Choose the correct answer for the following :-

1 (a) (i)
The law which failed to account for shorter wavelength region of black body radiation spectrum is,

(A) Wein's law

(B) Rayleigh-Jean's law

(C) Planck's law

(D) Maxwell's law

(A) Wein's law

(B) Rayleigh-Jean's law

(C) Planck's law

(D) Maxwell's law

1 M

1 (a) (ii)
The de-Broglie wavelength of a particle at rest is

(A) Zero

(B) infinite

(C) h/p

(D) h/v

(A) Zero

(B) infinite

(C) h/p

(D) h/v

1 M

1 (a) (iii)
If group velocity of particle is 4.7 × 10

(A) 6 × 10

(B) 4.7 × 10

(C) 9.4 × 10

(D) 1.91 × 10

^{6}m/s then its phase velocity is,(A) 6 × 10

^{9}m/s(B) 4.7 × 10

^{6}m/s(C) 9.4 × 10

^{6}m/s(D) 1.91 × 10

^{10}m/s
1 M

1 (a) (iv)
The particle velocity of wave is equal to,

(A) group velocity

(B) Phase velocity

(C) velocity of light

(D) velocity of sound

(A) group velocity

(B) Phase velocity

(C) velocity of light

(D) velocity of sound

1 M

1 (b)
Describe Davisson and Germer experiment for confirmation of de-Broglie hypothesis.

7 M

1 (c)
Derive de-Broglie wavelength using group velocity

5 M

1 (d)
Calculate the de-Broglie wavelength of particle of mass 0.65 MeV/C

^{2}has a kinetic energy 80 eV.
4 M

Choose the correct answer for the following :-

2 (a) (i)
In quantum mechanics the energy operation is represented as:

\[ (A)\ \dfrac {8x^2 m}{h^2} \dfrac {\partial^2}{\partial x^{2}} \\(B) \ -\dfrac{h^2}{4\pi^2 m} \dfrac {\partial^{2}}{\partial x^{2}}\\(C) \ -\dfrac{h^2}{8\pi^2 m} \dfrac {\partial^2}{\partial x^{2}}\\(D) \ \dfrac {h^2 }{2\pi^{2}m}\dfrac {\partial^{2}}{\partial x^{2}} \]

\[ (A)\ \dfrac {8x^2 m}{h^2} \dfrac {\partial^2}{\partial x^{2}} \\(B) \ -\dfrac{h^2}{4\pi^2 m} \dfrac {\partial^{2}}{\partial x^{2}}\\(C) \ -\dfrac{h^2}{8\pi^2 m} \dfrac {\partial^2}{\partial x^{2}}\\(D) \ \dfrac {h^2 }{2\pi^{2}m}\dfrac {\partial^{2}}{\partial x^{2}} \]

1 M

2 (a) (ii)
The probability of finding the particle with in an element of volume dτ is,

\[(A)\ zero\\(B)\ \int|\psi|^2d\tau \\(C) \int | \psi | d \tau \\(D) \int | \psi | d \tau \]

\[(A)\ zero\\(B)\ \int|\psi|^2d\tau \\(C) \int | \psi | d \tau \\(D) \int | \psi | d \tau \]

1 M

2 (a) (iii)
If an electron moves in one dimensional box of length 2 mm. the normalization constant is,

\[ (A) \ 1(nm)^\frac {-1}{2}\\(B) \ 2(nm)^{-1}\\ (C) \ \sqrt{2}(nm)^-1\\(D) \ zero \]

\[ (A) \ 1(nm)^\frac {-1}{2}\\(B) \ 2(nm)^{-1}\\ (C) \ \sqrt{2}(nm)^-1\\(D) \ zero \]

1 M

2 (a) (iv)
The energy of a particle E

(A) nh/8mL

(B) nh/8L

(C) n

(D) n

_{n}in one-dimensional potential box of width L and infinite height is,(A) nh/8mL

^{2}(B) nh/8L

(C) n

^{2}h^{2}/mL^{2}(D) n

^{2}h^{2}/8mL^{2}
1 M

2 (b)
Set up Schrodinger's time-independent wace equation.

8 M

2 (c)
Using uncertainly principle, prove that free electron does not exist inside the nucleus.

