ cos θ
4. d) lpθ2cos θ

Ans: A

Q.32) Which of the following set of phase space trajectories is not possible for a particle obeying Hamilton’s equation of motion?

1. a)
2. b)
3. c)
4. d)

Ans: B

Q.33) The wave function of a state of the hydrogen atom is given by Ψ=Ψ200+2Ψ211+3Ψ210+2Ψ21-1 Where Ψnlm is the normalized eigen function of the state with quantum numbers n,l,m in the usual notation, The expectation value of Lz in the state Ψ is

1. a) 15ℏ6
2. b) 11ℏ6
3. c) 3ℏ8
4. d) ℏ8

Ans: D

Q.34) The muon has mass 105MeV/c2 and mean life time 2.2 μs in its rest frame. The mean distance traversed by a muon of energy 315 MeV before decaying is approximately

1. a) 3 x 105 km
2. b) 2 cm
3. c) 6 μm
4. d) 98 km

Ans: D

Q.35) Let v,p and E denote the speed, the magnitude of the momentum, and the energy of a free particle of rest mass m .Then

1. a) dE⁄dp= constant
2. b) p=mv
3. c) v=cp⁄p2+m2c2
4. d) E=mc2

Ans: C

Q.36) Consider the energy level diagram shown below, which corresponds to the molecular nitrogen laser

1. a) 1014 cm-3 and 2×1012 cm-3
2. b) 2×1012 cm-3 and 1014 cm-3.
3. c) 2×1012 cm-3 and 2×106 cm-3
4. d) zero and 1020 cm-3

Ans: B

Q.37) Consider a hydrogen atom undergoing a 2P→1S transition. The lifetime tsp of the 2P state for spontaneous emission is 1.6 ns and the energy difference between the levels is 10.2 eV. Assuming that the refractive index of the medium n0 = 1,e ratio of Einstein coefficients for stimulated and spontaneous emission B21(ω)/A21(ω)

1. a) 683 × 1012 m3J-1s-1
2. b) 146 × 10-12 Jsm-3.
3. c) 83 × 1012 m3J-1s-1
4. d) 463 × 10-12 Jsm-3

Ans: A

Q.38) Consider a He-Ne laser cavity consisting of two mirrors of reflectivities R1 = 1 and R2 = 0.98 The mirrors are separated by a distance d = 20 cm and the medium in between has a refractive index n0= 1 and absorption coefficient α = 0. The values of the separation between the modes δv and the width ∆vp of each mode of the laser cavity are:

1. a) δv=75kHz,∆vp=24kHz
2. b) δv=100kHz,∆vp=100kHz
3. c) δv=750MHz,∆vp=2.4MHz
4. d) δv=2.4MHz,∆vp=750MHz

Ans: C

Q.39) In a band structure calculation, the dispersion relation for electrons is found to be εk=βcoskxa+coskya+coskza, where β is a constant and a is the lattice constant. The effective mass at the boundary of the Brillouin zone is

1. a) 2ℏ25βa2
2. b) 4ℏ25βa2
3. c) ℏ22βa2
4. d) ℏ23βa2

Ans: D

Q.40) A magnetic field sensor based on the Hall Effect is to be fabricated by implanting As into a Si film of thickness 1 μm. The specifications require a magnetic field sensitivity of 500 mV/Tesla at an excitation current of 1 mA. The implantation does is to be adjusted such that the average carrier density, after activation, is

1. a) 25×1026m-3
2. b) 25×1022m-3
3. c) 1×1021m-3
4. d) 1×1020m-3

Ans: B

Q.41) A 2 × 2 matrix A has eigenvalues eiπ/6and eiπ/6. The smallest value of n such that An = I is

1. a) 20
2. b) 30
3. c) 60
4. d) 120

Ans: C

Q.42) The graph of the function f(x) shown below is best described by

1. a) The Bessel function J0(x)
2. b) cos x
3. c) e-x cos x
4. d) 1xcos x|

Ans: A

Q.43) In a series of five Cricket matches, one of the captains calls “Heads” every time when the toss is taken. The probability that he will win 3 times and lose 2 times is

1. a) 1/8
2. b) 5/8
3. c) 3/16
4. d) 5/16

Ans: D

Q.44) A binary star system consists of two stars S1 and S2, with masses m and 2m respectively separated by a distance r. If both S1and S2 individually follow circular orbits around the centre of mass with instantaneous speeds v1 and v2respectively, the speeds ratio v1/v2 is

1. a) 2
2. b) 1
3. c) 1/2
4. d) 2

Ans: D

Q.45) Three charges are located on the circumference of a circle of radius R as shown in the figure below. The two charges Q subtend an angle 90° at the centre of the circle. The charge q is symmetrically placed with respect to the charges Q. If the electric field at the centre of the circle is zero, what is the magnitude of Q?

1. a) q/2
2. b) 2q
3. c) 2q
4. d) 4q

Ans: A

Q.46) The Taylor expansion of the function ln(cosh x), where x is real, about the point x = 0 starts with the following terms:

1. a) -12×2+112×4+⋯
2. b) 12×2-12×4+⋯
3. c) -12×2+16×4+⋯
4. d) 12×2+16×4+⋯

Ans: B

Q.47) Given a 2×2 unitary matrix U satisfying U†U = UU† = 1 with detU=e-iφ, one can construct a unitary matrix V(V †V = VV† = 1) with det V = 1 from it by

1. a) multiplying U by e-iφ/2
2. b) multiplying any single element of U by e-iφ
3. c) multiplying any row or column of U by e-iφ/2
4. d) multiplying U by e-iφ

Ans: A

Q.48) The value of the integral ∫cz3dzz2-5z+6, where C is a closed contour defined by the equation2|z|-5=0, traversed in the anti-clockwise direction, is

1. a) -16 πi
2. b) 16 πi
3. c) 8 πi
4. d) 2 πi

Ans: A

Q.49) The function f(x) obeys the differential equation d2fdx2-(3-2i)f=0 and satisfies the conditions f(0) = 1 and f(x) → 0 as x → ∞. The value of f(π) is

1. a) e2π
2. b) e-2π
3. c) -e-2π
4. d) -e2πi

Ans: C

Q.50) A planet of mass m moves in the gravitational field of the Sun (mass M). If the semi major and semi-minor axes of the orbit are a and b respectively, the angular momentum of the planet is

1. a) 2GMm2(a+b)
2. b) 2GMm2(a-b)
3. c) 2GMm2ab(a-b)
4. d) 2GMm2aba+b

Ans: D

Q.51) The Hamiltonian of a simple pendulum consisting of a mass m attached to a massless string of length l is H=(Pθ2)/(2ml2)+mgl(1-cosθ) If L denotes the Lagrangian, the value of dL/dt is:

1. a) -2glpθsin θ
2. b) -glpθsin 2θ
3. c) glpθsin 2θ
4. d) Ip2θsin 2θ

Ans: A

Q.52) Which of the following set of phase-space trajectories is not possible for a particle obeying Hamilton’s equations of motion?

1. a) a
2. b) b
3. c) c
4. d) d

Ans: C

Q.53) Two bodies of equal mass m are connected by a massless rigid rod of length l lying in the xy-plane with the centre of the rod at the origin. If this system is rotating about the z-axis with a frequency ω, its angular momentum is

1. a) ml2ω/4
2. b) ml2ω/2
3. c) ml2ω
4. d) 2ml2ω

Ans: B

Q.54) An infinite solenoid with its axis of symmetry along the z-direction carries a steady current I.