4 M

2 (d)
A spectral line of wavelenght 4000 A

^{°}U has width of 8×10^{-5}AU. Evaluate the minimum time spent by electrons in upper energy state between excitation and de-excitation process.
4 M

Choose the correct answer for the following :-

3 (a) (i)
The free electrons in classical free electron theory are treated as:

(A) rigidly fixed lattice point

(B) liquid molecules

(C) gas molecules

(D) none of these

(A) rigidly fixed lattice point

(B) liquid molecules

(C) gas molecules

(D) none of these

1 M

3 (a) (ii)
The temperature dependence of classical expression for electrical resistivity of a metal is,

(A) ραT

(B) ραT

(C) ρα1/T

(D) ρα1/T

(A) ραT

^{1/2}(B) ραT

^{2}(C) ρα1/T

^{2}(D) ρα1/T

1 M

3 (a) (iii)
The value of Fermi function in Fermi-level is at T ? 0 K,

(A) zero

(B) 0.5

(C) 0.75

(D) 1

(A) zero

(B) 0.5

(C) 0.75

(D) 1

1 M

3 (a) (iv)
IF E

(A) E=1.5E

(B) E

(C) E= 2/5 E

(D) E=3/5 E

_{F}is the Fermi energy at absolute zero, mean energy E of electron at absolute zero is(A) E=1.5E

_{F}(B) E

(C) E= 2/5 E

_{F}(D) E=3/5 E

_{F}
1 M

3 (b)
Explain failure of classical free electron theory.

6 M

3 (c)
What are the merits of quantum free electron theory?

6 M

3 (d)
Calculate the Fermi velocity and mean free path for conduction electron in silver, given that its Fermi energy is 5.5eV and relaxation time for electrons is 3.83 × 10

^{-14}s.
4 M

4 (a) (i)
The electric dipole moment per unit volume is

(A) Magnetization

(B) Dipole moment

(C) Electric polarization

(D) Electric susceptibility

(A) Magnetization

(B) Dipole moment

(C) Electric polarization

(D) Electric susceptibility

1 M

4 (a) (ii)
Claussius - Mussoti equation does not holds for,

(A) crystalline solids

(B) liquid

(C) gases

(D) vaccum

(A) crystalline solids

(B) liquid

(C) gases

(D) vaccum

1 M

4 (a) (iii)
The relation between B, M and H is.

(A) H=µ

(B) B=µ

(C) M=µ

(D) None of these

(A) H=µ

_{0}(M+B)(B) B=µ

_{0}(H+M)(C) M=µ

_{0}(H+B)(D) None of these

1 M

4 (a) (iv)
Above curie temperature ferromagnetic substance becomes:

(A) anti-ferromagnetic

(B) strongly ferromagnetic

(C) paramagnetic

(D) diamagnetic

(A) anti-ferromagnetic

(B) strongly ferromagnetic

(C) paramagnetic

(D) diamagnetic

1 M

4 (b)
Discuss polarization mechanism in dielectrics and their frequency dependence.

8 M

4 (c)
Differentiate hard and soft magnetic materials with suitable application.

4 M

4 (d)
An electric field of 10

^{5}V/m is applied on a sample of noen at NTP. Calculate the dipole moment induced in each atom. The dielectric constant of neon is 1.00014. Find the atomic polariziability of neon gas. At NTP 1 kg atom of Ne-gas occupies volume of 22.4 m^{3}.
4 M

Choose the correct answer for the following :-

5 (a) (i)
In He-Ne laser the laser emission takes place from,

(A) He-atoms only

(B) Ne-atoms only

(C) Both He and Ne atoms

(D) 50% from Helium and 50% from Neon

(A) He-atoms only

(B) Ne-atoms only

(C) Both He and Ne atoms

(D) 50% from Helium and 50% from Neon

1 M

5 (a) (ii)
Which of the following leads coherent light:

(A) induced absorption

(B) Spontaneous emission

(C) Stimulated emission

(D) None of these

(A) induced absorption

(B) Spontaneous emission

(C) Stimulated emission

(D) None of these

1 M

5 (a) (iii)
The pumping methhod used in semiconductor diode laser is,

(A) optical pumping

(B) electric discharge

(C) forward bias

(D) chemical reactions

(A) optical pumping

(B) electric discharge

(C) forward bias

(D) chemical reactions

1 M

5 (a) (iv)
The life time of metastable state is about,

(A) 10

(B) 10

(C) 10

(D) 10

(A) 10

^{-3}sec(B) 10

^{-13}sec(C) 10

^{2}sec(D) 10

^{-9}sec
1 M

5 (b)
Obtain an expression for energy density of radiation under equilibrium condition in terms of Einstein coefficient.

8 M

5 (c)
What is holography? Explain principle of hologram recording using laser.