1. a) Is constant inside and varies as R outside the solenoid
2. b) Varies as R inside and is constant outside the solenoid
3. c) Varies as 1 R inside and as R outside the solenoid
4. d) Varies as R inside and as 1 R outside the solenoid

Ans: D

Q.55) Consider an infinite conducting sheet in the xy-plane with a time dependent current density Kti^ where K is a constant. The vector potential at (x,y,z) is given by A=(μ0K)/4c(ct-z)2i^The magnetic field B→ is

1. a) μ0Kt2j^
2. b) -μ0Kt2cj^
3. c) -μ0Kt2cj^
4. d) −μ0K2c(ct−z) j^-\frac{\mu_0 K}{2c} (ct – z) \, \hat{j}

Ans: D

Q.56) When a charged particle emits electromagnetic radiation, the electric field E→ and the Poynting vector S→=1μ0E→×B at a larger distance r from emitter vary as 1rnand1rmrespectively. Which of the following choices for n and m are correct?

1. a) n = 1 and m = 1
2. b) n = 2 and m = 2
3. c) n = 1 and m = 2
4. d) n = 2 and m = 4

Ans: C

Q.57) Given a 2×2 unitary matrix U satisfying U†U = UU† = 1 with detU=e-iφ, one can construct a unitary matrix V(V †V = VV† = 1) with det V = 1 from it by

1. a) multiplying U by e-iφ/2
2. b) multiplying any single element of U by e-iφ
3. c) multiplying any row or column of U by e-iφ/2
4. d) multiplying U by e-iφ

Ans: A

Q.58) The perturbation H’=b(a-x),-a<x<a0,otherwiseacts on a particle of mass m confined in an infinite square well potential V(x)=0-a<x<a∞ otherwise

The first order correction to the ground state energy of the particle is

1. a) ba2
2. b) ba2
3. c) 2ba
4. d) ba

Ans: D

Q.59) Let 0 and 1 denote the normalized eigenstates corresponding to the ground and the first excited states of a one-dimensional harmonic oscillator. The uncertainty Δx in the state 12(∣0⟩ and ∣1⟩)\frac{1}{\sqrt{2}} (|0\rangle \, ext{and} \, |1\rangle) is Here is the content printed exactly as shown:

1. a) Δx=ℏ/2mω
2. b) Δx=ℏ/mω
3. c) Δx=2ℏ/mω
4. d) Δx=4ℏ/mω

Ans: C

Q.60) What would be the ground state energy of the Hamiltonian H=ℏ22md2dx2−αδ(x) if variational principle is used to estimate it with the trial wavefunction ψ(x)=Ae−bx2with bb as the variational parameter?

1. a) −ma2/2ℏ2
2. b) −ma2/πℏ2
3. c) −ma2/πℏ2
4. d) ma2/πℏ2

Ans: C

Q.61) The free energy difference between the superconducting and the normal states of a material is given by

ΔF=F3−FN=α∣ψ∣2, where ψ\psi is an order parameter and α\alpha and β\beta are constants such that α<0\alpha < 0 in the normal and α<0\alpha < 0 in the superconducting state, while β>0\beta > 0 always. The minimum value of ΔF is

1. a) −α2/β
2. b) −α2/2β
3. c) −3α2/2β
4. d) −5α2/2β

Ans: B

Q.62) A given quantity of gas is taken from the state A → C reversibly, by two paths, A → C directly and A → B → C as shown in the figure. During the process A → C the work done by the gas is 100 J and the heat absorbed is 150 J. If during the process A → B → C the work done by the gas is 30 J, the heat absorbed is

1. a) 20 J
2. b) 80 J
3. c) 220 J
4. d) 280 J

Ans: B

Q.63) 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 rr spin flips, the energy of the system is E=−NJ+2rJ and the number of configuration is NCr, rr varies from 0 to N. The partition function is

1. a) ∣a∣JkBTN
2. b) e−NJ/kBT
3. c) sinhJkBTN
4. d) coshJkBTN

Ans: D

Q.64) A magnetic field sensor based on the Hall Effect is to be fabricated by implanting. As into a Si film of thickness 1μM. The specifications require a magnetic field sensitivity of 500 mV/Tesla at an excitation current of 1 mA. The implantation does is to be adjusted such that the average carrier density, after activation is

1. a) 25×1026m−3
2. b) 25×1022m−3
3. c) 1×1021m−3
4. d) 1×1020m−3

Ans: B

Q.65) Band-pass and band-reject filters can be implemented by combining a low pass and a high pass filter in series and in parallel, respectively. If the cut-off frequencies of the low pass and high pass filters are ω0L\omega_0^L and ω0H\omega_0^H, respectively, the condition required to implement the band pass and high pass filters are respectively.