4 M

5 (d)
A pulsed laser with power 1 mw lasts for ions. If the number of photons emitted per second is 5 × 10

^{7}calcualte the wavelength of laser.
4 M

Choose the correct answer for the following :-

6 (a) (i)
According to BCS theory, the cooper pair is pair of,

(A) Electron-Proton

(B) Electron-Electron

(C) Proton-Proton

(D) Electron-Neutron

(A) Electron-Proton

(B) Electron-Electron

(C) Proton-Proton

(D) Electron-Neutron

1 M

6 (a) (ii)
High temperature superconductors bear the crystal structure of,

(A) cubic

(B) orthohombic

(C) diamond

(D) perovskite

(A) cubic

(B) orthohombic

(C) diamond

(D) perovskite

1 M

6 (a) (iii)
The acceptance angle of optical fibre whose RI of core and cladding of 1.55 and 1.50 respectively is,

(A) 32°

(B) 45°

(C) 223°

(D) 15°

(A) 32°

(B) 45°

(C) 223°

(D) 15°

1 M

6 (a) (iv)
According to Meissner effect, material in super conducting state is

(A) paramagnetic

(B) diamagnetic

(C) ferromagnatic

(D) anti-ferromagnetic

(A) paramagnetic

(B) diamagnetic

(C) ferromagnatic

(D) anti-ferromagnetic

1 M

6 (b)
What is refractive index profile? Describe three types of optical fibre with one application for each type.

8 M

6 (c)
Explain working of SQUID with application.

4 M

6 (d)
An optical fibre of 600 mts long has input power of 120 mw emerges out with power of 90 mw. Find attenuation in the fibre.

4 M

Choose the correct answer for the following :-

7 (a) (i)
The lattice paramter a = b ≠ c and α = β = γ = 90° represent,

(A) cubic

(B) tetragonal

(C) rhombohedral

(D) orthohombic

(A) cubic

(B) tetragonal

(C) rhombohedral

(D) orthohombic

1 M

7 (a) (ii)
The co-ordination number of rock salt is,

(A) 6

(B) 8

(C) 12

(D) 14

(A) 6

(B) 8

(C) 12

(D) 14

1 M

7 (a) (iii)
Which of the following has least packing fraction,

(A) sc

(B) bcc

(C) fcc

(D) diamond

(A) sc

(B) bcc

(C) fcc

(D) diamond

1 M

7 (a) (iv)
In a sample cubic lattice d

\[ (A) \ \sqrt{6}:\sqrt{3} : \sqrt{2} \\(B) \ \sqrt{2}: \sqrt{6}: \sqrt{3} \\(C) \ \sqrt{2}: \sqrt{3}: \sqrt{6}\\(D) \ \sqrt{3}: \sqrt{6}: \sqrt{2}\\\]

_{1111}: d_{110}: d_{100}=\[ (A) \ \sqrt{6}:\sqrt{3} : \sqrt{2} \\(B) \ \sqrt{2}: \sqrt{6}: \sqrt{3} \\(C) \ \sqrt{2}: \sqrt{3}: \sqrt{6}\\(D) \ \sqrt{3}: \sqrt{6}: \sqrt{2}\\\]

1 M

7 (b)
Derive expression for interplanner spacing of crystal in terms of Miller Indices.

7 M

7 (c)
What is atomic packing factor? Calculate packing factor for sc and bcc structure.

5 M

7 (d)
What is Miller index of plane making intercepts ratio 3a : 4b on x-and y-axis and parallel to z-axis a, b are primitive vectors?

4 M

Choose the correct answer for the following :

8 (a) (i)
A bulk material (three dimensions) reduced in one direction is called quantum:

(A) particle

(B) well

(C) dot

(D) wire

(A) particle

(B) well

(C) dot

(D) wire

1 M

8 (a) (ii)
Which belongs to fullerene family?

(A) C

(B) C

(C) C

(D) All

(A) C

_{60}(B) C

_{70}(C) C

_{120}(D) All

1 M

8 (a) (iii)
Velocity of ultrasound through liquid is proporational to,

(A) density

(B) volume

(C) bulk modulus

(D) rigidity modulus

(A) density

(B) volume

(C) bulk modulus

(D) rigidity modulus

1 M

8 (a) (iv)
Ultrasonic wave cannot be transmitted through.

(A) solid

(B) liquid

(C) gas

(D) vaccum

(A) solid

(B) liquid

(C) gas

(D) vaccum

1 M

8 (b)
What is NDT? Describe the NDT method of detection of flows in solid using ultrasound.

8 M

8 (c)
What are nano materials? Write the structure and applications of carbon nano tubes.

8 M

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