1. a) ω0HP<ω0L and ω0HP<ω0LP
2. b) ω0HP<ω0L and ω0HP>ω0LP
3. c) ω0HP>ω0L and ω0HP<ω0LP
4. d) ω0HP>ω0L and ω0HP>ω0LP

Ans: B

Q.66) The output characteristics of a solar panel at a certain level of irradiance is shown in the figure

1. a) 97 W
2. b) 73 W
3. c) 50 W
4. d) 45 W

Ans: D

Q.67) Consider the energy level diagram shown below, which corresponds to the molecular nitrogen laser

1. a) 1014cm-3 and 2×1012cm−3
2. b) 2×1012cm−3 and 1014cm−3
3. c) 2×1012cm−3and 2×106cm−32 \times 10^{6} cm^{-3}
4. d) zero and 1020cm-3

Ans: B

Q.68) Consider a hydrogen atom undergoing a 2P →\rightarrow1S transition. The lifetime tspof the 2P state for spontaneous emission is 1.6 ns and the energy difference between the levels is 10.2 eV. Assuming that the refractive index of the medium n0=1n_0 = 1, the ratio of Einstein coefficients for stimulated and spontaneous emission B21(ω)A21(ω) is given by

1. a) 683×1012m3J−1s−1
2. b) 146×1012Jsm−3
3. c) 83×1012m3J−1s−1
4. d) 463×10−12Jsm−3

Ans: A

Q.69) Consider a He-Ne laser cavity consisting of two mirrors of reflectivities R1=1 and R2=0.98. The mirrors are separated by a distance d = 20 cm and the medium in between has a refractive index n0 = 1 and absorption coefficient α = 0. The values of the separation between the modes δv and the width of each mode of the laser cavity are:

1. a) δv=75kHz,∆vp=24kHz
2. b) δv=100kHz,∆vp=100kHz
3. c) δv=750kHz,∆vp=2.4kHz
4. d) δv=2.4kHz,∆vp=750kHz

Ans: C

Q.70) Non-interacting bosons undergo Bose-Einstein Condensation (BEC) when trapped in a three dimensional isotropic simple harmonic potential. For BEC to occur, the chemical potential must be equal to

1. a) ℏω/2
2. b) ℏω
3. c) 3ℏω/2
4. d) 0

Ans: C

Q.71) In a band structure calculation, the dispersion relation for electrons is found to be

εk=β(cos kxa+cos kya+cos kza)

Where β\beta is a constant and aa is the lattice constant. The effective mass at the boundary of the first Brillouin zone is

1. a) 2ℏ25βa2
2. b) 4ℏ25βa2
3. c) ℏ22βa2
4. d) ℏ23βa2

Ans: D

Q.72) 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

1. a) 12π2a31/3
2. b) 3π2a31/3
3. c) πa31/3
4. d) 1a

Ans: A

Q.73) The muon has mass 105 MeV/c2and mean lifetime 2.2 μs in its rest frame. The mean distance traversed by muon of energy 315 MeV/c2before decaying is approximately

1. a) 3×105km
2. b) 2 cm
3. c) 6 μm
4. d) 98 km

Ans: D

Q.74) Consider the following particles: the proton p, the neutron n, the neutral pion π0 and the delta resonance Δ+\Delta^+, when ordered in terms of decreasing lifetime the correct arrangement is as follows

1. a) π0,n,p,Δ
2. b) p,n,Δ+,π0
3. c) p,n,π0,Δ+
4. d) Δ+,n,π0,p

Ans: C

Q.75) The single particle energy difference between the p-orbital’s (i.e. p3/2 and p1/2) of the nucleus 50114Sn is 3 MeV.

The energy difference between the states in its 1f orbital is

1. a) −7MeV
2. b) 7MeV
3. c) 5MeV
4. d) −5MeV

Ans: B